2b) • Using a Graphing calculator or spreadsheet program, create the least squares regression line of the median student loan debt for graduates versus the average salary after 10 years. Be sure to define any variables. • Identify and interpret the correlation coefficient and coefficient of determination. • By looking at the scatterplot and 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 ($)140,000130,000120,000110,000100,00090,00080,00070,00060,000Average Salary and Median Loan Debt10,00015,000●20,000Student Loans ($)25,00030,000 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

Median student debt Average salary after 10 years Harvard University 12665 136700 Princeton University 9623 95689 Yale University 13142 88655 Columbia University 29757 89871 Brown University 14500 91176 Dartmouth University 13000 78943 University of Pennsylvania 17000 91627 MIT 16763 103246 Sunny Buffalo 25080 111222Generating Scatter plot from the given data using excel Select the data Insert tab> Charts Group > Scatter The plot will be displayed as below:Correlation coefficient and Coefficient of Determination x y Median student debt Average salary after 10 years xy x2 y2 Harvard University 12665 136700 1731305500 160402225 18686890000 Princeton University 9623 95689 920815247 92602129 9156384721 Yale University 13142 88655 1165104010 172712164 7859709025 Columbia University 29757 89871 2674291347 885479049 8076796641 Brown University 14500 91176 1322052000 210250000 8313062976 Dartmouth University 13000 78943 1026259000 169000000 6231997249 University of Pennsylvania 17000 91627 1557659000 289000000 8395507129 MIT 16763 103246 1730712698 280998169 10659736516 Sunny Buffalo 25080 111222 2789447760 629006400 12370333284 Total 151530 887129 14917646562 2889450136 89750417541 r = n∑xy-∑x∑yn∑x2-∑x2n∑y2-∑y2=9*14917646562-151530*8871299*2889450136-15153029*89750417541-8871292=-16783831255169.83165*144069.0641=-0.021116343 Since, r =-0.02112, there exists a very week negative correlation between the median student loan debt and average salary after 10 years. R2 =r2=-0.021122=0.0004459 Coefficient of determination R2 = 0.0004459 Interpretation: The R2 = 0.0004459 indicates that 0% percent of the variation in the outcome in the model. Regression Using the least squares regression model y = a+bx The normal equations for interpreting the regression coefficients are: ∑y = na+b∑x∑xy = a∑x+b∑x2 Substituting the values in the normal equations: x y Median student debt Average salary after 10 years xy x2 12665 136700 1731305500 160402225 9623 95689 920815247 92602129 13142 88655 1165104010 172712164 29757 89871 2674291347 885479049 14500 91176 1322052000 210250000 13000 78943 1026259000 169000000 17000 91627 1557659000 289000000 16763 103246 1730712698 280998169 25080 111222 2789447760 629006400 151530 887129 14917646562 2889450136 887129 = 9a+151530b14917646562 = 151530a+2889450136b Solving these 2 equations a= 99498 and b=-0.0551 can be interpreted Hence, the regression line will be y = -0.0551x + 99498Predicting the university that can be believed for giving the best value Substituting the x values in the regression line x y Median student debt Average salary after 10 years Prediction = -0.0551x + 99498 Harvard University 12665 136700 98800.1585 Princeton University 9623 95689 98967.7727 Yale University 13142 88655 98773.8758 Columbia University 29757 89871 97858.3893 Brown University 14500 91176 98699.05 Dartmouth University 13000 78943 98781.7 University of Pennsylvania 17000 91627 98561.3 MIT 16763 103246 98574.3587 Sunny Buffalo 25080 111222 98116.092 Max(Prediction) = 98967.7727 Hence, the university that can be believed for giving the best value is Princeton UniversityResidual for the Harvard Univerity is computed as below: x y (Actual) Median student debt Average salary after 10 years Prediction = -0.0551x + 99498 Residual = Actual - Prediction Harvard University 12665 136700 98800.1585 37899.8415 Princeton University 9623 95689 98967.7727 -3278.7727 Yale University 13142 88655 98773.8758 -10118.876 Columbia University 29757 89871 97858.3893 -7987.3893 Brown University 14500 91176 98699.05 -7523.05 Dartmouth University 13000 78943 98781.7 -19838.7 University of Pennsylvania 17000 91627 98561.3 -6934.3 MIT 16763 103246 98574.3587 4671.6413 Sunny Buffalo 25080 111222 98116.092 13105.908 The residual based on the least square method for the Harvard university is 37899.8415 The value is more deviation from the actual value for Harvard University