Due Monday, April 11th Name: _________________________ Stat 3500-02 Homework 5 Minitab was used to fit a model that would allow me to predict a student's Exam 2 Score given their overall homework score (1 ), Exam 1 Score (2 ), and number of absences (3 ). The model was built on data from 27 students who had no missing assignments. The output is shown below. Coefficients Term Constant X1 X2 X3 Coef 20.1304 0.6046 0.1995 -0.1915 SE Coef T-Value 18.9181 1.064 0.1810 3.340 0.1092 1.826 0.6116 -0.313 P-Value 0.29833 0.00284 0.08086 0.75697 Model Summary S = 3.821 R-sq = 0.5081 R-sq(adj)= 0.444 Analysis of Variance Source Regression Error Total DF 3 23 26 SS 346.941 335.800 682.741 MS 115.647 14.600 F-Value 7.921 1. (5 points) Write down the least squares prediction equation? 2. (3 points) Interpret the value of 1 in the context of the problem. 3. (10 points) Test the global utility of the model. Is the model useful, YES or NO? Use = 0.05. 4. (5 points) Use a 95% confidence interval to estimate 2 . 5. (5 points) Predict the Exam 2 Score of a student who has an overall homework score of 92, scored an 88 on Exam 1, and has only missed one class. 6. (2 points) If we were to use the Backward Elimination fitting algorithm, which predictor variable would be removed using the 0.05 level of significance? 7. (6 points) After removing the appropriate variable, a new two-parameter model is fit. For this new model, 2 = 0.5061. Calculate the adjusted value of R-squared. Based on its value, which model would you deem the \"best\" model? Justify your choice. 2 of 2