Q.Find the Regression lines X on Y from the following data : $N = 25$, $\sum X = 125$, $\sum Y = 100$, $\sum X^2 = 650$, $\sum Y^2 = 436$, $\sum XY = 520$.

The term "regression" was coined by Sir Francis Galton.

Sir Francis Galton, while studying the relationship between the heights of parents and their children, observed that the heights of offspring tended to move ("regress") towards the average height of the population. He used the word "regression" to describe this tendency, and the term has since become standard in statistics for the study of the dependence of one variable on another.

…

There are two regression lines for two variables ($Y$ on $X$ and $X$ on $Y$), so at most two — option (d).

For a pair of variables $X$ and $Y$ there are two distinct lines of regression:

1. The regression line of $Y$ on $X$: $y - \bar{y} = b_{yx}(x - \bar{x})$,
2. The regression line of $X$ on $Y$: $x - \bar{x} = b_{xy}(y - \bar{y})$. …