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answerhappygod
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** R code allowed
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(15 points) An analysis is performed to study the relationship between three explana- tory variables, X1, X2, X3, and X4 and a response variable Y. Consider the following model: Y = Bo + B1X1 + B2X2 + B3X3 + B4X4+e where e ~ N(0,0%). The observed data is denoted by {(Y, X1, X2, X3i, X4i), i = 1,2,...,n} and we further assume that the Y, are independent. We fit the above model to this data set. The resulting (incomplete) ANOVA table is given below and the coefficient of determination is 0.5847. The ANOVA Table Analysis of Variance Source DF Sum of Square Mean Square F Stat Prob > F Model Error 1.293 C Total* * * 76 Answer the following questions: (a) (6 points) Fill in the missing values (denoted by "*") in the ANOVA table. (b) (2 points) State the null and alternative hypotheses for the F test in the ANOVA table. (c) (2 points) What is an estimated value of o2 based on the results from the ANOVA table? (d) (5 points) Under the null hypothesis H, specified in Part (b), find the distribution of R2 and and then compute P(RP > 0.5847) using this distribution. Is this prob- ability equal to the p-value in the ANOVA table computed in part (a)? Should these two probabilities be equal? Why or why not?
(15 points) An analysis is performed to study the relationship between three explana- tory variables, X1, X2, X3, and X4 and a response variable Y. Consider the following model: Y = Bo + B1X1 + B2X2 + B3X3 + B4X4+e where e ~ N(0,0%). The observed data is denoted by {(Y, X1, X2, X3i, X4i), i = 1,2,...,n} and we further assume that the Y, are independent. We fit the above model to this data set. The resulting (incomplete) ANOVA table is given below and the coefficient of determination is 0.5847. The ANOVA Table Analysis of Variance Source DF Sum of Square Mean Square F Stat Prob > F Model Error 1.293 C Total* * * 76 Answer the following questions: (a) (6 points) Fill in the missing values (denoted by "*") in the ANOVA table. (b) (2 points) State the null and alternative hypotheses for the F test in the ANOVA table. (c) (2 points) What is an estimated value of o2 based on the results from the ANOVA table? (d) (5 points) Under the null hypothesis H, specified in Part (b), find the distribution of R2 and and then compute P(RP > 0.5847) using this distribution. Is this prob- ability equal to the p-value in the ANOVA table computed in part (a)? Should these two probabilities be equal? Why or why not?