Question

In: Statistics and Probability

Conduct a multiple regression analysis with both Physic and Chem as your predictors. Discuss what you...

Conduct a multiple regression analysis with both Physic and Chem as your predictors. Discuss what you see/observe and evaluate (and discuss) whether the incorporation of Sex into your model would be useful and Using your “hold-out” sample, cross-validate the model you fit in QUESTION C. GIVE observe.

Student Sex math physic chem
401 F 83 53 60
402 M 66 58 61
403 F 78 49 62
404 M 71 66 60
405 F 77 43 46
406 M 71 49 50
407 F 80 54 59
408 M 70 60 58
409 F 82 54 56
410 M 70 52 57
411 F 80 48 52
412 M 70 53 47
413 F 80 48 47
414 M 68 50 58
415 F 82 62 60
416 M 71 55 51
417 F 76 55 66
418 M 78 65 46
419 F 82 55 54
420 M 67 47 52
421 F 78 48 52
422 M 64 57 60
423 F 79 52 56
424 M 73 52 51
425 F 82 50 57
426 M 69 65 64
427 F 77 49 55
428 M 73 52 51
429 F 81 58 60
430 M 70 53 53
431 F 76 56 56
432 M 70 49 51
433 F 92 68 60
434 M 73 58 52
435 F 82 56 59
436 M 79 63 41
437 F 83 48 50
438 M 74 58 46
439 F 74 52 48
440 M 64 54 51
441 F 78 57 52
442 M 69 51 54
443 F 82 55 50
444 M 68 64 64
445 F 77 52 58
446 M 72 56 53
447 F 85 54 47
448 M 59 46 62
449 F 84 67 46
450 M 81 63 49
451 F 81 51 58
452 M 67 51 59
453 F 79 63 52
454 M 67 51 53
455 F 76 49 54
456 M 65 48 55
457 F 78 59 53
458 M 71 55 55
459 F 80 47 47
460 M 75 64 59
461 F 84 59 48
462 M 74 52 49
463 F 75 52 50
464 M 62 56 71
465 F 81 57 51
466 M 64 43 54
467 F 77 51 55
468 M 68 45 50
469 F 80 47 58
470 M 64 44 55
471 F 70 41 57
472 M 73 64 61
473 F 83 65 55
474 M 71 53 51
475 F 82 48 58
476 M 71 59 59
477 F 70 58 59
478 M 74 52 48
479 F 79 54 59
480 M 75 61 58
481 F 74 54 69
482 M 73 54 50
483 F 81 57 56
484 M 70 48 47
485 F 79 46 56
486 M 74 54 44
487 F 87 72 56
488 M 74 44 47
489 F 78 49 48
490 M 72 60 61
491 F 71 49 60
492 M 71 49 51
493 F 90 64 54
494 M 74 54 43
495 F 81 56 58
496 M 73 54 51
497 F 81 52 58
498 M 73 54 47
499 F 79 58 59
500 M 62 36 56
501 F 77 54 55
502 M 78 65 47
503 F 79 57 69
504 M 71 52 57
505 F 79 58 49
506 M 77 59 59
507 F 71 47 56
508 M 66 52 61
509 F 88 59 59
510 M 62 55 66
511 F 85 58 59
512 M 76 62 49
513 F 84 67 56
514 M 69 52 59
515 F 81 52 50
516 M 71 60 51
517 F 78 54 65
518 M 73 60 59
519 F 79 52 66
520 M 74 64 53
521 F 78 60 56
522 M 72 52 43
523 F 78 57 60
524 M 70 56 59
525 F 86 57 61
526 M 68 45 54
527 F 81 57 53
528 M 66 53 59
529 F 80 60 52
530 M 69 55 52
531 F 86 61 49
532 M 73 70 64
533 F 82 52 50
534 M 73 59 54
535 F 79 57 64
536 M 65 57 63
537 F 78 44 48
538 M 69 56 58
539 F 74 54 54
540 M 64 41 58
541 F 76 56 55
542 M 66 62 59
543 F 77 51 65
544 M 66 60 70
545 F 78 60 59
546 M 75 59 53
547 F 78 51 58
548 M 67 58 67
549 F 82 51 49
550 M 68 55 52
551 F 76 45 54
552 M 67 61 62
553 F 80 67 64
554 M 72 64 57
555 F 84 53 48
556 M 71 58 61
557 F 75 58 59
558 M 69 63 59
559 F 86 68 65
560 M 76 71 55
561 F 85 57 50
562 M 76 62 54
563 F 79 49 56
564 M 72 49 46
565 F 79 59 51
566 M 67 51 54
567 F 80 56 58
568 M 59 57 73
569 F 80 57 66
570 M 68 58 56
571 F 81 56 66
572 M 67 55 59
573 F 82 59 56
574 M 72 58 55
575 F 81 54 45
576 M 60 55 64
577 F 85 65 52
578 M 72 50 52
579 F 79 51 57
580 M 73 58 57
581 F 81 56 57
582 M 79 58 42
583 F 78 47 62
584 M 73 65 53
585 F 87 55 50
586 M 69 52 53
587 F 85 42 55
588 M 69 59 61
589 F 82 56 58
590 M 74 54 45
591 F 80 41 51
592 M 74 53 56
593 F 71 51 58
594 M 61 53 61
595 F 81 63 59
596 M 73 53 52
597 F 79 48 54
598 M 74 70 61
599 F 82 48 45
600 M 65 45 56

Solutions

Expert Solution

math physic chem
83 53 60
66 58 61
78 49 62
71 66 60
77 43 46
71 49 50
80 54 59
70 60 58
82 54 56
70 52 57
80 48 52
70 53 47
80 48 47
68 50 58
82 62 60
71 55 51
76 55 66
78 65 46
82 55 54
67 47 52
78 48 52
64 57 60
79 52 56
73 52 51
82 50 57
69 65 64
77 49 55
73 52 51
81 58 60
70 53 53
76 56 56
70 49 51
92 68 60
73 58 52
82 56 59
79 63 41
83 48 50
74 58 46
74 52 48
64 54 51
78 57 52
69 51 54
82 55 50
68 64 64
77 52 58
72 56 53
85 54 47
59 46 62
84 67 46
81 63 49
81 51 58
67 51 59
79 63 52
67 51 53
76 49 54
65 48 55
78 59 53
71 55 55
80 47 47
75 64 59
84 59 48
74 52 49
75 52 50
62 56 71
81 57 51
64 43 54
77 51 55
68 45 50
80 47 58
64 44 55
70 41 57
73 64 61
83 65 55
71 53 51
82 48 58
71 59 59
70 58 59
74 52 48
79 54 59
75 61 58
74 54 69
73 54 50
81 57 56
70 48 47
79 46 56
74 54 44
87 72 56
74 44 47
78 49 48
72 60 61
71 49 60
71 49 51
90 64 54
74 54 43
81 56 58
73 54 51
81 52 58
73 54 47
79 58 59
62 36 56
77 54 55
78 65 47
79 57 69
71 52 57
79 58 49
77 59 59
71 47 56
66 52 61
88 59 59
62 55 66
85 58 59
76 62 49
84 67 56
69 52 59
81 52 50
71 60 51
78 54 65
73 60 59
79 52 66
74 64 53
78 60 56
72 52 43
78 57 60
70 56 59
86 57 61
68 45 54
81 57 53
66 53 59
80 60 52
69 55 52
86 61 49
73 70 64
82 52 50
73 59 54
79 57 64
65 57 63
78 44 48
69 56 58
74 54 54
64 41 58
76 56 55
66 62 59
77 51 65
66 60 70
78 60 59
75 59 53
78 51 58
67 58 67
82 51 49
68 55 52
76 45 54
67 61 62
80 67 64
72 64 57
84 53 48
71 58 61
75 58 59
69 63 59
86 68 65
76 71 55
85 57 50
76 62 54
79 49 56
72 49 46
79 59 51
67 51 54
80 56 58
59 57 73
80 57 66
68 58 56
81 56 66
67 55 59
82 59 56
72 58 55
81 54 45
60 55 64
85 65 52
72 50 52
79 51 57
73 58 57
81 56 57
79 58 42
78 47 62
73 65 53
87 55 50
69 52 53
85 42 55
69 59 61
82 56 58
74 54 45
80 41 51
74 53 56
71 51 58
61 53 61
81 63 59
73 53 52
79 48 54
74 70 61
82 48 45
65 45 56
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.358828677
R Square 0.128758019
Adjusted R Square 0.119912923
Standard Error 6.094260114
Observations 200
ANOVA
df SS MS F Significance F
Regression 2 1081.293752 540.646876 14.55699472 1.26961E-06
Residual 197 7316.581248 37.14000633
Total 199 8397.875
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 75.4745671 5.028207059 15.01023451 1.85874E-34 65.55854538 85.39058882 65.55854538 85.39058882
X Variable 1 0.294815531 0.069144688 4.2637481 3.11676E-05 0.158456742 0.431174321 0.158456742 0.431174321
X Variable 2 -0.300034697 0.073700626 -4.070992519 6.77531E-05 -0.445378156 -0.154691238 -0.445378156 -0.154691238

=75.4745671 ,p-value=1.85874E-34 <0.05 (significant)

=0.294815531 ,p-value=3.11676E-05 <0.05 (significant)

=-0.300034697 ,p-value=6.77531E-05 <0.05 (significant)

hence, since p-value<0.05 the model is significant.

Y=75.4745671+0.294815531 Physic-0.300034697 Chem

Now adding column of sex female =1, male=0:

math Sex Sex physic chem
83 F 1 53 60
66 M 0 58 61
78 F 1 49 62
71 M 0 66 60
77 F 1 43 46
71 M 0 49 50
80 F 1 54 59
70 M 0 60 58
82 F 1 54 56
70 M 0 52 57
80 F 1 48 52
70 M 0 53 47
80 F 1 48 47
68 M 0 50 58
82 F 1 62 60
71 M 0 55 51
76 F 1 55 66
78 M 0 65 46
82 F 1 55 54
67 M 0 47 52
78 F 1 48 52
64 M 0 57 60
79 F 1 52 56
73 M 0 52 51
82 F 1 50 57
69 M 0 65 64
77 F 1 49 55
73 M 0 52 51
81 F 1 58 60
70 M 0 53 53
76 F 1 56 56
70 M 0 49 51
92 F 1 68 60
73 M 0 58 52
82 F 1 56 59
79 M 0 63 41
83 F 1 48 50
74 M 0 58 46
74 F 1 52 48
64 M 0 54 51
78 F 1 57 52
69 M 0 51 54
82 F 1 55 50
68 M 0 64 64
77 F 1 52 58
72 M 0 56 53
85 F 1 54 47
59 M 0 46 62
84 F 1 67 46
81 M 0 63 49
81 F 1 51 58
67 M 0 51 59
79 F 1 63 52
67 M 0 51 53
76 F 1 49 54
65 M 0 48 55
78 F 1 59 53
71 M 0 55 55
80 F 1 47 47
75 M 0 64 59
84 F 1 59 48
74 M 0 52 49
75 F 1 52 50
62 M 0 56 71
81 F 1 57 51
64 M 0 43 54
77 F 1 51 55
68 M 0 45 50
80 F 1 47 58
64 M 0 44 55
70 F 1 41 57
73 M 0 64 61
83 F 1 65 55
71 M 0 53 51
82 F 1 48 58
71 M 0 59 59
70 F 1 58 59
74 M 0 52 48
79 F 1 54 59
75 M 0 61 58
74 F 1 54 69
73 M 0 54 50
81 F 1 57 56
70 M 0 48 47
79 F 1 46 56
74 M 0 54 44
87 F 1 72 56
74 M 0 44 47
78 F 1 49 48
72 M 0 60 61
71 F 1 49 60
71 M 0 49 51
90 F 1 64 54
74 M 0 54 43
81 F 1 56 58
73 M 0 54 51
81 F 1 52 58
73 M 0 54 47
79 F 1 58 59
62 M 0 36 56
77 F 1 54 55
78 M 0 65 47
79 F 1 57 69
71 M 0 52 57
79 F 1 58 49
77 M 0 59 59
71 F 1 47 56
66 M 0 52 61
88 F 1 59 59
62 M 0 55 66
85 F 1 58 59
76 M 0 62 49
84 F 1 67 56
69 M 0 52 59
81 F 1 52 50
71 M 0 60 51
78 F 1 54 65
73 M 0 60 59
79 F 1 52 66
74 M 0 64 53
78 F 1 60 56
72 M 0 52 43
78 F 1 57 60
70 M 0 56 59
86 F 1 57 61
68 M 0 45 54
81 F 1 57 53
66 M 0 53 59
80 F 1 60 52
69 M 0 55 52
86 F 1 61 49
73 M 0 70 64
82 F 1 52 50
73 M 0 59 54
79 F 1 57 64
65 M 0 57 63
78 F 1 44 48
69 M 0 56 58
74 F 1 54 54
64 M 0 41 58
76 F 1 56 55
66 M 0 62 59
77 F 1 51 65
66 M 0 60 70
78 F 1 60 59
75 M 0 59 53
78 F 1 51 58
67 M 0 58 67
82 F 1 51 49
68 M 0 55 52
76 F 1 45 54
67 M 0 61 62
80 F 1 67 64
72 M 0 64 57
84 F 1 53 48
71 M 0 58 61
75 F 1 58 59
69 M 0 63 59
86 F 1 68 65
76 M 0 71 55
85 F 1 57 50
76 M 0 62 54
79 F 1 49 56
72 M 0 49 46
79 F 1 59 51
67 M 0 51 54
80 F 1 56 58
59 M 0 57 73
80 F 1 57 66
68 M 0 58 56
81 F 1 56 66
67 M 0 55 59
82 F 1 59 56
72 M 0 58 55
81 F 1 54 45
60 M 0 55 64
85 F 1 65 52
72 M 0 50 52
79 F 1 51 57
73 M 0 58 57
81 F 1 56 57
79 M 0 58 42
78 F 1 47 62
73 M 0 65 53
87 F 1 55 50
69 M 0 52 53
85 F 1 42 55
69 M 0 59 61
82 F 1 56 58
74 M 0 54 45
80 F 1 41 51
74 M 0 53 56
71 F 1 51 58
61 M 0 53 61
81 F 1 63 59
73 M 0 53 52
79 F 1 48 54
74 M 0 70 61
82 F 1 48 45
65 M 0 45 56
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.876654399
R Square 0.768522936
Adjusted R Square 0.764979919
Standard Error 3.149275469
Observations 200
ANOVA
df SS MS F Significance F
Regression 3 6453.959547 2151.319849 216.9120524 5.18791E-62
Residual 196 1943.915453 9.917935983
Total 199 8397.875
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 69.40074955 2.611452582 26.57553502 6.70606E-67 64.25059627 74.55090284 64.25059627 74.55090284
X Variable 1 10.42666152 0.447982462 23.27470916 2.56866E-58 9.543176842 11.3101462 9.543176842 11.3101462
X Variable 2 0.373352246 0.035890249 10.40260947 1.8421E-20 0.302571606 0.444132886 0.302571606 0.444132886
X Variable 3 -0.362500296 0.038180049 -9.494495177 7.88895E-18 -0.437796745 -0.287203846 -0.437796745 -0.287203846

=69.40074955 ,p-value=6.70606E-67<0.05

=10.42666152 ,p-value=2.56866E-58<0.05

=0.373352246 ,p-value=1.8421E-20<0.05

=-0.362500296 ,p-value=7.88895E-18<0.05

since,p-value<0.05

hence, the model is significant YES,the incorporation of Sex into your model would be useful.

please rate my answer and comment for doubts.


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