high_GPA math_SAT verb_SAT comp_GPA univ_GPA 3.45 643 589 3.76 3.52 2.78 558 512
ID: 2949433 • Letter: H
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 3.41Explanation / Answer
Correlation matrix using Excel
high_GPA
math_SAT
verb_SAT
comp_GPA
univ_GPA
high_GPA
1
math_SAT
0.76814234
1
verb_SAT
0.726147777
0.835227176
1
comp_GPA
0.791472133
0.687720865
0.63875121
1
univ_GPA
0.779563121
0.662783694
0.65030121
0.93904588
1
Correlation matrix using minitab:
Correlation: high_GPA, math_SAT, verb_SAT, comp_GPA, univ_GPA
high_GPA math_SAT verb_SAT comp_GPA
math_SAT 0.768
0.000
verb_SAT 0.726 0.835
0.000 0.000
comp_GPA 0.791 0.688 0.639
0.000 0.000 0.000
univ_GPA 0.780 0.663 0.650 0.939
0.000 0.000 0.000 0.000
Cell Contents: Pearson correlation
P-Value
From both the correlation matrix we see that univ_GPA and comp_GPA are highly correlated. Math_SAT and high_GPA, verb_SAT and math_SAT, comp_GPA and high_GPA, univ_GPA and high_GPA and univ_GPA and comp_GPA these variable are highly correlated which is greater than 0.75 (>0.75).
2.AnS
Using Excel
ANOVA
df
SS
MS
F
Significance F
Regression
4
18.4906217
4.62265543
200.329927
8.19625E-47
Residual
100
2.30752114
0.02307521
Total
104
20.7981429
Coefficients
Standard Error
t Stat
P-value
Intercept
0.55957099
0.18674742
2.99640546
0.00344495
high_GPA
0.072054479
0.05557571
1.29651018
0.19778368
math_SAT
-0.00073385
0.00056294
-1.3035911
0.19536618
verb_SAT
0.000804469
0.0004434
1.81430508
0.07262917
comp_GPA
0.756812042
0.04892597
15.4685137
2.8011E-28
Using minitab we get following output:
Regression Analysis: univ_GPA versus high_GPA, math_SAT, verb_SAT, comp_GPA
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 18.4906 4.62266 200.33 0.000
high_GPA 1 0.0388 0.03879 1.68 0.198
math_SAT 1 0.0392 0.03921 1.70 0.195
verb_SAT 1 0.0760 0.07596 3.29 0.073
comp_GPA 1 5.5213 5.52132 239.27 0.000
Error 100 2.3075 0.02308
Total 104 20.7981
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.151905 88.91% 88.46% 87.90%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 0.560 0.187 3.00 0.003
high_GPA 0.0721 0.0556 1.30 0.198 3.72
math_SAT -0.000734 0.000563 -1.30 0.195 4.13
verb_SAT 0.000804 0.000443 1.81 0.073 3.51
comp_GPA 0.7568 0.0489 15.47 0.000 2.80
From Coefficients we see that P-Value of comp_GPA is significant variable which gives nearly equal to zero value (0.000<0.05). high_GPA, math_SAT and verb_SAT is not significant variable these variable have (>0.05)value.
(We get same result using excel and minitab.)
3.Ans
Regression Equation
univ_GPA = 0.560 + 0.0721*high_GPA - 0.000734*math_SAT + 0.000804*verb_SAT + 0.7568*comp_GPA
4.Ans
(if we again fit model in minitab using only significant variable then we get this model)
Regression Equation
univ_GPA = 0.5924 + 0.8249 comp_GPA
OR we can take
univ_GPA = 0.560 + 0.7568*comp_GPA
5.Ans
Observation 6,7,24,29,40,100 has largest residuals
Using minitab we get largest residuals output is:
Fits and Diagnostics for Unusual Observations
Obs univ_GPA Fit Resid Std Resid
6 2.3700 2.6874 -0.3174 -2.16 R
7 2.4000 2.9476 -0.5476 -3.64 R
24 3.3700 3.0714 0.2986 2.00 R
29 3.5800 3.2497 0.3303 2.21 R
40 2.7400 2.3623 0.3777 2.56 R
91 3.4200 3.4748 -0.0548 -0.41 X
100 2.0800 2.3762 -0.2962 -2.00 R
105 3.4100 3.3373 0.0727 0.53 X
R Large residual
X Unusual X
Step involve to obtain output in minitab
Copy data in minitab
Stat> Regression> Regression> fit regression model> select response and other continuous predictor > storage> select residuals >ok.
We get output
high_GPA
math_SAT
verb_SAT
comp_GPA
univ_GPA
high_GPA
1
math_SAT
0.76814234
1
verb_SAT
0.726147777
0.835227176
1
comp_GPA
0.791472133
0.687720865
0.63875121
1
univ_GPA
0.779563121
0.662783694
0.65030121
0.93904588
1
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