Question

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

use the first 160 of your observations for question A, B,C  and  use the last 40 for question D

a.What is a 90% confidence interval for the correlation between Math and Physic?

b. Conduct a simple regression analysis with Math as your dependent variable and Chem as your independent variable. Discuss what you see/observe.

c.Conduct a multiple regression analysis with both Physic and Chem as your predictors. Discuss what you see/observe. Having done this, evaluate (and discuss) whether the incorporation of Sex into your model would be useful.

Answer 1

As mentioned we have to take only 160 observations for question A,B,C:

a.What is a 90% confidence interval for the correlation between Math and Physic?

math	physic
83	53
66	58
78	49
71	66
77	43
71	49
80	54
70	60
82	54
70	52
80	48
70	53
80	48
68	50
82	62
71	55
76	55
78	65
82	55
67	47
78	48
64	57
79	52
73	52
82	50
69	65
77	49
73	52
81	58
70	53
76	56
70	49
92	68
73	58
82	56
79	63
83	48
74	58
74	52
64	54
78	57
69	51
82	55
68	64
77	52
72	56
85	54
59	46
84	67
81	63
81	51
67	51
79	63
67	51
76	49
65	48
78	59
71	55
80	47
75	64
84	59
74	52
75	52
62	56
81	57
64	43
77	51
68	45
80	47
64	44
70	41
73	64
83	65
71	53
82	48
71	59
70	58
74	52
79	54
75	61
74	54
73	54
81	57
70	48
79	46
74	54
87	72
74	44
78	49
72	60
71	49
71	49
90	64
74	54
81	56
73	54
81	52
73	54
79	58
62	36
77	54
78	65
79	57
71	52
79	58
77	59
71	47
66	52
88	59
62	55
85	58
76	62
84	67
69	52
81	52
71	60
78	54
73	60
79	52
74	64
78	60
72	52
78	57
70	56
86	57
68	45
81	57
66	53
80	60
69	55
86	61
73	70
82	52
73	59
79	57
65	57
78	44
69	56
74	54
64	41
76	56
66	62
77	51
66	60
78	60
75	59
78	51
67	58
82	51
68	55
76	45
67	61
80	67
72	64
84	53
71	58
75	58
69	63
86	68
76	71

hence, correlation between math and physic is calculated in excel using CORREL(array1,array2):

=CORREL(C2:C161,D2:D161)=

0.293303

Z=

Z=

Z=0.302

Zc=1.645

SE=

SE=

SE=0.0798

CI=(Z-Zc*SE,Z+Zc*SE)

CI=(0.302-1.645*0.0798, 0.302+1.645*0.0798)

CI=[0.1693, 0.4082]

b. Conduct a simple regression analysis with Math as your dependent variable and Chem as your independent variable. Discuss what you see/observe:

We have:

	CHEM	MATHS	CHEM*MATHS	CHEM2	MATHS2
	60	83	4980	3600	6889
	61	66	4026	3721	4356
	62	78	4836	3844	6084
	60	71	4260	3600	5041
	46	77	3542	2116	5929
	50	71	3550	2500	5041
	59	80	4720	3481	6400
	58	70	4060	3364	4900
	56	82	4592	3136	6724
	57	70	3990	3249	4900
	52	80	4160	2704	6400
	47	70	3290	2209	4900
	47	80	3760	2209	6400
	58	68	3944	3364	4624
	60	82	4920	3600	6724
	51	71	3621	2601	5041
	66	76	5016	4356	5776
	46	78	3588	2116	6084
	54	82	4428	2916	6724
	52	67	3484	2704	4489
	52	78	4056	2704	6084
	60	64	3840	3600	4096
	56	79	4424	3136	6241
	51	73	3723	2601	5329
	57	82	4674	3249	6724
	64	69	4416	4096	4761
	55	77	4235	3025	5929
	51	73	3723	2601	5329
	60	81	4860	3600	6561
	53	70	3710	2809	4900
	56	76	4256	3136	5776
	51	70	3570	2601	4900
	60	92	5520	3600	8464
	52	73	3796	2704	5329
	59	82	4838	3481	6724
	41	79	3239	1681	6241
	50	83	4150	2500	6889
	46	74	3404	2116	5476
	48	74	3552	2304	5476
	51	64	3264	2601	4096
	52	78	4056	2704	6084
	54	69	3726	2916	4761
	50	82	4100	2500	6724
	64	68	4352	4096	4624
	58	77	4466	3364	5929
	53	72	3816	2809	5184
	47	85	3995	2209	7225
	62	59	3658	3844	3481
	46	84	3864	2116	7056
	49	81	3969	2401	6561
	58	81	4698	3364	6561
	59	67	3953	3481	4489
	52	79	4108	2704	6241
	53	67	3551	2809	4489
	54	76	4104	2916	5776
	55	65	3575	3025	4225
	53	78	4134	2809	6084
	55	71	3905	3025	5041
	47	80	3760	2209	6400
	59	75	4425	3481	5625
	48	84	4032	2304	7056
	49	74	3626	2401	5476
	50	75	3750	2500	5625
	71	62	4402	5041	3844
	51	81	4131	2601	6561
	54	64	3456	2916	4096
	55	77	4235	3025	5929
	50	68	3400	2500	4624
	58	80	4640	3364	6400
	55	64	3520	3025	4096
	57	70	3990	3249	4900
	61	73	4453	3721	5329
	55	83	4565	3025	6889
	51	71	3621	2601	5041
	58	82	4756	3364	6724
	59	71	4189	3481	5041
	59	70	4130	3481	4900
	48	74	3552	2304	5476
	59	79	4661	3481	6241
	58	75	4350	3364	5625
	69	74	5106	4761	5476
	50	73	3650	2500	5329
	56	81	4536	3136	6561
	47	70	3290	2209	4900
	56	79	4424	3136	6241
	44	74	3256	1936	5476
	56	87	4872	3136	7569
	47	74	3478	2209	5476
	48	78	3744	2304	6084
	61	72	4392	3721	5184
	60	71	4260	3600	5041
	51	71	3621	2601	5041
	54	90	4860	2916	8100
	43	74	3182	1849	5476
	58	81	4698	3364	6561
	51	73	3723	2601	5329
	58	81	4698	3364	6561
	47	73	3431	2209	5329
	59	79	4661	3481	6241
	56	62	3472	3136	3844
Sum =	5432	7503	407045	298234	567003

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

MATHS = 83.9119 - 0.1635 CHEM

We observe that for every 1 mark increase in chemistry there is a deduction of 0.1635 marks in mathematics.

c.Conduct a multiple regression analysis with both Physic and Chem as your predictors. Discuss what you see/observe. Having done this, evaluate (and discuss) whether the incorporation of Sex into your model would be useful.:

open excel->enter values->goto data-->data analysis-->regression-->enter y and x range.

Taking physic and chem as predictors and maths as dependent variable:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.375862725
R Square	0.141272788
Adjusted R Square	0.130333588
Standard Error	5.923466072
Observations	160
ANOVA
	df	SS	MS	F	Significance F
Regression	2	906.264052	453.132026	12.91436175	6.42148E-06
Residual	157	5508.729698	35.08745031
Total	159	6414.99375
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	70.78329528	5.452669892	12.98140116	1.21582E-26	60.0132408	81.55335	60.0132408	81.55334976
X Variable 1	0.335604992	0.074211273	4.522291285	1.19951E-05	0.18902369	0.482186	0.18902369	0.482186294
X Variable 2	-0.257668501	0.081075428	-3.178133104	0.001785483	-0.417807807	-0.09753	-0.417807807	-0.097529195

here we have,

Intercept(p-value)=1.21582E-26<0.05

X Variable 1(p-value)=1.19951E-05<0.05

X Variable 2(p-value)=0.001785483<0.05

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

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

math	Sex	SEX	PHY	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

open excel->enter values->goto data-->data analysis-->regression-->enter y and x range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.876527207
R Square	0.768299945
Adjusted R Square	0.763844175
Standard Error	3.086731742
Observations	160
ANOVA
	df	SS	MS	F	Significance F
Regression	3	4928.639346	1642.879782	172.4280866	2.56101E-49
Residual	156	1486.354404	9.527912848
Total	159	6414.99375
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	66.60087055	2.848680815	23.37954825	7.56389E-53	60.97390693	72.22783418	60.97390693	72.22783418
X Variable 1	10.08032652	0.490605253	20.54671544	3.12959E-46	9.111240097	11.04941295	9.111240097	11.04941295
X Variable 2	0.393883631	0.038775543	10.15804285	6.34827E-19	0.317290785	0.470476478	0.317290785	0.470476478
X Variable 3	-0.331149071	0.042399683	-7.810177915	7.82555E-13	-0.414900636	-0.247397506	-0.414900636	-0.247397506

Intercept(p-value)=7.56389E-53<0.05

X Variable 1(p-value)=3.12959E-46<0.05

X Variable 2(p-value)=6.34827E-19<0.05

X variable 3(p-value)=7.82555E-13<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.