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Many college courses conclude by giving students the opportunity to evaluate the course and the instructor anonymously. However, the use of these student evaluations as an indicator of course quality and teaching effectiveness is often criticized because these measures may reflect the influence of non-teaching related characteristics, such as the physical appearance of the instructor. Researchers at the University of Texas, Austin collected data on teaching evaluation score (higher score means better) and standardized beauty score (a score of 0 means average, negative score means below average, and a positive score means above average) for a sample of 463 professors. The scatterplot below shows the relationship between these variables, and regression output is provided for predicting teaching evaluation score from beauty score. We want to test whether these data provide convincing evidence that the slope of the relationship between teaching evaluation and beauty is positive.

Estimate Std. Error tt value Pr(>|t|)(>|t|)
(Intercept) 4.01 0.0255 157.21 0
beauty
0.133 0.0322 4.13 0
  1. What will our hypotheses look like?
    • H0H0: β1=0β1=0
      HAHA: β1<0β1<0
    • H0H0: β1=0β1=0
      HAHA: β1≠0β1≠0
    • H0H0: β1=0β1=0
      HAHA: β1>0β1>0
  2. What is our test statistic for that test?
  3. At a significance level of α=α=0.05, would we reject the null hypothesis?
    • Reject H₀
    • Fail to reject H₀
  4. Write the equation of the regression line for predicting teaching evaluations from beauty.evaluation score == ++ ×× beauty score
  5. Given that R2=R2=0.6466, what is the correlation of heights in this data set?
  6. You have a professor whose standardized beauty score is -1.14. What would you expect to be the strength of this professor’s teaching evaluations?

 

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