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What are your expectations for the coefficients in this equation? Which ones are you unsure about?

Instruction:All calculations must be performed with R using the comma separated files provided on Canvas. For each question, I want the R output table included in the pdf-file using Courier New as the font. Use Arial or Times New Roman for the write-up. I would like you to turn in one(!) R script file that, when executed, loads the data from the .csv files and produces all the output. You should also upload one(!) pdf document that answers the questions below (e.g., interpretation of the results, etc.). Besides just estimating the models, also say something about the marginal effects (i.e., how a change in the independent variable changes the dependent variable).Question 1: Grade Point Average (gpa.csv) (10 Points) Consider the equationcolgpa=ß0 +ß1 •hsize+ß2 •hsize2 +ß3 •hsperc+ß4 •sat+ß5 • female+ß6 •athlete+ewhere colgpa is cumulative college grade point average, hsize is size of high school graduating class (in hundreds), hsperc is academic percentile in graduating class, sat is combined SAT score, f emale is a binary gender variable, and athlete is a binary variable, which is one for student-athletes.1. What are your expectations for the coefficients in this equation? Which ones are you unsure about?2. Estimate the equation in part (1) and report the results in the usual form. What is the estimated GPAdifferential between athletes and non-athletes? Is it statistically significant?3. Drop sat from the model and re-estimate the equation. Now, what is the estimated effect of being anathlete? Discuss why the estimate is different than that obtained in part (2).4. In the model from part (1), allow the effect of being an athlete to differ by gender and test the nullhypothesis that there is no difference between women athletes and women non-athletes.5. In the model from part (1), does the effect of sat on colgpa differ by gender? Justify your answer.6. Make sure to test for heteroscedasticity in all your models.1Question 2: Housing Prices (housing.csv) (10 points)This data set contains observations on housing selling prices. In your regression model, let y be the selling price of home in $1000 (price), x1 represents the size of the home (sqr f t), x2 are the number of bedrooms (bdrms), and x3 is the lot size in square feet (lotsize).1. Construct a scatterplot matrix. You will need to use the function pairs for this. Interpret what the resulting scatterplot matrix shows.2. Run the regression model in R. Write down the prediction equation, and interpret the coefficient of size of home by its effect.3. Report the t statistic for testing H0: ß2 = 0. Report the p-value for Ha: ß2

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