What can you say aboutSSE, SSR and the utility of the regression equation for making predictions if

a. $r^2=1?$

b.$r^2=0?$

The given equation is:

$r^2=1$

we have to determine SSE, SSR and the utility of the regression equation .

The coefficient of determination is given by $r^2=\frac{SSR}{SST}$

It is given that $r^2=1$, this means that SSR and SST will be equal to each other. The relationship between SST, SSR and SSE is given by

$SST=SSR+SSE$

Therefore, SSE$=0$. As it can be seen that the coefficient of determination is equal to $1$, therefore, the regression equation is very useful in making the predictions.

The given equation is:

$r^2=0$

we have to determine SSE, SSR and the utility of the regression equation.

The coefficient of determination is given by $r^2=\frac{SSR}{SST}$

It is given that $r^2=0$; this means that $SSR=0$because SST cannot be equal to zero. The relationship between SST, SSR and SSE is given by

$SST=SSR+SSE$

Therefore, SST = SSE.. As it can be seen that the coefficient of determination is equal to $0$, therefore, the regression equation is not useful in making the predictions.