Question: An experiment was done to see how closely people could estimate the number of hours of sleep they got each night. 15 volunteers were observed falling asleep in a private room in a lab. The actual number of hours of sleep they received was noted. The next morning each participant was asked how many hours of sleep they had gotten. The data was plotted and a regression analysis was performed. Results are shown below:

(A) How accurately were the volunteers able to estimate the actual number of hours of sleep they received? Explain.

(B) The coefficient of determination is 0.938. Interpret this in the context of this problem.

(C) Suppose that a person estimated that he had received 8.2 hours sleep when in fact he had actually received 8.5 hours. Compute the residual for this point.

(D) If the mean number of hours of sleep actually received is 6.70, what is the mean number of estimated hours of sleep?

(E) Comment on the shape and spread of what the residual plot must look like.

(F) Suppose the variables had been switched so that Estimated Hours was along the vertical axis and the Actual Hours was along the horizontal axis. What would be the value of the correlation coefficient?