d) What is the expected CS_GPA for a high school graduate with a math_SAT of 600

Question

d) What is the expected CS_GPA for a high school graduate with a math_SAT of 600?

We are trying to come up with a regression model that predicts CS_GPA using high math_SAT as a predictor. a) Is math_SAT a significant predictor for CS_GPA? b) What is the proportion of the variation in CS_GPA that can be explained by math_SAT? c) What is the correlation coefficient between CS_GPA and math_SAT? c) What is the correct regression equation?

d) What is the expected CS_GPA for a high school graduate with a math_SAT of 600?

math_SAT cs_GPA 643 3.76 558 2.87 583 2.54 685 3.83 592 3.29 562 2.64 573 2.86 559 2.03 552 2.81 617 3.41 684 3.61 568 2.48 604 3.21 619 3.52 642 3.41 683 3.52 703 3.84 712 3.64 564 2.14 557 2.21 591 3.17 599 3.01 607 3.17 619 3.01 700 3.72 718 3.78 580 2.51 562 2.1 683 3.21 717 3.68 701 3.48 691 3.71 714 3.81 689 3.84 554 2.09 564 2.17 668 2.98 691 3.28 573 2.74 568 2.19 607 3.28 651 3.68 604 3.17 560 3.17 604 3.31 574 3.07 564 2.38 607 2.94 619 2.84 647 3.17 651 3.72 571 2.17 583 2.42 554 2.49 568 3.38 574 2.07 605 3.22 591 2.71 642 3.31 608 3.28 574 3.19 643 3.24 608 3.53 709 3.72 691 3.98 667 3.09 656 3.42 554 2.07 692 3.17 684 3.51 717 3.49 712 3.51 641 3.4 675 3.38 692 3.54 684 3.48 564 3.09 554 3.14 685 3.28 671 3.41 571 3.02 582 2.97 621 4 651 3.34 673 3.28 651 3.32 672 3.51 591 3.68 582 3.07 609 2.78 554 3.68 612 3.3 628 3.34 567 3.17 619 3.07 691 3.19 564 2.15 650 3.11 551 2.17 568 2.14 605 3.74 692 3.27 680 3.19 617 2.98 516 3.28

Explanation / Answer

Below is the regression results from Excel.

(1) Here as p - value for math_SAT is less than 0.05/0.01 so we can say that math_ SAT is significant predictor of gpa.

(2) Here R - square is equals to 0.47296 that means 47.296% of varaition in gpa is explained by math_ SAT.

(3) Correlation coefficient between gpa and math_ SAT is 0.006512

(4) Correct regression equation

gpa = -0.9294 + 0.006512 * (math_ SAT)

(5) If math_ SAT = 600

then gpa = -0.9294 + 0.006512 * 600 = 2.9778

SUMMARY OUTPUT Regression Statistics Multiple R 0.687721 R Square 0.47296 Adjusted R Square 0.467843 Standard Error 0.371344 Observations 105 ANOVA df SS MS F Significance F Regression 1 12.74593 12.74593 92.43108 5.34E-16 Residual 103 14.20335 0.137897 Total 104 26.94928 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -0.9294 0.423578 -2.19415 0.030472 -1.76946 -0.08933 -1.76946 -0.08933 math_SAT 0.006512 0.000677 9.614109 5.34E-16 0.005169 0.007855 0.005169 0.007855

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