There was a study on the relationships between prostate specific antigen and a number of clinical variables for 123 men who were going to receive a radical prostatectomy. The response variable was "PSA" (prostate specific antigen). The explanatory variables of interest were "lcavol" (log cancer volume) and "svi" (seminal vesicle invasion)

SAS is used to t the multiple linear regression model PSAI- = ,80 + 31 X lcavoli + [32 X svii + 8i. The sums of squares are reported in the following ANOVA table. Analysis of Variance Sum of Mean Source DF Squares Square Model (regression) ?? 54799 ???? Error (residual) ?? 105204 ????? Corrected Total l22 160003 (a) What is the degrees of freedom for the regression? What is the degrees of freedom for the Error (Residual)? (b) Calculate the Mean Square of the Model and the Mean Square of the Error. (c) Researchers want to test whether the explanatory variables are collectively useful in predicting the response. In other words, they want to test H0: [31 = 32 = 0 against its logical complement. Calculate the observed value of the Fstatistic, determine the degrees of freedom, find the pvalue and state a conclusion