This data for this problem is fromhttps://stats.libretexts.org/Homework_Exercises/ General_Statistics/Exercises%3A_OpenStax/12.E%3A_Linear_Regression_and_Correlation_ (Exercises)

Mid- Career Salary(in thousands) Yearly Tuition

Princeton 137 28,540

Harvey Mudd 135 40,133

CalTech 127 39,900

US Naval Academy 122 0

West Point 120 0

MIT 118 42,050

Lehigh University 118 43,220

NYU-Poly 117 39,565

Babson College 117 40,400

Stanford 114 54,506

Suppose we want to predict the mid-career salary from a person based on the cost of the college they attended. To do tthis, apply linear regression to the above dataset, using the closed-form formula. Then answer the following questions.

(a)The closed form formula uses a matrixX. What is the value of the matrixXin this problem?

(b)Give the equation for the linear function (line) produced using linear regression, in the formg(x) =w1x+w0.

(c)Create aa scatter plot of the data, and plot the least squares line in your graph.

(d)Compute the determination of correlation,R.

(e)Using this linear function, what is the predicted the mid-career salary of a person whose yearly college tuition costs 40,000?

(f)Repeat the above steps where the outliers are removed (the outliers are the two service academies whose tuition is $0.00)