Please solve the problem using Rstudio. The data set sat is from library(faraway). Show the codes, please.

In this problem you will use the sat data set of package "faraway". This data has 50 rows and 7 columns, and it contains data collected to study the relationship between expenditures on public education and test results. Fit a model with the total SAT score as the response and expend, salary, ratio and takers as predictors. Perform regression diagnostics on this model to answer the following questions. Display any plots that are relevant. Do not provide any plots about which you have nothin. to say. Suggest possible improvements or corrections to the model where appropriate. a) Check the constant variance assumption for the errors. b) Check the normality assumption. c) Check for large leverage points. d) Check for outliers. e) Check for inuential points