2a) • Using a Graphing calculator or spreadsheet program create a least squares regression line of the tuition for 4 years versus the average salary after 10 years, define any variables that you used. • Identify and interpret the correlation coefficient and coefficient of determination. • By looking at the least squares regression line, determine the college that you believe is the best value. Explain your reasoning. • Using the college (Harvard University) you chose, identify and interpret its residual based on the least squares regression model. Average Salary ($)140,000130,000120,000110,000100,00090,00080,00070,00060,000●Average Salary of College Graduates50,000100,000150,0004-Year Tuition ($)200,000250,000 College Name:Harvard UniversityPrinceton UniversityYale UniversityCurrent YearlyTuition:$55,587$56,010$59,950Columbia University$63,530Cornell University$61,015Brown University$62,304Dartmouth College$60,870University of Pennsylvania $61,710SUNY BuffaloMassachusetts Institute of $55,878Technology$10,782 (In-state)Tuition (4 yearstotal):$222,348$224,040$239,800$254,120$244,060$249,216$243,480$246,840$223,512$43,128 (In-state)Median StudentLoan Debt forGraduates:$12,665$9,623$13,142$29,757$14,500$13,000$17,000$16,763$25,080$13,254Average Salary After 10Years:$136,700$95,689$88,655$89,871$91,176$78,943$91,627$103,246$111,222$62,022

(a) The objective is to create a least squares regression line of the tuition for 4 years versus the average salary after 10 years, define any variables that you used. (a) The least square regression line can be obtained using Excel. Enter the data in Excel sheet. Highlight the data Go to Insert tab Under Charts, select Scatterplot Add axis titles Click on 'Add Chart Element' Select Trendline > Linear Select 'Display equation on chart' Select 'Display R-squared value on chart' Excel output is given below: The equation of the least square regression line is: y=0.148164686x+62458.9737 Here, the dependent variable y is 'Average salary after 10 years'. The independent variable x is 'Tuition (4-years total)'. (b) Identify and interpret the correlation coefficient and coefficient of determination. From the above Excel output, R2-value is 0.2226 So, the correlation coefficient r=0.2226≈0.4718 Interpretation: There is a weak positive linear correlation between 'Tuition (4-years total)' and 'Average salary after 10 years'. The coefficient of determination R2 is 0.2226. Interpretation: About 22.26% of variation in Average salary after 10 years is explained by the variation in 4-year Tuition. (c) By looking at the least squares regression line, the college that I believe is the best value is Princeton University. Reason: Because, the point (224040, 95689) lies on the least squares regression line, it is considered as the best value and hence its corresponding college name is Princeton University. (d) For Harvard University, the actual y-value is $136,700 and x-value is $222348. Substitute x=222348 in the least square regression model to obtain the predicted y-value. y^=0.148164686x+62458.9737=0.148164686222348+62458.9737=95403.0953 Now, the residual is computed as follows: Residual=actual value-predicted value=136700-95403.0953=41296.9047≈41297 Interpretation: The difference between the observed average salary after 10 years and the predicted average salary after 10 years is $41297.