Q. 2 (14 points) A Regression Analysis (STAC67) class has assignments, two term tests and a...

 

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Q. 2 (14 points) A Regression Analysis (STAC67) class has assignments, two term tests and a final exam. The instructor wanted to know how well the final exam mark was related to the assignment and term test marks so she used least squares to fit a linear model to the marks for 20 students. Here is the resulting parameter estimates table. Estimate (Intercept) -11.87286 0.50015 0.55284 0.20775 (b) (4 pts) (c) (5 pts) testl test2 assn Std.Error tvalue Pr(> |t|) 8.17407 -1.45 0.1657 0.08800 5.68 < .0001 0.13449 4.11 0.12309 1.69 0.0008 0.1109 (a) (5 pts) If we are told that the total sum of squares is 2501 and the model sum of squares is 2314, construct the Analysis of Variance table for the fitted model. Estimate the standard deviation of the error terms. What final exam mark would you predict for a student who scored 70 on both term tests and 90 on the assignments? Give the appropriate formula to produce a prediction interval for this student and explain how such an interval should be interpreted. Q. 2 (14 points) A Regression Analysis (STAC67) class has assignments, two term tests and a final exam. The instructor wanted to know how well the final exam mark was related to the assignment and term test marks so she used least squares to fit a linear model to the marks for 20 students. Here is the resulting parameter estimates table. Estimate (Intercept) -11.87286 0.50015 0.55284 0.20775 (b) (4 pts) (c) (5 pts) testl test2 assn Std.Error tvalue Pr(> |t|) 8.17407 -1.45 0.1657 0.08800 5.68 < .0001 0.13449 4.11 0.12309 1.69 0.0008 0.1109 (a) (5 pts) If we are told that the total sum of squares is 2501 and the model sum of squares is 2314, construct the Analysis of Variance table for the fitted model. Estimate the standard deviation of the error terms. What final exam mark would you predict for a student who scored 70 on both term tests and 90 on the assignments? Give the appropriate formula to produce a prediction interval for this student and explain how such an interval should be interpreted.

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Solution The given Summary Output of the fitted model is based on a Linear Model for marks of 20 stu... View the full answer