Meaning and Concept of Linear Regression

Linear regression is a statistical technique that studies the nature and extent of the relationship between two variables and uses that relationship to estimate the probable value of one variable when the value of the other is known. While correlation only tells us the degree and direction of association between two variables, regression goes a step further — it develops a mathematical (functional) equation that lets us predict one variable from the other.

In any regression problem, the variable whose value is to be estimated is called the dependent variable, and the variable used to make the estimate is called the independent variable. If we are estimating $Y$ from a known $X$, then $Y$ is dependent and $X$ is independent; if we are estimating $X$ from a known $Y$, the roles reverse.

The Gujarat Std-12 Commerce Statistics (GSHSEB) syllabus places linear regression right after correlation for exactly this reason — once a student knows how strongly two variables such as advertising expenditure and sales, or study hours and marks, move together, regression teaches how to actually use that relationship to make a numerical prediction.

Because errors can be measured in two different directions — the vertical distance of each point from a fitted line (errors in $Y$) or the horizontal distance (errors in $X$) — minimizing one gives a different best-fit line than minimizing the other. This is why linear regression produces two distinct regression lines for the same data, except in the special case of perfect correlation.