The data is in R. To load the data, use library(alr4) in R. 6.10 Rat eMyProfesso

Question

The data is in R. To load the data, use library(alr4) in R.

6.10 RateMyProfessor.com (Data file: Rateprof) In the professor ratings data introduced in Problem 1.6, suppose we were interested in modeling the quality rating. We take as potential predictors characteristics of the instructor, including ender of the professor, the number of years numYear in which the instructor had ratings, between 1999 and 2009, a factor discipline, with levels for humanities, social science, pre-professional, and stem for science technology, engineering, and mathematics. Additional potential predictors are easiness , average rating of the easiness of the course, raterInterest in the course material. A final predictor is pepper, a factor with levels no and yes . A value of yes means that the consensus is that the instructor is physically attractive. The variables helpfulness and clarity have been excluded, since these are essentially the same as quality (Section 5.5). Data are included for n = 366 professors.

6.10.1 Fit the first-order regression model quality ~ gender + numYears + pepper + discipline + easiness + raterInterest, and print the summary table of coefficient estimates. Suppose that 2 is the coefficient for numYears . Provide a test and significance level for the following three hypothesis tests:(1)NH:2 =0versusAH:2 =0;(2)NH:2 =0versus AH:2 0;(1)NH:2 =0versusAH:2 0.

6.10.2 Obtain the Type II analysis of variance table. Verify that the F- tests in the table are the squares of the t-tests in the regression coefficient table, with the exception of the tests for the dummy regressors for d pl ne. Summarize the results of the tests.

6.10.3 Draw the effects plot for discipline. It will suggest that the adjusted quality varies by discipline, in agreement with the test for discipline. Describe as carefully you can the discipline effect. You may want to report further tests.

6.10.4 Summarize the dependence of quality on the predictors.

Below is some of my answers:

I am not sure are they correct and how to do 6.10.4, please check my answer and give some hint on the last problem

Thanks.

6.10 RateMvProfessor.com 6.10.1 m0 lm(quality gender + numYears + pepper discipline summary (mO) easiness raterInterest, Rateprof) ## Call: ## lm (formula quality - gender + numYears + pepper + discipline + easiness + rater!nterest, data = Rateprof) ## Residuals: Min 3Q 1QMedian ##-1.63978-0.42534 0.03105 0.41535 1.26088 Max ## Coefficients: Estimate Std. Error t value Pr(>ltl) -0.18066 0.24240 -0.745 0.45658 0.04678 0.06492 0.721 0.47162 0.01760 0.01005 1.751 0.08085 0.56166 0.099345.654 3.22e-08 ##disciplineSocScì 0.01865 0.08889 0.210 0.83393 0.29475 0.08148 3.618 0.00034 ##disciplinePre-prof 0.09656 0.09139 1.057 0.29144 0.51288 0.04245 12.082

Explanation / Answer

Your outputs are corrct.

6.10.4

You should put all the predictors of the model and their significance value (last value in the coefficient table)

Then you should put the Adjusted R Squared value of the two models and see that, when only selected predictors are taken, the R squared is larger so the quality of fitting increases

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