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Q3: [50] Instructor Ratings The data set Instructor Ratings includes a summary of teaching evaluation ratings for 366 instructors at a large campus of a university in the Midwest United States (Bleske-Rechek and Fritsch, 2011). Each instructor included in the data set had at least 10 teaching evalu- ations over several years. Students provided ratings on a 5-point scale. The data set provides the average teaching evaluation rating and additional characteris- ties of the instructors. It includes 366 observations and the following 12 variables: Variable Description gender A categorical variable representing instructor's gender DunYears A numerical variable representing number of years in which the instructor had teaching evaluation ratings between 1999 and 2009. numraters Number of teaching evaluation ratings num Courses Number of different course titles included in the teaching evaluation rating of the instructor A categorical variable with levels Yes and No. In addition to rating for quality, pepper instructors are rated as attractive or not. A value of yes means that the consensus is that the instructor is attractive A categorical variable representing the instructor's discipline. Hum for Discipline humanities, Secs for social sciences, STEM for science technology, engineering and mathematics, and Pre-proffor professional training. Dept A categorical variable with department names including Accounting, Anthropology, Art, Art and design, Art History. Astronomy/Physics, etc. Quality Average quality rating from 1 Awful) to 5 (Excellent) Helpfulness Average helpfulness rating from 1 (Awful) to 5 (Excellent) clarity Average clarity rating from 1 Awful) to 5 (Excellent) Easiness Average easiness rating from 1 (Awful) to 5 (Excellent) caterinterest Average rater interest, from 1 Awful) to 5 (Excellent) (a) [6] Plot the variable Quality against the variable Helpfulness and against the variable raterInterest separately. Use scatter plots. What do the plots suggest in terms of the relationship between the variable Quality and the other two variables? (MINITAB) (b) (6) Use MINITAB to perform two (2) simple linear regressions, one using Quality as the dependent (or response) variable and Helpfulness as the predictor (or independent) variable (Model 1) and the other using Quality as the response variable and raterin- terest as the predictor or independent variable (Model 2). Compare the two models in terms of R2 value. Which of these two variables is a better predictor of Quality? Explain why. (MINITAB) (c) [10] Use Model 1 in part (b) to calculate a 95% confidence interval for the average Quality rating when Helpfulness is rated as 1.5. What information does this confi- dence interval provide? In other words, how can it be interpreted? Show manually how the standard error for the confidence interval is calculated. (Manual Calculation) (d) [10] Use Model 1 in part (b) to calculate a 95% prediction interval for an individual Quality rating when Helpfulness is rated as 1.5. What information does the prediction interval provides? In other words, how can it be interpreted? Show manually how the standard error for the prediction interval is calculated. (Mamal Calculation) (e) (8) Perform an F-test for the overall usefulness of the Model 1 in part (b) using a 5% significance level and both critical value and p-value approaches. Make sure you follow all the steps for hypothesis testing and clearly state your conclusion. (f) (10) Test manually if the Helpfulness variable is significant in the model 1 in part (b) using critical value, p-value and confidence interval approaches. Make sure you follow all the steps for hypothesis testing and clearly state your conclusion. Q3: [50] Instructor Ratings The data set Instructor Ratings includes a summary of teaching evaluation ratings for 366 instructors at a large campus of a university in the Midwest United States (Bleske-Rechek and Fritsch, 2011). Each instructor included in the data set had at least 10 teaching evalu- ations over several years. Students provided ratings on a 5-point scale. The data set provides the average teaching evaluation rating and additional characteris- ties of the instructors. It includes 366 observations and the following 12 variables: Variable Description gender A categorical variable representing instructor's gender DunYears A numerical variable representing number of years in which the instructor had teaching evaluation ratings between 1999 and 2009. numraters Number of teaching evaluation ratings num Courses Number of different course titles included in the teaching evaluation rating of the instructor A categorical variable with levels Yes and No. In addition to rating for quality, pepper instructors are rated as attractive or not. A value of yes means that the consensus is that the instructor is attractive A categorical variable representing the instructor's discipline. Hum for Discipline humanities, Secs for social sciences, STEM for science technology, engineering and mathematics, and Pre-proffor professional training. Dept A categorical variable with department names including Accounting, Anthropology, Art, Art and design, Art History. Astronomy/Physics, etc. Quality Average quality rating from 1 Awful) to 5 (Excellent) Helpfulness Average helpfulness rating from 1 (Awful) to 5 (Excellent) clarity Average clarity rating from 1 Awful) to 5 (Excellent) Easiness Average easiness rating from 1 (Awful) to 5 (Excellent) caterinterest Average rater interest, from 1 Awful) to 5 (Excellent) (a) [6] Plot the variable Quality against the variable Helpfulness and against the variable raterInterest separately. Use scatter plots. What do the plots suggest in terms of the relationship between the variable Quality and the other two variables? (MINITAB) (b) (6) Use MINITAB to perform two (2) simple linear regressions, one using Quality as the dependent (or response) variable and Helpfulness as the predictor (or independent) variable (Model 1) and the other using Quality as the response variable and raterin- terest as the predictor or independent variable (Model 2). Compare the two models in terms of R2 value. Which of these two variables is a better predictor of Quality? Explain why. (MINITAB) (c) [10] Use Model 1 in part (b) to calculate a 95% confidence interval for the average Quality rating when Helpfulness is rated as 1.5. What information does this confi- dence interval provide? In other words, how can it be interpreted? Show manually how the standard error for the confidence interval is calculated. (Manual Calculation) (d) [10] Use Model 1 in part (b) to calculate a 95% prediction interval for an individual Quality rating when Helpfulness is rated as 1.5. What information does the prediction interval provides? In other words, how can it be interpreted? Show manually how the standard error for the prediction interval is calculated. (Mamal Calculation) (e) (8) Perform an F-test for the overall usefulness of the Model 1 in part (b) using a 5% significance level and both critical value and p-value approaches. Make sure you follow all the steps for hypothesis testing and clearly state your conclusion. (f) (10) Test manually if the Helpfulness variable is significant in the model 1 in part (b) using critical value, p-value and confidence interval approaches. Make sure you follow all the steps for hypothesis testing and clearly state your conclusion

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