Question

For the regression equation, Ŷ = +20X + 200 what can be determined about the correlation between X and Y?

Answer 1

There is a positive correlation between X and Y.

Explanation:

The estimated regression equation is:

`\hat Y=20X+200`

The general form of a regression equation is:

`\hat Y=b_(yx)X+a`

Here,
`b_(yx)` is the slope of a line of Y on X.

The formula of slope is:

`b_(yx)=r(X,Y)\cdot (\sigma_(y))/(\sigma_(x))`

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.