Tyler Clark - Homework 8 ECON

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Feb 20, 2024

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Tyler Clark – Homework 8 ECON a. The expected increase in final college grade point average corresponding to a one point increase in high school grade point average is .0235 when SAT mathematics score does not change. Similarly, the expected increase in final college grade point average corresponding to a one point increase in the SAT mathematics score is .00486 when the high school grade point average does not change. b. -1.41 + 0.0235(84) + 0.00486(540) = -1.41 + 1.974 + 2.6244 = 3.1884

a. Predictor Coef SE Coef T Constant -1.4053 0.4848 -2.899 X1 0.23467 0.008666 2.7 X2 0.00486 0.001077 4.51 S = 0.1298; R-SQ: 93.73% ; R-SQ (adj): c. 91.9% Source of Variation Sum of Squares Degrees of Freedom Mean Square F-test stat. Treatments 1.76209 2 0.881 51.824 Error 0.11791 7 0.017 Total 1.88 9 X2 Coef: X2 value from equation: 0.00486 T-values: -1.4053 / 0.4848 = -2.899 ; 0.23467 / 0.008666 = 2.7 ; 0.00486 / 0.001077 = 4.51 R-SQ: (SOS Treatments / SOS Total)*100% = (1.76209/1.88)*100% = 93.73% R-SQ (adj): (1 - (MS Error) / (SS Total / DOF Total)) = (1- (0.017 / (1.88/9))*100% = 91.9% Degrees of freedom: # of regressors – 1 = 2 treatment DOF ; 9 – 2 = 7 error DOF Mean squares: 1.76209 / 2 = 0.881 ; 0.11791 / 7 = 0.017 F-Test stat: Quotient of Mean Squares: 0.881 / 0.017 = c. 51.824 b. F 0.05 : 4.74 Because the F-Test stat of 51.824 > 4.74, there is a significant relationship. Actual p-value =.000

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Since the p-value of .000 < 0.05, there is a significant relationship. c. Hypothesis: B 1 = 0; T-test: 2.7; p-value with 9 DOF: 0.0244; Reject hypothesis. Hypothesis: B 2 = 0; T-test: 4.51; p-value with 9 DOF: 0.0015; Reject hypothesis. d. Regression = (SOS Treatment / SOS Total) = (1.76209/1.88) = .9373 R = 1 – (1 – Regression)(SOS Total DOF/ SOS Treatment DOF) = R = 1 – (1 – 0.9373)(9/7) = 0.9193 Since 92% (.9193) of the variation is explained from the regression equation, the regression equation does require a good fit.

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