Documentation For Teaching Ratings Data. Teaching Ratings Co ✓ Solved

Documentation for TeachingRatings Data. TeachingRatings cont

Documentation for TeachingRatings Data. TeachingRatings contains data on course evaluations, course characteristics, and professor characteristics for 463 courses. These data were used in Hamermesh and Parker's paper on beauty in the classroom (Economics of Education Review, 2005).

Variable definitions: Course_eval is the course overall teaching evaluation score, on a scale of 1 to 5; Beauty is the rating of instructor appearance by a panel of six students, averaged and centered to have mean zero; Female is 1 if the instructor is female, 0 if male; Minority is 1 if the instructor is non-White, 0 if White; NNenglish is 1 if the instructor is not a native English speaker, 0 if native; intro is 1 if the course is introductory; onecredit is 1 if the course is a single-credit elective; age is the professor's age.

Question prompts: 1) Import the TeachingRatings data in RStudio. a) How many variables and observations? b) Provide a summary of variables Course_eval, Beauty, Female, Minority, NNenglish, Intro, Age, Onecredit: what they are and their units. c) What is the mean of Female? 2) Run a simple linear regression of Course_eval on Beauty. a) State population equation and regression equation. b) Is the coefficient on Beauty significant? Provide hypothesis tests and meaning of significance. c) Give the 95% confidence interval for the slope. d) What is the average Beauty in the data? Using the average Beauty, what is the predicted Course_eval for Bob with average Beauty? e) What is the effect of Beauty on Course_eval (the slope)? f) Would omitting Age bias the results? If yes, in which direction? g) Provide the scatter plot and fitted line. 3) Run a regression of Course_eval on Female. a) State model and predicted equation. b) Provide scatter plot and fitted line. c) Is Female a significant predictor? What does it imply about gender differences in the population? 4) Run a multiple regression of Course_eval on Beauty, Female, Minority, NNenglish, Intro, Age, Onecredit. a) State model and predicted equation. b) Interpret the NNenglish coefficient. c) If Bob is male, average Beauty, not minority, native English, Intro course, age 30, what is his predicted Course_eval? d) What is R-squared? e) Which variables are statistically significant and why?

Paper For Above Instructions

Introduction and data overview

The TeachingRatings dataset provides a platform to examine how instructor characteristics relate to student evaluations of teaching. The analysis here follows the four-part prompt described in the cleaned instructions, focusing on descriptive statistics, simple and multiple regressions, and interpretation of results. The exercise mirrors standard econometric practice in applied microeconomics and education economics, with emphasis on interpretation of coefficients, hypothesis testing, and model specification (Angrist & Pischke, 2009; Wooldridge, 2019).

Data and variables

Key variables, as defined in the prompt, are as follows: Course_eval (dependent variable in all regressions) measures course-wide teaching quality on a 1–5 scale. Beauty is a panel-rated appearance score, centered so its mean is zero. Female is a dummy (1 = female, 0 = male). Minority is a dummy (1 = non-White, 0 = White). NNenglish is a dummy (1 = not native English speaker, 0 = native). Intro is a dummy (1 = introductory course). Onecredit is a dummy (1 = single-credit elective). Age is the professor's age in years. The dataset comprises 463 observations across the courses in the relevant academic period (Hamermesh & Parker, 2005). These variables allow straightforward application of simple and multiple linear regression to isolate the association between appearance and teaching evaluations while accounting for other instructor characteristics (Stock & Watson, 2015). The core intuition is to estimate how a one-unit increase in Beauty relates to Course_eval, and then to see how this relationship changes when additional controls are added (Wooldridge, 2019).

Question 1 — Descriptive statistics and data introduction

Descriptive results depend on the actual data run in R, but the following outline explains what should be reported. There are 463 observations (courses) and 8 primary variables (Course_eval, Beauty, Female, Minority, NNenglish, Intro, Onecredit, Age). A summary of each variable typically includes the mean, standard deviation, and the minimum and maximum values (or, for binary variables, the proportion of 1s). Notably, Beauty is centered to have a mean of zero by construction, so its sample mean will be exactly zero or very close due to rounding, whereas the dummy variables have means equal to their observed shares in the sample (e.g., mean(Female) around 0.5 if the sample is balanced by gender). The overall Course_eval score tends to cluster in the mid-range of the 1–5 scale (often around 3.0 to 3.8 in teaching-evaluation datasets). This descriptive snapshot provides context for subsequent causal and correlational analyses (Field, 2013; Wooldridge, 2019).

Question 2 — Simple regression: Course_eval on Beauty

Population equation: E(Course_eval | Beauty) = β0 + β1 Beauty. Regression equation: Course_eval = β0 + β1 Beauty + u, where u is the error term with E(u) = 0.

Hypotheses: H0: β1 = 0 (Beauty has no association with Course_eval) versus H1: β1 ≠ 0. If the p-value is small (p

95% confidence interval for β1 is obtained as β1_hat ± 1.96 * SE(β1_hat). A interval not containing zero supports significance at the 5% level (Angrist & Pischke, 2009).

Average beauty: since Beauty is centered, its sample mean is zero. Using the regression equation with Beauty = 0 yields the predicted Course_eval for Bob if all other covariates are at their reference or zero values. If Bob’s attributes are not specified beyond average Beauty, the baseline prediction is β0_hat. This illustrates the interpretation of the intercept in a regression with a centered regressor (Wooldridge, 2019).

Effect of Beauty (slope β1): The estimated β1_hat captures the marginal association between Beauty and Course_eval holding constant the included error term. A statistically significant positive β1_hat implies that instructors deemed more attractive (compared to the centered mean) are predicted to receive higher course evaluations (Angrist & Pischke, 2009).

Omitted variable bias: If Age is correlated with both Beauty and Course_eval, omitting Age from the regression could bias the estimate of β1_hat. If older instructors tend to have particular Beauty scores and different Course_eval scores, the sign of the bias depends on the correlations; common reasoning suggests potential bias in either direction depending on the data-generating process (Wooldridge, 2019).

Scatter plot and fitted line: A scatter plot of Course_eval (y) versus Beauty (x) with the regression line provides a visual check of linearity and fit. In the presence of heteroskedasticity or nonlinearities, robust standard errors or nonlinear modeling might be considered (Field, 2013).

Question 3 — Simple regression: Course_eval on Female

Population equation: E(Course_eval | Female) = γ0 + γ1 Female. Regression equation: Course_eval = γ0 + γ1 Female + v.

Predicted equation: With Female as a dummy, γ1_hat represents the average difference in Course_eval between female and male instructors, holding other factors constant if additional covariates are included in extended models. The scatter plot and fitted line will typically show a gap between male and female groups if γ1_hat is significant (Angrist & Pischke, 2009).

Interpretation: A statistically significant γ1_hat indicates that gender is a meaningful predictor of Course_eval in the population. The sign indicates whether female instructors receive higher or lower ratings on average, conditional on the simple model specification. If γ1_hat is not significant, gender differences in population Course_eval cannot be distinguished from sampling variation given this model (Stock & Watson, 2015).

Question 4 — Multiple regression: Course_eval on Beauty, Female, Minority, NNenglish, Intro, Age, Onecredit

Population equation: E(Course_eval | Beauty, Female, Minority, NNenglish, Intro, Age, Onecredit) = δ0 + δ1Beauty + δ2Female + δ3Minority + δ4NNenglish + δ5Intro + δ6Age + δ7*Onecredit.

Predicted equation: Course_eval_hat = δ0_hat + δ1_hatBeauty + δ2_hatFemale + δ3_hatMinority + δ4_hatNNenglish + δ5_hatIntro + δ6_hatAge + δ7_hat*Onecredit.

Interpretation of NNenglish: δ4_hat represents the average difference in Course_eval between non-native English-speaking instructors and native English-speaking instructors, holding all other covariates constant. A significant δ4_hat would suggest language-related differences in student evaluations after accounting for Beauty, gender, ethnicity, course type, age, and course length (Gujarati & Porter, 2009; Angrist & Pischke, 2009).

Bob’s predicted Course_eval: Suppose Bob is male (Female = 0), Beauty = average (Beauty = 0), Minority = 0, NNenglish = 0 (native English), Intro = 1, Onecredit = 0 (course is not single-credit), Age = 30. Then Bob's predicted Course_eval is:

Course_eval_hat = δ0_hat + δ1_hat0 + δ2_hat0 + δ3_hat0 + δ4_hat0 + δ5_hat1 + δ6_hat30 + δ7_hat*0.

In practice, the actual numeric prediction depends on estimated coefficients; a worked example would insert the estimated values from the regression output (Wooldridge, 2019).

R-squared and significance: The model's R-squared indicates the proportion of variance in Course_eval explained by the eight regressors. In applied work, researchers examine the statistical significance of each coefficient to determine which variables meaningfully predict Course_eval after controlling for others. The standard approach uses t-tests for each coefficient and an overall F-test for joint significance (Stock & Watson, 2015; Wooldridge, 2019).

Discussion: interpretation, causality, and limitations

The exercises above illustrate core econometric concepts: how to specify a simple regression, how to interpret the slope on Beauty, and how to extend to a multivariate setting. It is important to recognize that these analyses identify associations rather than causal effects unless the data generating process supports causal inference assumptions (Imbens & Rubin, 2015). Potential omitted variables beyond Age (e.g., instructor seniority, course discipline, class size, or semester fixed effects) could bias estimates if they are correlated with Beauty and Course_eval. Robust standard errors can address heteroskedasticity in cross-sectional educational data, and graphical diagnostics help assess linearity and model fit (Field, 2013).

Conclusion

Using the TeachingRatings dataset, the four-part analysis demonstrates how to describe the data, estimate simple and multiple regressions, interpret coefficients, and assess potential omitted variable bias. The exercise reinforces the importance of model specification, hypothesis testing, and careful interpretation of statistical results in applied econometrics, particularly in the economics of education literature that investigates the role of perceptions and characteristics in teaching evaluations (Hamermesh & Parker, 2005; Angrist & Pischke, 2009).

References

  • Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empirical Guide for Data Analysis. Princeton University Press.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. SAGE.
  • Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics. McGraw-Hill.
  • Hamermesh, D. S., & Parker, A. (2005). Beauty in the Classroom: Instructors' Pulchritude and Putative Pedagogical Productivity. Economics of Education Review, 24(4).
  • Imbens, G. W., & Rubin, D. B. (2015). Causal Inference in Statistics: An Introduction to Data Science. Cambridge University Press.
  • Stock, J. H., & Watson, M. W. (2015). Introduction to Econometrics. Pearson.
  • Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
  • Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach. Cengage Learning.
  • Greene, W. H. (2018). Econometric Analysis. Pearson.
  • R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing.

Related Assignments