What Regression Analysis Is: Definition, Types & Formula

Regression analysis is a statistical method for modelling the relationship between one outcome, called the dependent variable, and one or more factors that may influence it, called independent variables or predictors. In plain terms, it answers questions of the form: as this factor changes, how does that outcome change, and by how much? For example, how does advertising spend relate to sales, or how does page load time relate to conversion rate? Regression fits a mathematical line or curve to your data that best captures the pattern, and from that fit you get two things: an explanation of how strongly each predictor is associated with the outcome, and a way to predict the outcome for new values of the predictors. It is one of the most widely used techniques in statistics, marketing analytics, and data science, because so many practical questions come down to understanding and quantifying how variables move together. The important caution is that regression describes association, not proof of cause, which is why it is a tool for finding relationships and generating hypotheses rather than for confirming that one thing causes another.

The type of regression you use depends on how many predictors you have and what kind of outcome you are modelling. Simple linear regression models the straight-line relationship between one predictor and a continuous outcome, for example how ad spend relates to sales. Multiple linear regression extends this to several predictors at once, so you can estimate the effect of each while holding the others constant, for example how price, ad spend, and season together relate to sales. Logistic regression is used when the outcome is categorical, usually a yes/no, such as whether a visitor converts or not; instead of a continuous number it predicts a probability. Polynomial regression fits a curved rather than a straight line, for outcomes that rise and then level off or otherwise bend. There are more specialised forms (ridge, lasso, and others that handle many correlated predictors or prevent overfitting), but simple linear, multiple, logistic, and polynomial regression cover the great majority of everyday uses. The right choice is dictated by your data: a continuous outcome and a straight-line pattern call for linear regression, a yes/no outcome calls for logistic regression, and a curved pattern calls for polynomial.

The formula for simple linear regression is y = a + bx, where y is the outcome you want to predict (the dependent variable), x is the predictor (the independent variable), a is the intercept (the value of y when x is zero), and b is the slope (how much y changes for each one-unit increase in x). The slope b is the heart of the result: it quantifies the relationship. If a regression of monthly sales on ad spend gives a = 200 and b = 5, the equation is sales = 200 + 5 × ad spend, meaning that with no advertising you would expect 200 in sales, and each additional unit of ad spend is associated with 5 more units of sales. To predict sales at an ad spend of 100, you calculate 200 + 5 × 100 = 700. Multiple regression uses the same idea with more terms, y = a + b1x1 + b2x2 + …, one slope for each predictor. The method finds the values of a and b that make the line fit the data as closely as possible, usually by minimising the squared differences between the predicted and actual values (the least squares method). These are standard statistical formulas, not figures specific to any one business.

No. Regression analysis measures how variables are associated, not whether one causes the other, and confusing the two is the most common and most costly mistake in interpreting it. A strong regression relationship between two variables can arise for several reasons besides direct cause: the influence might run the other way, both might be driven by a third, unmeasured factor (a confounder), or the pattern might be coincidence. The classic example is that ice cream sales and drowning incidents rise together, not because ice cream causes drowning, but because hot weather drives both. Regression is excellent for spotting and quantifying relationships in existing (observational) data and for generating hypotheses about what might matter, but it cannot on its own establish that changing a predictor will change the outcome. To make a genuine causal claim, you need a controlled experiment, such as an A/B test, where you deliberately change one variable at random and observe the effect. In practice, the two work together: regression on your data suggests where a relationship might exist, and an experiment confirms whether acting on it actually changes the result.

In marketing and eCommerce, regression analysis is used to understand and quantify the drivers behind outcomes like sales, conversions, and customer value, and to make forecasts. Common uses include estimating how marketing spend across channels relates to revenue (to inform budget allocation), modelling how factors such as price, discount depth, or delivery time relate to conversion rate, forecasting demand or sales from historical patterns and seasonality, and identifying which customer attributes are associated with higher lifetime value or a greater likelihood of churn. Logistic regression in particular is widely used to model the probability of a binary outcome, such as whether a visitor will convert or a customer will churn, from a set of predictors. The value of regression here is that it turns a vague sense that 'these things seem related' into a quantified estimate of how strongly, while controlling for other variables. But because it works on observational data, its findings should be treated as informed hypotheses about what drives the business, the ones worth confirming with a controlled test before you bet real budget on them.

Regression analysis and A/B testing answer related but different questions, and they are strongest used together. Regression is an observational method: it looks at data you already have and quantifies how variables are associated, which is ideal for exploring relationships, spotting patterns, and forecasting, but it cannot prove that one variable causes another because you did not control the conditions. A/B testing is an experimental method: you deliberately change one thing, split traffic at random between the versions, and measure the difference, which lets you make a genuine causal claim, that the change caused the lift, because randomisation rules out other explanations. Put simply, regression tells you what is related in your existing data, while A/B testing tells you what actually happens when you make a change. The best workflow uses both: regression and other data analysis surface promising relationships and generate hypotheses, and an A/B test then confirms whether acting on a hypothesis truly moves the outcome. One finds the candidates; the other proves the winners.

Omniconvert Explore is an A/B testing and experimentation platform, and it complements regression analysis by supplying the causal proof that regression alone cannot. Regression is powerful for finding relationships in your existing data, that page speed seems to relate to conversion, that a certain segment appears more valuable, but those are associations, not confirmed causes, and acting on them blindly can waste budget on a pattern that turns out to be coincidence or a confounder. Explore closes that gap. It lets you take a relationship suggested by your analysis, turn it into a hypothesis, and run a controlled experiment on live traffic, deliberately changing one element, splitting visitors at random, and measuring conversion rate and revenue per visitor for each version with statistical significance. Because the assignment is random, any difference can be credited to the change rather than to a hidden third factor, which is exactly what regression cannot guarantee. Its segmentation also lets you see where an effect holds. Across more than 70,000 experiments, with an average uplift of 23.2%, Explore is how the relationships you find in your data get confirmed, or ruled out, as real, actionable causes.