Question

what happens to the prediction interval and the confidence interval when SSE=0

Answer 1

Given that SSE = 0

Assuming that this question is related to the Regression, When SSE = 0

SST = SS_Regression

R² =  (SS_Regression )/ (SST) = 1

If SSE = 0, MSE = 0.

The prediction interval can be calculated using the below formula

PI =

From this fromula we can see that if MSE = 0, we dont get any interval we get only the observed value .

Similarly Confidence interval is calculated using the formula , since MSE = 0, we dont get any interval we get only the observed value .

Hence we can say that PI = CI = observed value .