In this question, we explore some of the factors predicting costs at American universities. Let TC =

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In this question, we explore some of the factors predicting costs at American universities.

Let TC = Real ($2008) total cost per student

FTUG = Number of full-time undergraduate students (in 1000s)

FTGR = Number of full-time graduate students (in 1000s)

FTEF = Number of full-time faculty per 100 students

CF = Number of contract faculty per 100 students

FTST = Number of full-time nonacademic staff per 100 students

Estimate the linear regression of TC on the above variables and report the estimated coefficients, use the output from R with 2 decimals or 4 decimals for very small numbers (example: 653.47 or 0.0345)

If you run Shapiro test, you will encounter problems with Normality, but the sample is large, so we can tolerate it. Evaluate the residuals plots, and decide if the Dependent Variable in log form is a better fit for this problem. Do not use log transformations in the explanatory variables.

Y_hat = B₀+B₁FTUG+B₂FTGR+B₃FTEF+B₄CF+B₅FTST+ε

data - https://www.dropbox.com/s/wy8hqak42hx4ahw/CollegeCost.xlsx?dl=0

How many variables (slope coefficients) were statistically significant in this model (Model1)?

What is the predicted effect of an increase in undergraduate students on total cost per student (TC) in dollars? Use the original scale of the the variables to answer this question.
Increase or decrease -?
Effect in dollars or percentage -?
What is the predicted effect of an increase in graduate students on total cost per student (TC) in dollars? Use the original scale of the the variables to answer this question.
Increase or decrease - ?
Effect in dollars or percentage -?
Test the hypothesis that an increase in the number contract faculty per 100 students (CF) decreases total cost per student (TC). Show the hypothesis you are testing, the t-value and the p-value relevant to this test, and your conclusion. Use Model1.
What is a 95% confidence interval for the effect FTGR on TC?
Conduct the below joint hypothesis test for B₃ and B_{5. Report the F-statistics that you obtained from comparing the full and reduced models.}
H₀: B₃=0; B₅=0
H₁: At least one of them is not zero.
Do you reject the null hypothesis (joint test for B₃and B₅)? (Yes/No)
Now consider the below indicator variable:
PRIVATE_i = 1 if i is a private school; 0 if i is a public school.
Add the indicator variable PRIVATE to Model1. Use the output from R with 2 decimals for coefficients or 4 decimals for very small numbers (example: 653.47 or 0.0345) This is Model 2.
Y_hat = B₀+B₁FTUG+B₂FTGR+B₃FTEF+B₄CF+B₅FTST+B₆PRIVATE+ε
How many variables (slope coefficients) were statistically significant in this model (Model2)?
Do you predict higher or lower total cost per student at private universities? Is this a statistically significant factor in predicting total cost per student? Briefly explain.