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 average. The results obtained and displayed in the following table.

ATST 586 461.75 491.1 565 462 532.1 477.6 515.2 493 528.3 575.9 532.5 530.5

AGE 4.4 14 10.1 6.7 11.5 9.6 12.4 8.9 11.1 7.75 5.5 8.6 7.2

Solve the problem using R and provide codes

Show every step please

A) Determine the least-squares estimates of the slope and intercept for the straight regression of ATST (Y) on AGE (X). Draw the estimated line on the accompanying scatter diagram, and comment on the fit.

B) Are any of the assumptions for straight-line regression clearly not satisfied in this example?

C) Test the null hypothesis that the true slope 1 (the in your textbook) is 0; be sure to interpret your result.

D) Obtain a 95% confidence interval for 1. Interpret your result.

E) Would you reject the null hypothesis H0: 1=0 based on the confidence interval you calculated in part D)? Explain