STAT 331 Homework 6 For questions 1 - 3 use the following information: For a multiple linear regression analysis there are 3 independent variables (X1, X2, X3), and a sample size of n = 30. Find degrees of freedom for error and regression for the following models: 1. First order linear model: Df for Error = _________ Df for Regression = ________ 2. Complete second order model: Df for Error = _________ Df for Regression = ________ 3. Complete second order model with all interaction: Df for Error = _________ Df for Regression = _________ For questions 4 - 8 use the following information: A multiple regression analysis with n = 20 was done to fit the model: Y = 0 + 1X1 + 2X2 + 3X12 + 4X22 + 5X1X2 + 4. Finish filling out the ANOVA table given below. (Round your answers to two decimal places where necessary.) Source Regression Error Total Df SS MS F 4.8 3.2 5. What is the value of S for the above model? (Round your answer to two decimal places.) 6. Calculate adj R2. (Enter your solution in decimal representation, not percentages, and round to two decimal places.) 7. What are the null and alternative hypothesis used to test if the model is useful? a) H0: 1 = 2 = 3 = 0 vs. Ha: at least one 0 b) H0: 1 = 2 =...= 5 = 0 vs. Ha: at least one 0 c) H0: 0 = 0 vs. Ha: 0 0 d) H0: 3 = 5 = 0 vs. Ha: at least one 0 8. What critical value from the F-table would be used in an Analysis of Variance F test