{"id":278412,"date":"2026-10-06T23:53:52","date_gmt":"2026-10-06T18:23:52","guid":{"rendered":"https:\/\/imarticus.org\/blog\/?p=278412"},"modified":"2026-10-06T23:53:56","modified_gmt":"2026-10-06T18:23:56","slug":"regression-analysis","status":"publish","type":"post","link":"https:\/\/imarticus.org\/blog\/regression-analysis\/","title":{"rendered":"Regression Analysis: Meaning, Formula, Types, And Examples"},"content":{"rendered":"\n<style>\n  .wrap {\n    margin: 24px 0;\n    width: 100%;\n    box-sizing: border-box;\n  }\n  .card {\n    box-sizing: border-box;\n    width: 100%;\n    max-width: 720px;\n    margin: 0 auto;\n    background: #eaf6ec;\n    border: 1.5px solid #b0dabb;\n    border-radius: clamp(16px, 3vw, 26px);\n    padding: clamp(22px, 4.5vw, 44px);\n    text-align: center;\n    font-family: 'Manrope', Arial, Helvetica, sans-serif;\n  }\n  .card * {\n    box-sizing: border-box;\n  }\n  .badge {\n    display: block;\n    text-align: left;\n    margin: 0 0 10px 0;\n    color: #2f7a4d;\n    font-weight: 800;\n    font-size: 15px;\n    letter-spacing: 0.04em;\n    text-transform: uppercase;\n  }\n  .card p {\n    font-size: clamp(14.5px, 1.8vw, 16.5px);\n    line-height: 1.7;\n    color: #2c3e33;\n    margin: 0;\n    text-align: left;\n    overflow-wrap: break-word; \/* Prevents long text from pushing width *\/\n  }\n  .card strong {\n    color: #1f3d2a;\n    font-weight: 700;\n  }\n<\/style>\n\n<div class=\"wrap\">\n  <div class=\"card\">\n    <div class=\"badge\">Summary<\/div>\n    <p>\n    <strong> Regression analysis is a way to measure how changes in one variable are linked to changes in another. <\/strong> For example, you can use it to check whether advertising spend is linked to higher sales, or whether house size helps explain its price. The analysis produces measures such as coefficients, R\u00b2 and residuals, which help assess the direction and strength of relationships and how closely the model fits the available data. <strong> It is commonly used to estimate outcomes, test relationships and support decisions in areas such as finance, business, research and economics. <\/strong>\n    <\/p>\n  <\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">A spreadsheet can show you that sales went up. It can show you that prices fell at the same time. It can even show you that website traffic increased. The harder question comes after that. How much does each factor matter? That is where regression analysis becomes useful. You can use it to study an outcome and see how it changes when one or more other variables change.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You will find it in business reports, research papers, finance models and everyday analytics work. You can also use it with simple tools such as Excel before moving into R or Python. If you want to build these skills across real business data, a practical <a href=\"https:\/\/imarticus.org\/postgraduate-program-in-data-science-analytics\/\"><strong>data analytics course<\/strong><\/a> can help you bring statistics, Excel, SQL, Python and machine learning together.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>What Is Regression Analysis?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When you ask what is regression analysis, you are really asking how you can measure a relationship in data. Take a simple case. You run a coffee shop. You record daily sales and the number of customers who visit. You can see that busy days often have higher sales. That observation gives you a starting point. You can then ask how much sales tend to change when customer visits increase. A regression model gives you an estimated answer. Say your model produces this equation:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Sales = 800 + 14 \u00d7 Customer Visits<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The coefficient is 14. So, within the data used for the model, one extra customer visit is linked with an estimated \u00a314 rise in sales. That number needs context. Rainy weather may reduce visits. A local event may increase them. A bank holiday can change the whole pattern. The model only knows about the variables you give it. This is the part of the regression analysis meaning that often gets missed. The method can measure a relationship very well, but the meaning of that relationship still depends on the data and the question behind it.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>The Terms You Need To Know<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">You will see the same terms in almost every statistics package. Get these clear first and the rest becomes much easier.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Term<\/strong><\/td><td><strong>Also Called<\/strong><\/td><td><strong>Simple Meaning<\/strong><\/td><\/tr><tr><td><strong>Outcome<\/strong><\/td><td>Dependent variable<\/td><td>The result you want to study<\/td><\/tr><tr><td><strong>Predictor<\/strong><\/td><td>Independent variable<\/td><td>A variable used to explain the outcome<\/td><\/tr><tr><td><strong>Coefficient<\/strong><\/td><td>Slope estimate<\/td><td>Estimated change linked with a predictor<\/td><\/tr><tr><td><strong>Intercept<\/strong><\/td><td>Constant<\/td><td>Model value when predictors equal zero<\/td><\/tr><tr><td><strong>Residual<\/strong><\/td><td>Error<\/td><td>Difference between actual and fitted value<\/td><\/tr><tr><td><strong>Fitted Value<\/strong><\/td><td>Predicted value<\/td><td>Value produced by the model<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">These terms give you the basic language of regression analysis. Once you know them, a model output stops looking like a collection of random numbers.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#7bdbb426\"><strong>Also Read:<\/strong><a href=\"https:\/\/imarticus.org\/blog\/what-is-data-visualization\/\">What Is Data Visualisation And Why Is It Important?<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>How Does Regression Analysis Work?<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The easiest way to follow regression analysis is to start with a question rather than a formula. Suppose you want to understand house prices. You have data on:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Selling price<\/li>\n\n\n\n<li>Floor area<\/li>\n\n\n\n<li>Number of bedrooms<\/li>\n\n\n\n<li>Property age<\/li>\n\n\n\n<li>Distance from the city centre<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">You could study price against floor area first. Then you could add age, bedrooms and distance. The estimated floor-area coefficient may change after those variables enter the model. That can tell you that the first relationship was partly reflecting other differences between the properties. This is where multiple regression analysis earns its place. You can put several predictors into one model and look at each one while the others remain part of the equation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Why Your Question Matters<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A vague question creates a vague model.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u201cWhich things affect sales?\u201d gives you little direction.<\/li>\n\n\n\n<li>\u201cIs monthly sales revenue related to advertising spend after accounting for price and website visits?\u201d gives you a much clearer starting point.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Now you have an outcome. You have possible predictors. You also have a reason for keeping those predictors in the analysis. That small change in wording can improve the whole piece of work.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Residuals Show You<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A residual is simply the difference between an observed value and the value predicted by your model. Suppose the model predicts a house will sell for \u00a3420,000.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The actual sale price is \u00a3450,000.<\/li>\n\n\n\n<li>The residual is \u00a330,000.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">One residual tells you little. A group of residuals can tell you much more.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If they sit in a loose and fairly random band around zero, your model may be capturing the main pattern.<\/li>\n\n\n\n<li>If they form a curve, a funnel or another clear shape, you have something to investigate.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Penn State recommends using residual plots to check issues such as non-linearity, unequal spread and unusual observations. That is why I would never judge a model from its equation alone.&nbsp;&nbsp;<\/p>\n\n\n\n<!--  Widget: WordPress-safe scoped embed -->\n<style>\n\n#ra-widget{margin:0;background:#f5f7fb;color:#182033;font:16px\/1.5 system-ui,-apple-system,Segoe UI,Arial}.wrap{max-width:1050px;margin:auto;padding:28px 16px}.hero{padding:12px 0 18px}h1{font-size:clamp(30px,5vw,50px);line-height:1.05;margin:8px 0}.lead{color:#657084;font-size:18px}.nav{display:flex;gap:8px;overflow:auto;position:sticky;top:0;padding:12px 0;background:#f5f7fb;z-index:3}.nav button,.chip{border:1px solid #dce2eb;background:white;border-radius:99px;padding:9px 13px;font-weight:700;cursor:pointer}.nav button.on{background:#3157d5;color:#fff}.layer{display:none}.layer.on{display:block}.card{background:white;border:1px solid #dce2eb;border-radius:18px;padding:20px;margin-bottom:16px;box-shadow:0 8px 25px #25345a0a}.grid{display:grid;grid-template-columns:1.25fr .75fr;gap:18px}.metrics{display:grid;grid-template-columns:repeat(3,1fr);gap:9px}.metric{border:1px solid #dce2eb;border-radius:12px;padding:12px}.metric b{display:block;font-size:21px}.metric span,.small{color:#657084;font-size:12px}svg{width:100%;height:auto}.note{padding:12px 14px;border-left:4px solid #3157d5;background:#f1f4ff;border-radius:8px}.good{border-color:#159b7d;background:#eefaf6}.warn{border-color:#d97706;background:#fff7eb}.controls{display:grid;gap:12px}.control{border:1px solid #dce2eb;border-radius:12px;padding:11px}.control label{font-weight:700;display:flex;justify-content:space-between}.control input{width:100%}table{width:100%;border-collapse:collapse}th,td{text-align:left;padding:9px;border-bottom:1px solid #e2e6ee}.cta{background:linear-gradient(135deg,#17264e,#3157d5);color:white;border-radius:20px;padding:25px}.cta p{color:#e9edff}.cta a{display:inline-block;background:white;color:#17306f;text-decoration:none;font-weight:800;padding:11px 16px;border-radius:9px}@media(max-width:750px){.grid{grid-template-columns:1fr}.metrics{grid-template-columns:1fr 1fr}}\n\n#ra-widget, #ra-widget * { box-sizing: border-box; }\n#ra-widget { isolation: isolate; width: 100%; max-width: 100%; }\n#ra-widget button, #ra-widget input { font: inherit; }\n<\/style>\n\n<div id=\"ra-widget\">\n<div class=\"wrap\">\n<div class=\"hero\"><div class=\"small\">INTERACTIVE REGRESSION ANALYSIS<\/div><h1>From Question to Model to Residuals<\/h1><p class=\"lead\">Work through a house-price example in five layers. Change the inputs and see how the model responds.<\/p><\/div>\n<div class=\"nav\"><button class=\"on\" onclick=\"go(1)\">1. Ask<\/button><button onclick=\"go(2)\">2. Fit<\/button><button onclick=\"go(3)\">3. Add variables<\/button><button onclick=\"go(4)\">4. Residuals<\/button><button onclick=\"go(5)\">5. Take action<\/button><\/div>\n\n<section class=\"layer on\" id=\"l1\"><div class=\"card\"><h2>1. Start with the question<\/h2><p>Suppose the outcome is house price and the first predictor is floor area.<\/p><div class=\"grid\"><svg id=\"q\" viewBox=\"0 0 650 360\"><\/svg><div><p><b>Question:<\/b> Is selling price related to floor area?<\/p><p>Other available variables:<\/p><p><span class=\"chip\">Bedrooms<\/span> <span class=\"chip\">Property age<\/span> <span class=\"chip\">Distance to centre<\/span><\/p><div class=\"note\">A clear question gives the model a reason for existing. It also helps decide which variables belong in the analysis.<\/div><\/div><\/div><\/div><\/section>\n\n<section class=\"layer\" id=\"l2\"><div class=\"card\"><h2>2. Fit a simple regression<\/h2><p>Move the sliders and watch the estimated price and residual change.<\/p><div class=\"grid\"><svg id=\"fit\" viewBox=\"0 0 650 390\"><\/svg><div><div class=\"metrics\"><div class=\"metric\"><span>Estimated<\/span><b id=\"pred\">420k<\/b><\/div><div class=\"metric\"><span>Residual<\/span><b id=\"rr\">30k<\/b><\/div><div class=\"metric\"><span>R\u00b2<\/span><b id=\"r2\">0.84<\/b><\/div><\/div><div class=\"controls\"><div class=\"control\"><label>Floor area <span id=\"av\">110 m\u00b2<\/span><\/label><input id=\"area\" type=\"range\" min=\"60\" max=\"220\" value=\"110\"><\/div><div class=\"control\"><label>Actual price <span id=\"pv\">450k<\/span><\/label><input id=\"price\" type=\"range\" min=\"250\" max=\"700\" value=\"450\"><\/div><\/div><p class=\"note\">The gap between the actual point and the fitted line is the residual.<\/p><\/div><\/div><\/div><\/section>\n\n<section class=\"layer\" id=\"l3\"><div class=\"card\"><h2>3. Why multiple regression matters<\/h2><p>Adding relevant predictors can change the floor-area coefficient because the first relationship may have reflected other property differences.<\/p><div class=\"grid\"><svg id=\"multi\" viewBox=\"0 0 650 390\"><\/svg><div><p><label><input id=\"bed\" type=\"checkbox\" checked> Bedrooms<\/label><\/p><p><label><input id=\"age\" type=\"checkbox\"> Property age<\/label><\/p><p><label><input id=\"dist\" type=\"checkbox\"> Distance from centre<\/label><\/p><div class=\"metrics\"><div class=\"metric\"><span>Floor-area coefficient<\/span><b id=\"coef\">\u00a33.1k\/m\u00b2<\/b><\/div><div class=\"metric\"><span>Model R\u00b2<\/span><b id=\"mr2\">0.84<\/b><\/div><div class=\"metric\"><span>Interpretation<\/span><b>Adjusted effect<\/b><\/div><\/div><p class=\"note\">Multiple regression estimates a predictor while the other included variables remain in the model.<\/p><\/div><\/div><\/div><\/section>\n\n<section class=\"layer\" id=\"l4\"><div class=\"card\"><h2>4. Read the residuals<\/h2><p>Residual = observed value \u2212 predicted value. Select a pattern to see why residual plots matter.<\/p><div class=\"grid\"><svg id=\"res\" viewBox=\"0 0 650 390\"><\/svg><div><div class=\"metrics\"><div class=\"metric\"><span>Observed<\/span><b>\u00a3450k<\/b><\/div><div class=\"metric\"><span>Predicted<\/span><b>\u00a3420k<\/b><\/div><div class=\"metric\"><span>Residual<\/span><b>\u00a330k<\/b><\/div><\/div><p><button class=\"chip\" onclick=\"res('random')\">Random<\/button> <button class=\"chip\" onclick=\"res('curve')\">Curve<\/button> <button class=\"chip\" onclick=\"res('funnel')\">Funnel<\/button><\/p><div id=\"rt\" class=\"note good\">A loose, random band around zero is broadly what you want to see.<\/div><\/div><\/div><\/div><\/section>\n\n<section class=\"layer\" id=\"l5\"><div class=\"card\"><h2>5. Put the result to work<\/h2><p>A useful regression result answers a sensible question and survives basic checks.<\/p><table><tr><th>Check<\/th><th>Question<\/th><th>Why it matters<\/th><\/tr><tr><td>Outcome<\/td><td>Is the target clearly defined?<\/td><td>Keeps the model tied to the question.<\/td><\/tr><tr><td>Predictors<\/td><td>Do variables have a reason to be included?<\/td><td>Supports clearer interpretation.<\/td><\/tr><tr><td>Coefficients<\/td><td>What does each estimate mean?<\/td><td>Turns output into an explanation.<\/td><\/tr><tr><td>R\u00b2<\/td><td>How much variation is explained?<\/td><td>Useful fit information, not a quality guarantee.<\/td><\/tr><tr><td>Residuals<\/td><td>Is there a visible pattern?<\/td><td>Can reveal model problems.<\/td><\/tr><\/table><\/div><div class=\"cta\"><h2>Build the skills behind the model<\/h2><p>Regression becomes more useful when it sits alongside Excel, SQL, Python, statistics and practical analytics work. 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n=(bed.checked?1:0)+(age.checked?1:0)+(dist.checked?1:0),co=3.1-n*.35,r=.84+n*.035,l=document.createElementNS(NS,\"line\");l.setAttribute(\"x1\",X(60));l.setAttribute(\"y1\",Y(45));l.setAttribute(\"x2\",X(220));l.setAttribute(\"y2\",Y(45+co*160));l.setAttribute(\"stroke\",\"#159b7d\");l.setAttribute(\"stroke-width\",4);s.appendChild(l);coef.textContent=\"\u00a3\"+co.toFixed(1)+\"k\/m\u00b2\";mr2.textContent=Math.min(r,.95).toFixed(2)}\n[bed,age,dist].forEach(x=>x.onchange=multi);multi();\nfunction res(mode){let s=base(\"res\",\"Residual plot\",\"Predicted value\",\"Residual\");let z=document.createElementNS(NS,\"line\");z.setAttribute(\"x1\",65);z.setAttribute(\"x2\",620);z.setAttribute(\"y1\",200);z.setAttribute(\"y2\",200);z.setAttribute(\"stroke\",\"#9aa5b5\");z.setAttribute(\"stroke-dasharray\",\"5 5\");s.appendChild(z);for(let i=0;i<18;i++){let y=mode===\"random\"?(Math.sin(i*3.7)*12+(i%3-1)*6):mode===\"curve\"?(i-9)*(i-9)*1.6-45:(Math.random()-.5)*(i+2)*7,c=document.createElementNS(NS,\"circle\");c.setAttribute(\"cx\",X(70+i*8.2));c.setAttribute(\"cy\",200-y*2);c.setAttribute(\"r\",5);c.setAttribute(\"fill\",\"#3157d5\");s.appendChild(c)}rt.className=\"note \"+(mode===\"random\"?\"good\":\"warn\");rt.textContent=mode===\"random\"?\"A loose, random band around zero is broadly what you want to see.\":\"A visible \"+mode+\" pattern is a reason to investigate the model before trusting its output.\"}\nres(\"random\");\nfunction go(n){document.querySelectorAll(\"#ra-widget .layer\").forEach((e,i)=>e.classList.toggle(\"on\",i===n-1));document.querySelectorAll(\"#ra-widget .nav button\").forEach((e,i)=>e.classList.toggle(\"on\",i===n-1));window.scrollTo({top:0,behavior:\"smooth\"})}\n\n})();\n<\/script>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Regression Analysis Formula<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The basic regression analysis formula for simple linear regression is:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Y = \u03b2\u2080 + \u03b2\u2081X + \u03b5<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Y is your outcome.<\/li>\n\n\n\n<li>X is your predictor.<\/li>\n\n\n\n<li>\u03b2\u2080 is the intercept.<\/li>\n\n\n\n<li>\u03b2\u2081 is the coefficient.<\/li>\n\n\n\n<li>\u03b5 is the part of the outcome that remains unexplained by the model.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Now use a simple example:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sales = 1,000 + 25 \u00d7 Customer Visits<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If customer visits increase by ten, the fitted value rises by \u00a3250. That is the mechanical part. The interpretation comes next. You need to know how the variables are measured. You also need to know whether the model is being used within a sensible range.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What Does The Slope Tell You?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The slope tells you the estimated change in the outcome for a one-unit change in the predictor.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A positive coefficient means the fitted outcome rises as the predictor rises.<\/li>\n\n\n\n<li>A negative coefficient means the fitted outcome falls.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The size can only be understood with the units attached. A coefficient of 5 means little on its own. Five pounds, five thousand pounds and five percentage points are very different things.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What Does The Intercept Tell You?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The intercept gives you the fitted value when the predictors are zero. Sometimes that has a useful real-world meaning. Sometimes it does not. If zero is far outside the range of your data, the intercept may mainly exist because the equation needs a constant term.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Multiple Regression Analysis Formula<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The multiple regression analysis formula adds more predictors:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"><strong>Y = \u03b2\u2080 + \u03b2\u2081X\u2081 + \u03b2\u2082X\u2082 + \u03b2\u2083X\u2083 + \u03b5<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine that you are estimating house prices using floor area, property age and distance from the city centre. Each coefficient now belongs to the same model. The floor-area coefficient describes the estimated change linked with floor area while the other included predictors remain in the model. That is a more precise statement than saying floor area \u201ccauses\u201d the price to rise.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Why Least Squares Is Used<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">You can calculate the difference between every observed value and its fitted value. Those differences are residuals. Some will be positive. Some will be negative. If you simply add them, they can cancel each other out. Least squares squares each residual before adding them. The fitted coefficients are then chosen to minimise the total of those squared errors.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#7bdbb426\"><strong><em>Interesting Insight \u2192<\/em><\/strong> <em>NIST describes linear least squares regression as the most widely used modelling method and notes that it forms part of several other modelling approaches. The calculation is mathematical. The reasoning around the calculation is where much of your analytical judgement comes in. (<\/em><a href=\"https:\/\/www.itl.nist.gov\/div898\/handbook\/pmd\/section1\/pmd141.htm\/\"><em>Source<\/em><\/a><em>)<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Types Of Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The types of regression analysis become much easier to sort once you look at the outcome first. Ask yourself what you are trying to predict. Then look at the number of predictors. Finally, look at the shape of the relationship.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Method<\/strong><\/td><td><strong>Outcome<\/strong><\/td><td><strong>Typical Situation<\/strong><\/td><\/tr><tr><td><strong>Linear Regression<\/strong><\/td><td>Continuous value<\/td><td>Relationship is roughly straight<\/td><\/tr><tr><td><strong>Multiple Regression<\/strong><\/td><td>Continuous value<\/td><td>Several predictors explain one outcome<\/td><\/tr><tr><td><strong>Polynomial Regression<\/strong><\/td><td>Continuous value<\/td><td>Relationship bends or curves<\/td><\/tr><tr><td><strong>Logistic Regression<\/strong><\/td><td>Binary or categorical<\/td><td>You want a probability or class<\/td><\/tr><tr><td><strong>Ridge Regression<\/strong><\/td><td>Continuous value<\/td><td>Predictors overlap strongly<\/td><\/tr><tr><td><strong>Lasso Regression<\/strong><\/td><td>Continuous value<\/td><td>You want predictor selection<\/td><\/tr><tr><td><strong>Elastic Net<\/strong><\/td><td>Continuous value<\/td><td>You want both shrinkage approaches<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">This gives you a useful starting point. You still need to look at your data before choosing the final model.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Linear Regression Analysis<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/imarticus.org\/blog\/linear-regression-definition-types-examples\/\">Linear regression<\/a> analysis works well when a straight line gives a sensible description of the relationship. Think about delivery distance and delivery time. A short journey will often take less time than a long one. Within a suitable range, a straight line can give you a useful estimate. The important phrase is \u201cwithin a suitable range\u201d. A fitted line can look good across your observed data and behave poorly far outside it.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Multiple Regression Analysis<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/imarticus.org\/blog\/mastering-multiple-regression-analysis-in-financial-modelling\/\">Multiple regression<\/a> analysis lets you include several predictors for one outcome. You might model sales using advertising spend, product price and website visits. The model can then estimate the relationship between each predictor and sales while keeping the other predictors in the model. This can be very useful when a single-variable model leaves out factors that clearly matter.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Polynomial Regression<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">You can use polynomial regression when the relationship has a curve. Consider crop yield and temperature. Yield may increase as temperature rises, then stop increasing, and eventually fall. A straight line misses that bend. A polynomial model gives you more freedom to represent the shape.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Logistic Regression<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/imarticus.org\/blog\/how-to-use-logistic-regression-in-python\/\">Logistic regression<\/a> is useful when your outcome is a category. A common example is customer renewal. You may want to estimate the chance that a customer renews a subscription based on usage, tenure and support history. The result is a probability rather than a raw sales value.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Ridge, Lasso, And Elastic Net<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">These methods become useful when you have many predictors or predictors that carry similar information.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ridge shrinks coefficients towards zero.<\/li>\n\n\n\n<li>Lasso can shrink some coefficients to zero.<\/li>\n\n\n\n<li>Elastic net combines the two ideas.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">You often see these methods in predictive modelling when a basic model becomes unstable or overly complex.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"599\" src=\"https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/types-of-regression-analysis-1024x599.webp\" alt=\"regression analysis types\" class=\"wp-image-278414\" srcset=\"https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/types-of-regression-analysis-1024x599.webp 1024w, https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/types-of-regression-analysis-300x175.webp 300w, https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/types-of-regression-analysis-766x448.webp 766w, https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/types-of-regression-analysis.webp 1129w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Multiple And Multivariate Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The words \u201cmultiple\u201d and \u201cmultivariate\u201d sound close enough to cause trouble. The difference is worth remembering.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiple regression usually means one outcome and several predictors.<\/li>\n\n\n\n<li><a href=\"https:\/\/imarticus.org\/blog\/visualisation-of-multivariate-data\/\">Multivariate regression<\/a> analysis involves more than one outcome.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose you study salary using experience, education and location. You have one outcome. Now suppose you study both blood pressure and cholesterol using the same set of predictors. You have more than one outcome.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Model<\/strong><\/td><td><strong>Outcomes<\/strong><\/td><td><strong>Predictors<\/strong><\/td><td><strong>Example<\/strong><\/td><\/tr><tr><td><strong>Simple Regression<\/strong><\/td><td>1<\/td><td>1<\/td><td>Sales from advertising<\/td><\/tr><tr><td><strong>Multiple Regression<\/strong><\/td><td>1<\/td><td>3<\/td><td>Sales from price, ads and visits<\/td><\/tr><tr><td><strong>Multivariate Regression<\/strong><\/td><td>2 or more<\/td><td>Several<\/td><td>Blood pressure and cholesterol<\/td><\/tr><tr><td><strong>Logistic Regression<\/strong><\/td><td>1<\/td><td>Several<\/td><td>Renewal probability<\/td><\/tr><tr><td><strong>Polynomial Regression<\/strong><\/td><td>1<\/td><td>Several<\/td><td>Curved sales relationship<\/td><\/tr><tr><td><strong>Ridge Regression<\/strong><\/td><td>1<\/td><td>Many<\/td><td>Model with overlapping inputs<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">You can also see this distinction in R. The official documentation for <em>lm()<\/em> covers linear models and multivariate linear models. I would check the number of outcomes before using the term multivariate regression analysis. That one step keeps the terminology accurate.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#7bdbb426\"><strong>Also Read:<\/strong> <a href=\"https:\/\/imarticus.org\/blog\/data-science\/\">How Does Data Science Work In Real-World Projects?<\/a><strong><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Regression Analysis In Statistics: What You Need To Check<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Once you know the equation, regression analysis in statistics moves into a more serious stage. You now have to decide whether the model is a reasonable description of your data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Checking Linearity<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Start with the shape. If you fit a straight line to a strongly curved relationship, the model is missing part of the story. A residual plot can help here. If the residuals form a curve, you have a useful warning sign.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Checking The Spread Of Errors<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You also want to look at how widely the residuals spread. Suppose the points are tightly packed for smaller fitted values and spread much more at larger values. That change can affect the model&#8217;s error estimates. Penn State shows examples where fanning or funnel shapes in residual plots reveal unequal variance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Checking Independence<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Your observations may be connected. Daily sales from the same shop can have a weekly pattern. Measurements taken repeatedly from the same person can also be linked. You need to account for that structure when it matters.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Checking Multicollinearity<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You may have several predictors that contain much of the same information. Floor area and number of rooms are a simple example. Both may be related to house size. Strong overlap can make individual coefficients harder to estimate with precision. Penn State discusses this problem in its material on multicollinearity and model building.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Checking Outliers<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I would investigate unusual observations before removing them. A value can look strange because of an error. It can also look strange because the observation is genuinely unusual. Those are very different situations.&nbsp;&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>A Practical Regression Checklist<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">You can keep your first model review fairly simple.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Look at the outcome and predictors together because a sensible model starts with variables that fit the question.<\/li>\n\n\n\n<li>Plot the main relationships before fitting the model because unusual shapes often become obvious very quickly.<\/li>\n\n\n\n<li>Study residual plots after fitting because they can reveal patterns that the main regression table hides.<\/li>\n\n\n\n<li>Check whether predictors overlap heavily because similar inputs can make individual coefficients difficult to interpret.<\/li>\n\n\n\n<li>Investigate unusual observations before removing them because a genuine extreme case may carry useful information.<\/li>\n\n\n\n<li>Keep predictions inside a sensible range whenever possible because estimates become less dependable when you move far beyond observed data.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">These checks take time. They also prevent many poor conclusions.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>How To Perform Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When you want to perform regression analysis, I would keep your workflow in this order. Start with the question. Then choose the outcome. Then decide which predictors have a good reason to be included. Only after that should you fit the model.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1: Define the Outcome:<\/strong> Suppose you want to understand delivery time. Your outcome could be delivery time in minutes. That gives the model a clear target.<\/li>\n\n\n\n<li><strong>Step 2: Choose the Predictors:<\/strong> You may have delivery distance, order size and number of stops. You should have a reason for including each one. A database column is not automatically a useful predictor.<\/li>\n\n\n\n<li><strong>Step 3: Inspect the Data:<\/strong> Check missing values. Check units. Look for duplicate rows. Look at the distributions. Plot the main relationships.<\/li>\n\n\n\n<li><strong>Step 4: Choose the Model:<\/strong> A continuous outcome with a roughly linear relationship may suit linear regression. A binary outcome may suit logistic regression. Several predictors can lead you towards multiple regression analysis.<\/li>\n\n\n\n<li><strong>Step 5: Fit the Model:<\/strong> Now you can estimate the coefficients and inspect the output.<\/li>\n\n\n\n<li><strong>Step 6: Check the Results:<\/strong> Look at the residuals. Check for unusual observations. Look at predictor overlap. Think about whether the equation makes sense.<\/li>\n\n\n\n<li><strong>Step 7: Validate the Model:<\/strong> Prediction requires more than a good fit on the data used to create the model. A model can work very well on historical records and then perform poorly on new data. You should keep that in mind when adding variables simply because they improve the fit.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"593\" src=\"https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/regression-analysis-steps-1024x593.webp\" alt=\"steps of regression analysis\" class=\"wp-image-278415\" srcset=\"https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/regression-analysis-steps-1024x593.webp 1024w, https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/regression-analysis-steps-300x174.webp 300w, https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/regression-analysis-steps-767x444.webp 767w, https:\/\/imarticus.org\/blog\/wp-content\/uploads\/2026\/10\/regression-analysis-steps.webp 1388w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Regression Analysis Example: A Small Worked Problem<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A useful regression analysis example should let you see what the numbers are doing. The figures below are illustrative. Suppose you track advertising spend and weekly sales for a small retailer.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Week<\/strong><\/td><td><strong>Advertising Spend (\u00a3000)<\/strong><\/td><td><strong>Sales (\u00a3000)<\/strong><\/td><td><strong>Fitted Sales (\u00a3000)<\/strong><\/td><\/tr><tr><td>1<\/td><td>2<\/td><td>21<\/td><td>20.8<\/td><\/tr><tr><td>2<\/td><td>3<\/td><td>23<\/td><td>23.1<\/td><\/tr><tr><td>3<\/td><td>4<\/td><td>25<\/td><td>25.4<\/td><\/tr><tr><td>4<\/td><td>5<\/td><td>28<\/td><td>27.7<\/td><\/tr><tr><td>5<\/td><td>6<\/td><td>29<\/td><td>30.0<\/td><\/tr><tr><td>6<\/td><td>7<\/td><td>32<\/td><td>32.3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The fitted line in this illustration is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sales = 16.2 + 2.3 \u00d7 Advertising Spend<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Take week five.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Advertising spend is \u00a36,000.<\/li>\n\n\n\n<li>The fitted sales value is \u00a330,000.<\/li>\n\n\n\n<li>Actual sales were \u00a329,000.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">So the residual is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>29 \u2212 30 = -1<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The model overestimated sales by \u00a31,000. That is one observation. You then look at the full set of residuals.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#7bdbb426\"><strong>Interesting insight \u2192<\/strong> Anscombe&#8217;s quartet contains four datasets with 11 observations each. The datasets share the same traditional summary statistics, correlation and fitted regression line, yet their plotted relationships are very different. R records the common fitted line as <strong>y = 3 + 0.5x<\/strong> and the R-squared value as <strong>0.67<\/strong>.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>How To Interpret Regression Analysis Results<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Regression output becomes much easier when you stop trying to read every number at once. Start with the coefficient table. Then look at uncertainty. Then look at model fit. Finally, check the diagnostics.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Output<\/strong><\/td><td><strong>Question To Ask<\/strong><\/td><td><strong>What It Gives You<\/strong><\/td><\/tr><tr><td><strong>Coefficient<\/strong><\/td><td>How does the outcome change?<\/td><td>Estimated relationship<\/td><\/tr><tr><td><strong>Standard Error<\/strong><\/td><td>How precise is the estimate?<\/td><td>Measure of uncertainty<\/td><\/tr><tr><td><strong>P-Value<\/strong><\/td><td>What does the test show?<\/td><td>Evidence under a stated hypothesis<\/td><\/tr><tr><td><strong>R-Squared<\/strong><\/td><td>How much sample variation is explained?<\/td><td>Model fit measure<\/td><\/tr><tr><td><strong>Adjusted R-Squared<\/strong><\/td><td>Does added complexity help?<\/td><td>Model comparison aid<\/td><\/tr><tr><td><strong>VIF<\/strong><\/td><td>Do predictors overlap?<\/td><td>Multicollinearity clue<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The numbers work together. You should avoid making a decision from one column.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Coefficients<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose your advertising coefficient is 2.3. If advertising is measured in thousands of pounds and sales are also measured in thousands of pounds, you can say: <strong>A \u00a31,000 increase in advertising is associated with an estimated \u00a32,300 increase in sales, within the model and its observed range.<\/strong> That is a useful interpretation. It is also precise.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>R-Squared:<\/strong> R-squared measures the proportion of variation in the outcome that the fitted model accounts for in the sample. Penn State gives the standard expression as:<\/li>\n\n\n\n<li><strong>R\u00b2 = 1 \u2212 SSE \/ SSTO:<\/strong> You should avoid calling this \u201caccuracy\u201d. A high R-squared does not by itself guarantee good predictions or a sensible model.<\/li>\n\n\n\n<li><strong>Adjusted R-Squared:<\/strong> Adjusted R-squared takes the number of predictors into account. This can help when you compare models with different numbers of inputs. Penn State notes that ordinary R-squared will stay the same or increase when predictors are added, even when the added variables are not useful. Adjusted R-squared can fall when unnecessary variables are introduced.<\/li>\n\n\n\n<li><strong>P-Values:<\/strong> A p-value belongs to a specific statistical test. A small p-value can provide evidence against a chosen null hypothesis. It does not tell you the size of the effect. It also does not tell you whether a result is commercially useful. A tiny effect can matter statistically in a large dataset and still have little practical value.<\/li>\n\n\n\n<li><strong>Confidence Intervals:<\/strong> A confidence interval gives you a range around an estimate. Suppose your estimated price effect is \u00a32,000. The interval is \u00a31,100 to \u00a32,900. That gives you a clearer picture of the estimate than \u00a32,000 alone.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>RMSE And MAE<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You will often see RMSE and MAE when prediction is important. RMSE gives larger errors more weight. MAE gives you the average absolute error. Both can be expressed in the units of your outcome, which makes them easy to explain to people who do not work in statistics. &nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#7bdbb426\"><strong>Also Read:<\/strong> <a href=\"https:\/\/imarticus.org\/blog\/data-analyst-course\/\">Is a Data Analyst Course Suitable for Beginners?<\/a><strong><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Correlation And Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When you study correlation and regression analysis, you are looking at two related ways of working with relationships between variables. Correlation tells you how strongly two variables move together. Regression gives you a model built around an outcome. That difference becomes clear with a simple example.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose umbrella sales rise when rainfall increases. You can use correlation to measure the association. You can use regression to estimate umbrella sales from rainfall. A third factor can still exist. Weather may also affect customer footfall or hot drink sales.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Difference Between Correlation And Regression Analysis<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The difference between correlation and regression analysis becomes easier to remember when you focus on the question each method answers.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Feature<\/strong><\/td><td><strong>Correlation<\/strong><\/td><td><strong>Regression Analysis<\/strong><\/td><td><strong>Practical Meaning<\/strong><\/td><\/tr><tr><td><strong>Main Purpose<\/strong><\/td><td>Measure association<\/td><td>Model an outcome<\/td><td>Your question decides<\/td><\/tr><tr><td><strong>Variable Roles<\/strong><\/td><td>More symmetric<\/td><td>Outcome and predictors<\/td><td>Roles matter<\/td><\/tr><tr><td><strong>Prediction<\/strong><\/td><td>Limited<\/td><td>Directly supported<\/td><td>Regression gives an equation<\/td><\/tr><tr><td><strong>Multiple Predictors<\/strong><\/td><td>No equivalent structure<\/td><td>Supported<\/td><td>Several factors can enter<\/td><\/tr><tr><td><strong>Causation<\/strong><\/td><td>Not established<\/td><td>Not established alone<\/td><td>Study design still matters<\/td><\/tr><tr><td><strong>Main Output<\/strong><\/td><td>Correlation coefficient<\/td><td>Estimated coefficients<\/td><td>Different interpretation<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The difference between correlation and regression analysis matters when you need to predict an outcome or include several predictors.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Regression Analysis In Research<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The value of regression analysis in research often comes from the ability to study an outcome alongside several measured variables. Imagine a study of exam performance. You have:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exam score<\/li>\n\n\n\n<li>Study hours<\/li>\n\n\n\n<li>Attendance<\/li>\n\n\n\n<li>Previous score<\/li>\n\n\n\n<li>Access to learning resources<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">You can use multiple regression analysis to study the relationship between these variables and exam score. You still need to consider how the data were collected. An observational study can reveal relationships in measured data. It does not automatically prove that one variable caused another to change.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>How To Report The Results<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Good reporting gives the reader enough detail to understand the model.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>State the outcome clearly so the reader knows exactly what the analysis is trying to explain.<\/li>\n\n\n\n<li>Name each predictor and its measurement unit so the coefficients can be interpreted correctly.<\/li>\n\n\n\n<li>Explain why the selected model fits the outcome and the research question being examined.<\/li>\n\n\n\n<li>Report estimates alongside suitable uncertainty measures so readers can judge both size and precision.<\/li>\n\n\n\n<li>Mention important limitations because the data collection process can affect what the model supports.<\/li>\n\n\n\n<li>Describe the main diagnostic checks so readers can see how you assessed the model before interpreting it.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">That makes regression analysis in research much easier to review and understand.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Regression Analysis In Excel<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Regression analysis in Excel is a useful option when your data already sit in a spreadsheet. Microsoft&#8217;s desktop <a href=\"https:\/\/imarticus.org\/blog\/mastering-excel-for-data-analysis\/\">Excel<\/a> application includes the Regression tool in the Analysis ToolPak. Microsoft says the tool uses the least-squares method and can analyse one dependent variable against one or more independent variables.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You can keep the setup fairly simple. Put your outcome in one column. Put each predictor in its own column. Keep the labels clear. Then select Data Analysis, choose Regression, select your Y range and your X range, and choose where you want Excel to place the output.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What To Read In The Output<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">I would focus on a few parts first.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>R Square<\/strong> gives you a model-fit measure.<\/li>\n\n\n\n<li><strong>Coefficients<\/strong> give you the estimated relationships.<\/li>\n\n\n\n<li><strong>Standard Error<\/strong> gives you an uncertainty measure.<\/li>\n\n\n\n<li><strong>P-value<\/strong> belongs to the related coefficient test.<\/li>\n\n\n\n<li><strong>Residuals<\/strong> help you inspect what the model leaves behind.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The Excel output can look complete even when the model is poor. You still need to check the data and the residuals.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Regression Analysis In R<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">You can also work with regression analysis in <a href=\"https:\/\/imarticus.org\/blog\/what-is-r-programming-for-data-science\/\">R<\/a>. The basic R code for regression analysis is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>model &lt;- lm(sales ~ advertising, data = cafe)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>summary(model)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you add more predictors:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>model &lt;- lm(sales ~ advertising + price + visits, data = cafe)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>summary(model)<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The part before the tilde is the outcome. The parts after it are predictors. R&#8217;s official documentation describes lm() as a function for fitting linear models and includes multivariate linear models in its scope.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Uses Of Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The uses of regression analysis cover a wide range of decisions. The common thread is simple. You have an outcome, you have useful predictors, and you want to understand the relationship or make a reasonable estimate.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Area<\/strong><\/td><td><strong>Outcome<\/strong><\/td><td><strong>Predictors<\/strong><\/td><td><strong>Possible Use<\/strong><\/td><\/tr><tr><td><strong>Retail<\/strong><\/td><td>Sales<\/td><td>Price, promotion, visits<\/td><td>Demand planning<\/td><\/tr><tr><td><strong>Marketing<\/strong><\/td><td>Customer response<\/td><td>Spend, channel, offer<\/td><td>Budget decisions<\/td><\/tr><tr><td><strong>Finance<\/strong><\/td><td>Return or risk<\/td><td>Market factors, rates<\/td><td>Risk assessment<\/td><\/tr><tr><td><strong>Operations<\/strong><\/td><td>Delivery time<\/td><td>Distance, volume, stops<\/td><td>Capacity planning<\/td><\/tr><tr><td><strong>Manufacturing<\/strong><\/td><td>Defect rate<\/td><td>Machine settings, load<\/td><td>Process improvement<\/td><\/tr><tr><td><strong>Education<\/strong><\/td><td>Test score<\/td><td>Study, attendance, prior score<\/td><td>Research<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The best uses of regression analysis start with a decision that needs evidence. The model should have a clear job.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Marketing:<\/strong> You can examine sales or customer response using advertising spend, channel, offer and price. A model can help you estimate relationships between these variables. You should still check seasonality and major changes in the market.<\/li>\n\n\n\n<li><strong>Finance:<\/strong> You can study relationships between returns and selected financial factors. <a href=\"https:\/\/imarticus.org\/blog\/financial-data-with-database-manipulation-techniques\/\">Financial data<\/a> also have a strong time element, so you need to think about how the observations relate to one another.<\/li>\n\n\n\n<li><strong>Operations:<\/strong> You can model delivery time from distance, order size and number of stops. That can help with planning.<\/li>\n\n\n\n<li><strong>Education:<\/strong> You can examine measurable outcomes such as test scores, attendance or completion rates. The model can reveal patterns in your dataset. The study design still determines what you can reasonably claim.\u00a0<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Finance roles are evolving as automation, analytics, and AI reshape how financial teams work. Alongside core financial knowledge, professionals increasingly need to interpret data, use digital tools, and turn financial information into decisions that support business growth.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Will AI Make Finance Degrees Useless in 2026?\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/gOKw_K3_LUw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Application Of Regression Analysis In Business<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The application of regression analysis becomes particularly useful when a business decision has several factors moving at the same time. Take pricing. Sales fall after a price increase. That seems clear. Then you check the period and notice that advertising also fell and store visits declined.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now you have several possible explanations. A model can bring those measured variables together. You can then see how the price relationship changes once the other predictors enter the model. That gives you a better starting point for a business decision.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Forecasting:<\/strong> You can use historical relationships to estimate future outcomes. The forecast still needs testing. Customer behaviour can change. Markets can move. Pricing can change. A model built on old data should always be checked against new information.<\/li>\n\n\n\n<li><strong>Planning:<\/strong> You can estimate staffing needs, order volume or delivery demand. Suppose website traffic usually moves with order volume. You can build a model using historical data and estimate future workload from expected traffic. That is a straightforward application of regression analysis.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Importance Of Regression Analysis<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The importance of regression analysis becomes easier to see when a simple pattern needs a number behind it. A graph may tell you that sales rise when visits increase. A model can estimate how much they tend to rise. You can then add price, advertising and season. The coefficient may change. That change tells you something about the relationship between the variables in your model.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Makes A Model Useful?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">I would look for four things.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The model should answer a clear question that matters to the decision or research task being examined.<\/li>\n\n\n\n<li>The variables should make sense for the question and be measured well enough to support the intended analysis.<\/li>\n\n\n\n<li>The results should survive sensible diagnostic checks rather than relying only on attractive summary numbers.<\/li>\n\n\n\n<li>The final interpretation should match the evidence and the limits imposed by the <a href=\"https:\/\/imarticus.org\/blog\/data-collection-methods-how-do-we-collect-and-prepare-data\/\">data collection<\/a> process.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The importance of regression analysis comes from this discipline. You get a structured way to ask questions of data and challenge your own assumptions. &nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Regression analysis is only one part of the work involved in turning raw data into useful business insights. Data analysts typically spend time cleaning information, finding patterns, testing assumptions, building reports, and translating numbers into decisions that teams can act on.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"The Truth About Being a Data Analyst in 2026\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/v3klJkbw7HI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Common Mistakes In Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">You can avoid many problems by watching for a few simple traps.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mistake 1: Treating Correlation As Causation:<\/strong> Two variables can move together because another factor affects both. Rain may increase umbrella sales while also changing hot drink sales. The relationship is real. The cause still needs investigation.<\/li>\n\n\n\n<li><strong>Mistake 2: Treating R-Squared as Accuracy:<\/strong> R-squared describes variation accounted for by the fitted model. It does not tell you exactly how well the model will predict new observations. Penn State specifically cautions against using R-squared on its own when judging a model.<\/li>\n\n\n\n<li><strong>Mistake 3: Adding Every Variable:<\/strong> A larger model is not automatically a better model. Too many predictors can increase uncertainty and encourage overfitting.<\/li>\n\n\n\n<li><strong>Mistake 4: Ignoring Outliers:<\/strong> An unusual observation can affect the fitted relationship. Check it before you remove it.<\/li>\n\n\n\n<li><strong>Mistake 5: Predicting Far Outside Your Data:<\/strong> A model fitted between two known points does not automatically behave sensibly far beyond them. Extrapolation should be treated with care.<\/li>\n\n\n\n<li><strong>Mistake 6: Chasing Small P-Values:<\/strong> Statistical evidence and practical importance are different questions. A very small effect can produce a small p-value when your dataset is large.\u00a0\u00a0<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Choosing The Right Regression Model<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">You can narrow your choice by looking at the outcome, the number of predictors and the shape of the relationship.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Question<\/strong><\/td><td><strong>Situation<\/strong><\/td><td><strong>Starting Point<\/strong><\/td><\/tr><tr><td><strong>What is your outcome?<\/strong><\/td><td>Continuous number<\/td><td>Linear regression<\/td><\/tr><tr><td><strong>Do you have several predictors?<\/strong><\/td><td>Yes<\/td><td>Multiple regression<\/td><\/tr><tr><td><strong>Is the outcome binary?<\/strong><\/td><td>Yes<\/td><td>Logistic regression<\/td><\/tr><tr><td><strong>Does the relationship curve?<\/strong><\/td><td>Yes<\/td><td>Polynomial regression<\/td><\/tr><tr><td><strong>Do predictors overlap strongly?<\/strong><\/td><td>Yes<\/td><td>Ridge or elastic net<\/td><\/tr><tr><td><strong>Do you need predictor selection?<\/strong><\/td><td>Yes<\/td><td>Lasso<\/td><\/tr><tr><td><strong>Do you have several outcomes?<\/strong><\/td><td>Yes<\/td><td>Multivariate approach<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Use this as a first filter. Your final decision should come after looking at the actual data.&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Why Imarticus Learning Is Worth Considering<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A course can teach you SQL, Python, Excel and statistics. That part is fairly easy to find. What caught my attention about Imarticus Learning is the amount of work and career support built into the programme itself. You get 300+ hours of live training, 35+ tools and projects, a 3-week project bootcamp and internship opportunities. You also get time with mentors and a programme manager instead of being left on your own once the classes are over.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>10 guaranteed interviews<\/strong> through the 100% Job Assurance offering.<\/li>\n\n\n\n<li><strong>300+ hours of live training<\/strong>.<\/li>\n\n\n\n<li><strong>35+ tools and projects<\/strong> during the programme.<\/li>\n\n\n\n<li><strong>3-week project bootcamp<\/strong>.<\/li>\n\n\n\n<li><strong>Internship opportunities<\/strong> in Data Science and AI.<\/li>\n\n\n\n<li><strong>40+ hours of live placement preparation<\/strong>.<\/li>\n\n\n\n<li><strong>Personal mentorship and a dedicated programme manager<\/strong>.<\/li>\n\n\n\n<li><strong>Data Science &amp; AI Studio<\/strong> with hackathons and masterclasses.<\/li>\n\n\n\n<li><strong>Training in ChatGPT, Copilot and prompt engineering<\/strong>.<\/li>\n\n\n\n<li><strong>NSDC and Skill India-backed certification<\/strong> on completion.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">That is the part I would pay attention to when looking at the programme. You are getting the classes, but there is also a defined path towards projects, internships and interviews.&nbsp;&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center has-background wp-block-paragraph\" style=\"background-color:#7bdbb426\"><strong><em>EXPLORE THE<\/em> <a href=\"https:\/\/imarticus.org\/postgraduate-program-in-data-science-analytics\/\"><em>DATA ANALYTICS COURSE<\/em><\/a> <em>WITH IMARTICUS LEARNING<\/em><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>FAQs About Regression Analysis<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">From understanding the basic formula to choosing the right model and interpreting coefficients, these answers clear up the frequently asked questions that come up when working with regression analysis in statistics, research and real-world datasets.&nbsp;&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Is Regression Analysis Used For?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Regression analysis is used to examine the relationship between an outcome variable and one or more predictor variables. It helps estimate how changes in predictors are associated with changes in the outcome, test statistical relationships, identify important variables, and make predictions. It is widely used in finance, economics, marketing, healthcare, research, and business analytics.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Is ANOVA A Regression Analysis Test?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">ANOVA is not a separate regression analysis technique, but both methods fall within the general linear model framework. ANOVA primarily tests whether the means of different groups differ significantly, while regression estimates relationships between an outcome and one or more predictors. Regression can also incorporate categorical variables and perform analyses similar to ANOVA.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Is The Difference Between Correlation And Regression Analysis?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Correlation measures the strength and direction of association between two variables without distinguishing between dependent and independent variables. Regression analysis models an outcome variable using one or more predictors and produces coefficients that quantify their relationships. Correlation describes association, while regression is used for estimation, prediction, hypothesis testing, and modelling relationships.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Are The 7 Types Of Regression Analysis Techniques?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Seven commonly used regression analysis techniques are linear regression, multiple regression, polynomial regression, logistic regression, ridge regression, lasso regression, and elastic net regression. Each method suits different data structures and analytical goals. Linear and multiple regression are commonly used for continuous outcomes, while logistic regression is designed for categorical or binary outcomes.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Is The Main Purpose Of Regression Analysis Testing?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The main purpose of regression analysis testing is to determine whether a statistically meaningful relationship exists between an outcome and one or more predictor variables. It helps evaluate the strength and direction of relationships, test hypotheses, estimate effects, assess model fit, and determine whether predictors provide useful information about the outcome.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Who Is The Father Of Regression Analysis?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Francis Galton is widely regarded as the father of regression analysis. His research on hereditary stature introduced the concept of regression toward the mean. Galton developed the statistical idea while studying relationships between parents&#8217; and children&#8217;s heights, providing an important foundation for modern regression analysis and statistical modelling.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Is A Real-Life Example Of Regression Analysis?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">House price prediction is a common real-life example of regression analysis. A regression model can use factors such as property size, location, number of bedrooms, and age to estimate a home&#8217;s price. The resulting coefficients show how each predictor is associated with the estimated price, while the model can be used for future predictions.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>What Is The R Code For Regression Analysis?<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The basic R code for regression analysis is model &lt;- lm(y ~ x, data = dataset). The lm() function fits a linear regression model using the specified outcome and predictor variables. To view the model results, use summary(model), which reports coefficients, standard errors, statistical tests, R-squared, and other regression statistics.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Taking Regression Analysis From Theory To Practice&nbsp;<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Regression analysis makes more sense once you see where it fits in actual work. You start with a question, choose the variables that can help answer it, build the model and then look closely at what comes back. The formula does the calculation. Your job is to decide whether the result makes sense.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Keep a few things in mind when you read the results. Correlation does not prove that one variable caused another. A high R\u00b2 does not mean the model is automatically good. Adding more variables does not necessarily improve it. A regression output can look convincing and still lead you in the wrong direction if the data, variables or assumptions are poor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A structured <a href=\"https:\/\/imarticus.org\/postgraduate-program-in-data-science-analytics\/\"><strong>data analytics course<\/strong><\/a> from Imarticus Learning can help you build that wider skill set across statistics, Excel, SQL, Python, visualisation and machine learning. Do not stop at knowing what the numbers mean. Learn to work with them. Use them to ask better questions. Then make decisions that have evidence behind them.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Regression Analysis covers the formula, assumptions, coefficients, model types and examples used to interpret data.<\/p>\n","protected":false},"author":1,"featured_media":278413,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"om_disable_all_campaigns":false,"_lmt_disableupdate":"","_lmt_disable":"","_monsterinsights_skip_tracking":false,"footnotes":""},"categories":[5957],"tags":[],"class_list":["post-278412","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-analytics"],"acf":{"youtube-url-id":"","publised_date":"","ls_key":"","recommended_posts":""},"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.1.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Discover how regression analysis works, 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