Question 15: What assumptions do we require for the confidence interval to be valid? Are these different from those required for the confidence interval for the correlation coefficient?
The differences between the observed head circumferences and the mean head circumference estimated by the regression line will follow a Normal distribution, the variance of the this Normal distribution will be unrelated to height, and the observations are independent. These are the same as the assumptions required for the test of significance in regression.
These are different from the assumptions required for the confidence interval for a correlation coefficient, which requires that the two variables each follow an approximately Normal distribution. These are more stringent than those required for the significance test for the correlation coefficient.
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