740 Rate my professor Many college courses conclude by givin

7.40 Rate my professor. 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 e ectiveness is often criticized because these measures may reect the infuence of non-teaching related characteristics, such as the physical appearance of the instructor. Researchers at 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 also provided is a regression output for predicting teaching evaluation score from beauty score.

(a) Given that the average standardized beauty score is -0.0883 and average teaching evaluation
score is 3.9983, calculate the slope. Alternatively, the slope may be computed using just the
information provided in the model summary table.
(b) Do these data provide convincing evidence that the slope of the relationship between teaching
evaluation and beauty is positive? Explain your reasoning.
(c) List the conditions required for linear regression and check if each one is satis ed for this model
based on the following diagnostic plots.

5 Estimate Std. Error t value Prt (Intercept) beauty 2 4.010 0.0255 157.21 0.0000 0.0322 1 3 4.13 0.0000 2 Beauty

Solution

We know that t=b/se

b/0.0322 =4.13

b=0.1330

slope =0.1330

Yes, the data provide convincing evidence that the slope of the relationship between teaching evaluation and beauty is positive.

The calculated t=4.13, P=0.0000 is significant.( this is two sided)

Even for the one sided test of > 0, the test is significant, P=0.000.

(c) List the conditions required for linear regression and check if each one is satis ed for this model based on the following diagnostic plots.

1). Linear relationship between dependent and independent variables

2). Independence of the errors

3). Homoscedasticity (constant variance) of the errors

4). Normality of the error distribution

All the four conditions are satisfied for this model.

There is no pattern in the residuals.

The histogram is nearly bell shaped.

The normal plot is almost straight line.

There is no pattern in the order of the data.