Here is a simple linear regression with just one independent variable x. The predicted y (Save Columns -> Pred Formula) as well as upper and lower 95% confidence values (Save Columns -> Mean Confidence Limit Formula) are shown too. Have a look at the second data point:
The upper and lower confidence values match with the plot (16.99 and 12.30 on the y axis are very close to the calculated values in the table, marked red and blue). However in multiple linear regression it doesn't match. Example with two independent variables x1 and x2 (have a look at the third data point):
From the table above I expected 14.58 for the lower 95% value but it is 15.4. The upper 95% value (18.67) deviates too (17.8).
This is the scatter plot in excel. Clearly the confidence region looks different (broader):
So my question is, how are the confidence bands in the actual by predicted plot calculated? It looks like the uncertainty around the mean is lower than on the edges but what is the math behind the confidence calculation? Thanks.
