Question
Note: Reference MAT 2375 Introduction to statistics and MAT3378 Analysis of experience plans Project: Use the SAT and College GPA data set (Below) Consider the
Note: Reference MAT 2375 Introduction to statistics and MAT3378 Analysis of experience plans
Project:
Use the SAT and College GPA data set (Below)
Consider the multiple linear regression model
Y=0+1X1+2X2+3X3+4X4+
Where Y is the general average of the university.
1. high_GPA = Weighted average of grades obtained in high school
2. math_SAT = SAT score in mathematics
3. verb_SAT = Verbal note to the SAT
4. comp_GPA = Weighted average in computer science
5. univ_GPA = General average of grades obtained at university
Question:
1. Perform multiple linear regression using all predictors (independent variables) and interpret the results;
2. Test the hypohesisH0:4=0compared toH1:4=0
3. Is the university average linearly related to the high school average?
4. Select the best model using the stepAIC function of the MASS library;
5. Compare the selected model (obtained from 3.) and the complete model (i.e. with all predictors) using adjusted R2 and AIC;
6. Perform all the steps of the adequacy of the selected model.
Note: the SAT and College GPA data set
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 |
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