high_GPA math_SAT verb_SAT comp_GPA univ_GPA 3.45 643 589 3.76 3.52 2.78 558 512

Question

high_GPA math_SAT verb_SAT comp_GPA univ_GPA 3.45 643 589 3.76 3.52 2.78 558 512 2.87 2.91 2.52 583 503 2.54 2.4 3.67 685 602 3.83 3.47 3.24 592 538 3.29 3.47 2.1 562 486 2.64 2.37 2.82 573 548 2.86 2.4 2.36 559 536 2.03 2.24 2.42 552 583 2.81 3.02 3.51 617 591 3.41 3.32 3.48 684 649 3.61 3.59 2.14 568 592 2.48 2.54 2.59 604 582 3.21 3.19 3.46 619 624 3.52 3.71 3.51 642 619 3.41 3.58 3.68 683 642 3.52 3.4 3.91 703 684 3.84 3.73 3.72 712 652 3.64 3.49 2.15 564 501 2.14 2.25 2.48 557 549 2.21 2.37 3.09 591 584 3.17 3.29 2.71 599 562 3.01 3.19 2.46 607 619 3.17 3.28 3.32 619 558 3.01 3.37 3.61 700 721 3.72 3.61 3.82 718 732 3.78 3.81 2.64 580 538 2.51 2.4 2.19 562 507 2.1 2.21 3.34 683 648 3.21 3.58 3.48 717 724 3.68 3.51 3.56 701 714 3.48 3.62 3.81 691 684 3.71 3.6 3.92 714 706 3.81 3.65 4 689 673 3.84 3.76 2.52 554 507 2.09 2.27 2.71 564 543 2.17 2.35 3.15 668 604 2.98 3.17 3.22 691 662 3.28 3.47 2.29 573 591 2.74 3 2.03 568 517 2.19 2.74 3.14 607 624 3.28 3.37 3.52 651 683 3.68 3.54 2.91 604 583 3.17 3.28 2.83 560 542 3.17 3.39 2.65 604 617 3.31 3.28 2.41 574 548 3.07 3.19 2.54 564 500 2.38 2.52 2.66 607 528 2.94 3.08 3.21 619 573 2.84 3.01 3.34 647 608 3.17 3.42 3.68 651 683 3.72 3.6 2.84 571 543 2.17 2.4 2.74 583 510 2.42 2.83 2.71 554 538 2.49 2.38 2.24 568 519 3.38 3.21 2.48 574 602 2.07 2.24 3.14 605 619 3.22 3.4 2.83 591 584 2.71 3.07 3.44 642 608 3.31 3.52 2.89 608 573 3.28 3.47 2.67 574 538 3.19 3.08 3.24 643 607 3.24 3.38 3.29 608 649 3.53 3.41 3.87 709 688 3.72 3.64 3.94 691 645 3.98 3.71 3.42 667 583 3.09 3.01 3.52 656 609 3.42 3.37 2.24 554 542 2.07 2.34 3.29 692 563 3.17 3.29 3.41 684 672 3.51 3.4 3.56 717 649 3.49 3.38 3.61 712 708 3.51 3.28 3.28 641 608 3.4 3.31 3.21 675 632 3.38 3.42 3.48 692 698 3.54 3.39 3.62 684 609 3.48 3.51 2.92 564 591 3.09 3.17 2.81 554 509 3.14 3.2 3.11 685 694 3.28 3.41 3.28 671 609 3.41 3.29 2.7 571 503 3.02 3.17 2.62 582 591 2.97 3.12 3.72 621 589 4 3.71 3.42 651 642 3.34 3.5 3.51 673 681 3.28 3.34 3.28 651 640 3.32 3.48 3.42 672 607 3.51 3.44 3.9 591 587 3.68 3.59 3.12 582 612 3.07 3.28 2.83 609 555 2.78 3 2.09 554 480 3.68 3.42 3.17 612 590 3.3 3.41 3.28 628 580 3.34 3.49 3.02 567 602 3.17 3.28 3.42 619 623 3.07 3.17 3.06 691 683 3.19 3.24 2.76 564 549 2.15 2.34 3.19 650 684 3.11 3.28 2.23 551 554 2.17 2.29 2.48 568 541 2.14 2.08 3.76 605 590 3.74 3.64 3.49 692 683 3.27 3.42 3.07 680 692 3.19 3.25 2.19 617 503 2.98 2.76 3.46 516 528 3.28 3.41 Multiple Regression The data provided is being used to predict University GPA from a list of 4 independent variables as shown below DESCRIPTIONS OF VARTABLes VARIABLE DESCRIPTION high GPA High school grade point average math SAT Math SAT score verb SAT Verbal SAT score comp GPA Computer science grade point average univ GPA Overall university grade point average Your job is to see which, if any of the independent variables can be used to predict University GPA Exercise 1: Calculate the correlations between all the variables. Which variables are highly correlated 0.75)]? Which are not (40.25)? Exercise 2: Run a multiple regression on the data, using University GPA as the dependent y variable. Determine which of the independent variables are significant and which are not. Provide p-values. Use ? =0.05. Include the residuals. Exercise 3: Provide the regression equation using ALL the variables. Exercise 4: Provide the regression equation with only the significant variables. Exercise 5: Which observation had the largest residual? Exercise 6: Use exercise 4 to predict the University GPA with the following attributes: high GPA math SAT verb SAT comp GPA 3.36 612 499 3.51 Exercise 7: Were the variables that were not significant highly correlated? If so, which ones? Exercise 8. Rerun the regression with only math SAT and verbal SAT. Record the regression equation. Were either significant? Are the two variables correlated? Exercise 9. From part 8, how much of the university GPA is attributed to mat SAT score? To verbal SAT score? (Hint: check the coefficients. Which is a greater influence and why do you think it is greater? Exercise 10. provided a higher R value? Compare the coefficient of determinations between exercise 2 and exercise S. Which one

Explanation / Answer

Solution1:

In excel get the correlation matriix by

data>data analysis>correlation.

you get:

comp_GPA is strongly correlated with univ_GPA r=0.939

also high_GPA is strongly correlated with Univ_GPA

Solution2:

Run regression in excel

data>data analysis>regression slecet Ya s univ_gpa

rest all independent variables as X

click ok

Residual output is

high_GPA math_SAT verb_SAT comp_GPA univ_GPA high_GPA 1 math_SAT 0.768142 1 verb_SAT 0.726148 0.835227 1 comp_GPA 0.791472 0.687721 0.638751 1 univ_GPA 0.779563 0.662784 0.650301 0.93904588 1

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