A group of 13 children and adolescents (considered healthy) participated in a psychological study designed to analyze the relationship between AGE (X) and average total sleep time (ATST) (Y). The REG Procedure Model: MODEL1 Dependent Variable: y 'ATST' Number of Observations Read 13 Number of Observations Used 13 Source Model Error Corrected Total Analysis of Variance Sum of Mean DF Squares Square F Value Root MSE 13.15238 R-Square Dependent Mean 519.30385 Adj R-Sq 0.8968 Coeff Var 2.53269 Parameter Estimates Parameter Standard Estimate Variable Label DF Intercept Intercept 1 646.48334 'Age Error t Value 12.91773 1 -14.04105 1.36812 (a) Determine the ANOVA table for regression of ATST (Y) on AGE (X) if SSY = 20123. (8 points) (b) Use the table in part (a) to perform the F test for testing the significance of the straightline regression (Use a-0.10). Interpret your results. (5 points) (c) Test if the value of the slope of simple regression is different from zero using a t-test (Use a=0.10). (5 points) (d) Verify that the tests in (b) and (c) are equivalent. (Check if the F-stat in (b) is same as t-stat2 in (c); Similarly check if the critical value in (b) is same as square of critical value in (c)) (2 points) e) Calculate r 2 (equivalently R 2 )and interpret it.