Regression models with interactions: The folder Beauty contains data (use file beauty.csv) Beauty and teaching evaluations from Hamermesh and Parker XXXXXXXXXXon student evaluations of instructors’...

Regression models with interactions: The folder Beauty contains data (use file beauty.csv) Beauty and teaching evaluations from Hamermesh and Parker (2005) on student evaluations of instructors’ beauty and teaching quality for several courses at the University of Texas. The teaching evaluations were conducted at the end of the semester, and the beauty judgments were made later, by six students who had not attended the classes and were not aware of the course evaluations. (a) Run a regression using beauty (the variable beauty) to predict course evaluations (eval), adjusting for various other predictors. Graph the data and fitted model, and explain the meaning of each of the coefficients along with the residual standard deviation. Plot the residuals versus fitted values. (b) Fit some other models, including beauty and also other predictors. Consider at least one model with interactions. For each model, explain the meaning of each of its estimated coefficients.
part IITake the model from that predicts course evaluations from beauty and other predictors. (a) Display and discuss the fitted model. Focus on the estimate and standard error for the coefficient of beauty. (b) Compute the median and mad sd of the posterior simulations of the coefficient of beauty, and check that these are the same as the output from printing the fit. (c) Fit again, this time setting iter = 1000 in your stan_glm call. Do this a few times in order to get a sense of the simulation variability. (d) Repeat the previous step, setting iter = 100 and then iter = 10. (e) How many simulations were needed to give a good approximation to the mean and standard error for the coefficient of beauty?