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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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