5. A group of 13 children and adolescents (considered healthy) participated in a psychological study designed to analyze the relationship between age and average total sleep time (ATST). To obtain a measure for ATST (in minutes), recordings were taken on each subject on three consecutive nights and then averaged. A display of the data and some related regression output is shown below.

The regression equation is

ATST = 646 - 14.0 Age

R-Sq = 90.5%

(a) What does the plot suggest about the relationship between these two variables? [3 pts]

(b) Interpret the slope of the regression line in this case. [5 pts]

(c) Use the equation of the regression line to predict the sleep time for a child aged 5.5 years. [3 pts]

(d) How much of the variability in sleep time can be associated with differences in age? [4 pts]

(e) What is the value for the correlation coefficient in this case? [6 pts]

(f) One of the children (Alice) is exactly 10 years old and her ATST was 491 minutes. What was her residual? Write a sentence explaining to Alice's parents what this residual means. [5 pts]