I had a question for confidence intervals:
the situation in the question :so we have a number of scatter plots with each showing an estimated regression line (based on a valid model) and associated individual 95% confidence intervals (CI) for the regression function at each x-value, as well as the observed data. A professor asks 'I don't understand how 95% of the observations fall outside the 95% CI as depicted in the figures'. Briefly explain how is is entirely possible that 95% of the observations fall outside the 95% CI as depicted in the figures.(We weren't given actual figures)
Anyway I thought that it may have been due to the fact that a lot of outliers affected the regression line calculated, and so a confidence interval formed from a bad regression line would be bad - resulting in 95% of observations falling outside the 95% CI.
I guess a good one would look like this: https://stats.stackexchange.com/questions/47563/plotting-the-fitted-values-and-their-confidence-intervals, where most observations are inside the confidence interval.
I also considered that some gauss assumptions were violated; such as the zero conditional mean assumption. So then the coefficients and their standard errors would be invalid, resulting in an invalid confidence interval. Still, 95% of observations falling outside the CI seems ridiculous.
Does anyone know the real reason(s) why this could be the case?