Question

Your friend is having trouble understanding linear regression and correlation. He thinks that having a large slope for his regression line indicated a strong correlation between the variables he is comparing. Why is he wrong, and what should he look at (instead of slope), to determine the strength of the relationship?

Answer 1

Correlation is a statistical technique that can show whether and how strongly pairs of variables are related

Whereas Slope indicates change in one quantity with respect to other quantity

These two are entirely different things

For ex. If y = 2*x it indicates that when x changes by 1 then y will change by 2 units which is slope of the equation

and y = 3*x indicates that when x changes by 1 then y will change by 3 units which is slope of the equation

However, when we talk about correlation we talk about fitting the points on a line. It may not follow for all points

For ex. If we consider (x,y) as (1,2) (3,6) they follow y = 2*x

But if we take (4,9) it will be a bit off the line ideally (4,8) will be true. Thus, we can say the correlation is reduced as point is not on line.

If we have more such points which are off the line the correlation is weak. Thus, correlation is having a equation and mapping points to find if the fit the equation or not