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

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.

orchestra answered 2 years ago

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