Data given: ApplicantGPAIQSESEX17.9411167128.29210743134.64310052147.4710766158.88211458067.58511551177.6511171182.4129751196100490108.833112511117.47104350125.52889540137.167104541147.571102640154.791560168.167114690177.822114550187.598103650194106401206.231105660217.643113551221.76109201246.419108560269.6481136812710.71306902810.58128701299.429128801308118531319.585113651329.571120670338.998132620348.333111390358.175124711368127591379.333128600389.5136641399.1671067114010.14118720419.9991195404310.76123641449.763124581459.41126701469.167116721479.348127701488.167119471503.64797521513.40886460523.936102661537.167110671547.647120631566.173115671577.29593611587.29572540598.938111600607.882103600618.353123631625.06279301638.175119541648.235110661657.588110441687.647107491695.23774440717.825105671727.333112640749.167105731767.996110591778.714107370787.833103630794.8857736180898640833.8290421845.93696280859112600869.5112700876.057114511886.05793210896.938106561 d) What percent of the total variation in MBA applicant GPAs can be explained by thestraight-line relationship for each of the continuous explanatory variables separately(Hint run simple linear regression models)? How much does self-esteem (SE)contribute to explaining GPA after the effect of IQ on GPA is taken into account?(StatCrunch)e) Now, perform another multiple regression analysis including GPA as the response ordependent variable, IQ and SE as the continuous explanatory variables and SEX asa categorical variable (Note: refer to this model as Model 2 which includes thecategorical variable SEX without any interaction terms); comment on the validity andsignificance of this model. (StatCrunch)f) Which model (Model 1 or Model 2) is a better model? (Justify your answer)g) Write the regression equation for the full model 2 and the separate regressionequations for males and females and compare their coefficients (Hint: create a maleand a female subset of the base data and run separate multiple regressions oneach subset) (StatCrunch) The admission committee of an MBA program at a Canadian university is consideringusing a psychometric test of self-esteem (SE) in addition to the IQ test they administerto MBA applicants to help in their selection process. They want to assess the influenceof self-esteem on candidate bachelor's GPA above and beyond IQ and sex. TheAssign4Data.xlsx file contains a random sample of 77 GPA records of MBA applicantswith the corresponding IQ, SE, and sex information (Female=0, Male=1). Treating GPAas the response variable and IQ, SE, and SEX as explanatory variables, answer thefollowing questions using a 1% significance level.

Question

Data given: ApplicantGPAIQSESEX17.9411167128.29210743134.64310052147.4710766158.88211458067.58511551177.6511171182.4129751196100490108.833112511117.47104350125.52889540137.167104541147.571102640154.791560168.167114690177.822114550187.598103650194106401206.231105660217.643113551221.76109201246.419108560269.6481136812710.71306902810.58128701299.429128801308118531319.585113651329.571120670338.998132620348.333111390358.175124711368127591379.333128600389.5136641399.1671067114010.14118720419.9991195404310.76123641449.763124581459.41126701469.167116721479.348127701488.167119471503.64797521513.40886460523.936102661537.167110671547.647120631566.173115671577.29593611587.29572540598.938111600607.882103600618.353123631625.06279301638.175119541648.235110661657.588110441687.647107491695.23774440717.825105671727.333112640749.167105731767.996110591778.714107370787.833103630794.8857736180898640833.8290421845.93696280859112600869.5112700876.057114511886.05793210896.938106561 d) What percent of the total variation in MBA applicant GPAs can be explained by thestraight-line relationship for each of the continuous explanatory variables separately(Hint run simple linear regression models)? How much does self-esteem (SE)contribute to explaining GPA after the effect of IQ on GPA is taken into account?(StatCrunch)e) Now, perform another multiple regression analysis including GPA as the response ordependent variable, IQ and SE as the continuous explanatory variables and SEX asa categorical variable (Note: refer to this model as Model 2 which includes thecategorical variable SEX without any interaction terms); comment on the validity andsignificance of this model. (StatCrunch)f) Which model (Model 1 or Model 2) is a better model? (Justify your answer)g) Write the regression equation for the full model 2 and the separate regressionequations for males and females and compare their coefficients (Hint: create a maleand a female subset of the base data and run separate multiple regressions oneach subset) (StatCrunch) The admission committee of an MBA program at a Canadian university is consideringusing a psychometric test of self-esteem (SE) in addition to the IQ test they administerto MBA applicants to help in their selection process. They want to assess the influenceof self-esteem on candidate bachelor's GPA above and beyond IQ and sex. TheAssign4Data.xlsx file contains a random sample of 77 GPA records of MBA applicantswith the corresponding IQ, SE, and sex information (Female=0, Male=1). Treating GPAas the response variable and IQ, SE, and SEX as explanatory variables, answer thefollowing questions using a 1% significance level.

Accepted Answer

Given information:

Applicant
GPA
IQ
SE
SEX

1
7.94
111
67
1

2
8.292
107
43
1

3
4.643
100
52…

Applicant	GPA	IQ	SE	SEX
1	7.94	111	67	1
2	8.292	107	43	1
3	4.643	100	52	1
4	7.47	107	66	1
5	8.882	114	58	0
6	7.585	115	51	1
7	7.65	111	71	1
8	2.412	97	51	1
9	6	100	49	0
10	8.833	112	51	1
11	7.47	104	35	0
12	5.528	89	54	0
13	7.167	104	54	1
14	7.571	102	64	0
15	4.7	91	56	0
16	8.167	114	69	0
17	7.822	114	55	0
18	7.598	103	65	0
19	4	106	40	1
20	6.231	105	66	0
21	7.643	113	55	1
22	1.76	109	20	1
24	6.419	108	56	0
26	9.648	113	68	1
27	10.7	130	69	0
28	10.58	128	70	1
29	9.429	128	80	1
30	8	118	53	1
31	9.585	113	65	1
32	9.571	120	67	0
33	8.998	132	62	0
34	8.333	111	39	0
35	8.175	124	71	1
36	8	127	59	1
37	9.333	128	60	0
38	9.5	136	64	1
39	9.167	106	71	1
40	10.14	118	72	0
41	9.999	119	54	0
43	10.76	123	64	1
44	9.763	124	58	1
45	9.41	126	70	1
46	9.167	116	72	1
47	9.348	127	70	1
48	8.167	119	47	1
50	3.647	97	52	1
51	3.408	86	46	0
52	3.936	102	66	1
53	7.167	110	67	1
54	7.647	120	63	1
56	6.173	115	67	1
57	7.295	93	61	1
58	7.295	72	54	0
59	8.938	111	60	0
60	7.882	103	60	0
61	8.353	123	63	1
62	5.062	79	30	1
63	8.175	119	54	1
64	8.235	110	66	1
65	7.588	110	44	1
68	7.647	107	49	1
69	5.237	74	44	0
71	7.825	105	67	1
72	7.333	112	64	0
74	9.167	105	73	1
76	7.996	110	59	1
77	8.714	107	37	0
78	7.833	103	63	0
79	4.885	77	36	1
80	8	98	64	0
83	3.82	90	42	1
84	5.936	96	28	0
85	9	112	60	0
86	9.5	112	70	0
87	6.057	114	51	1
88	6.057	93	21	0
89	6.938	106	56	1