A college's economics department is attempting to determine if verbal or mathematical proficiency is...

Question

A college's economics department is attempting to determine if verbal or mathematical proficiency is more important for predicting academic success in the study of economics. The department faculty have decided to use the grade point average (GPA) in economics courses for graduates as a measure of success. Verbal proficiency is measured by the SAT verbal and the ACT English entrance examination test scores. Mathematical proficiency is measured by the SAT ma thematics and the ACT mathematics entrance examination scores. The data for 112 students are available in a data file named Student GPA. The designation of the variable columns is presented in the Chapter 11 appendix. You should use your local statistical computer program to perform the analysis for this problem.
a. Prepare a graphical plot of the economics GPA versus each of the two verbal proficiency scores and each of the two mathematical proficiency scores. Which variable is a better predictor? Note any unusual patterns in the data.
b. Compute the linear model coefficients and the regression analysis statistics for the models that predict economics GPA as a function of each verbal and each mathematics score. Using both the SAT mathematics and verbal measures and the ACT mathematics and English measures, determine whether mathematical or verbal proficiency is the best predictor of economics GPA.c. Compare the descriptive statistics-mean, standard deviation, upper and lower quartiles, and range-for the predictor variables. Note the differences and indicate how these differences affect the capability of the linear model to predict.

student-gpa-3-qvu1j42t.csv

Shakeel · Accepted Answer

student-gpa-3-qvu1j42t
	sex	GPA	SATverb	SATmath	Acteng	ACTmath	ACTss	ACTcomp	HSPct	EconGPA
	1	2.839999914	50	63					87	2.871400118
	1	2.410000086	49	57	21	24	19	23	83	2.14289999
	0	2.75			20	25	26	23	87	2.636399984
	1	3.569999933							97	3.599999905
	1	3.799999952	56	61					99	3.950000048
	0	2.720000029			17	20	22	19	87	2.589999914
	0	2.730000019			23	27	26	26	93	2.549999952
	1	3.069999933	46	56					93	2.674999952
	1	3.099999905							99	3.32859993
	0	2.829999924	53	61	22	26	31	27	78	2.940000057
	0	2.779999971	38	60						2.859999895
	1	3.279999971	57	62					91	2.924999952
	1	3.380000114			23	27	21	23	87	3.825000048
	0	3.079999924			19	25	24	24	88	3.111099958
	1	3.210000038	60	61	25	28	31	29		3.200000048
	1	3.660000086			27	31	31	30	99	4
	1	3.400000095	49	65					85	3.174999952
	1	3.660000086			22	21	30	24	97	3.900000095
	0	3.079999924	43	61	23	28	24	25	91	3.529999971
	0	3.680000067			25	33	31	30	96	3.571399927
	0	3.019999981	48	55					93	3.011100054
	0	2.329999924			19	24	28	24	73	2.099999905
	1	3.400000095	69	67	25	33	33	31	95	3.385699987
	0	2.609999895	44	64	18	26	25	25		2.775000095
	0	3.720000029	58	75	28	36	32	32	96	3.862499952
	1	3.599999905	57	68	26	31	23	28	93	3.488899946
	0	2.119999886	42	41	22	21	20	22	46	2.288899899
	0	3.119999886	61	60	24	29	28	29	57	2.859999895
	0	2.220000029			20	18	26	23	77	1.914299965
	0	3.430000067			26	34	31	31	74	3.681799889
	0	3.00999999			21	20	23	23	73	2.723099947
	0	3.289999962	52	66					96	3
	0	3.650000095	52	62					93	3.5
	1	2.549999952	39	61	22	26	21	22	97	1.799999952
	0	3.109999895	55	52	22	25	29	27	68	2.420000076
	0	2.890000105			22	29	22	25	85	2.883300066
	1	3.430000067	68	54	25	26	34	29	94	3.400000095
	0	2.400000095	42	59					45	2.444400072
	1	2.430000067			20	23	22	23	91	2.518199921
	0	2.920000076			22	24	23	25	59	2.614300013
	0	3.180000067	55	70	27	29	26	29	99	3.316699982
	0	3.730000019			23	26	30	28	90	3.875
	0	2.920000076			28	28	28	26	91	2.116699934
	1	3.349999905	51	60					96	3.549999952
	0	3.150000095	64	62	22	27	31	28	70	3.614300013
	0	2.49000001			24	27	31	29	78	2.18569994
	0	2.970000029							67	3.625
	0	2.890000105	58	45						2.781800032
	1	3.410000086			26	27	24	26	72	3.32859993
	1	3.430000067	51	60	22	28	24	26	93	3.599999905
	0	2.660000086	44	49					66	2.166699886
	0	3.460000038	42	57	22	26	25	25	71	3.5
	0	2.50999999			26	25	27	27	85	2.528599977
	1	3.160000086	53	62					92	2.869999886
	0	3.559999943	58	67	23	32	30	29	97	3.444400072
	0	3.059999943	52	67					66	3.266700029
	0	2.75999999	56	60	23	26	28	27	78	3.044399977
	0	3.089999914	48	56					77	2.85710001
	1	3.410000086			23	18	24	22	99	3.572700024
	0	2.940000057			22	24	25	23	76	2.771399975
	0	2.440000057			18	22	14	21	79	2.125
	0	3.390000105	63	73					99	3.712500095
	0	3.609999895	59	66					98	3.333300114
	0	3.619999886	53	59	23	30	32	28	89	3.869999886
	0	2.470000029	31	48	18	27	24	23	75	2.412499905
	0	3.410000086			22	26	30	27	87	3.299999952
	0	2.839999914	49	62					98	2.845499992
	0	2.619999886	48	71	21	33	23	26	98	2.537499905
	0	2.970000029			18	26	22	24	89	2.727299929
	0	3.440000057	51	62						3.25
	0	3.210000038			22	30	32	29	94	3.488899946
	0	2.609999895	49	60					86	2.754499912
	0	3.25	63	65					88	2.950000048
	0	2.710000038	42	65	19	29	26	26	86	2.690900087
	0	3.24000001	47	56	18	30	29	28	93	3.474999905
	1	2.519999981	44	35					62	2.236399889
	1	3.25999999	52	65					31	3.281800032
	1	2.569999933							89	2.411099911
	1	2.349999905	42	53	23	26	19	23	78	2.442899942
	1	3.680000067			27	24	20	24	96	3.839999914
	1	3.109999895			22	26	30	27	91	3.021399975
	0	2.970000029	50	66	24	29	24	26	94	2.433300018
	0	2.940000057	66	64	25	30	29	29	87	2.528599977
	0	3.140000105	65	62	24	27	30	27	88	3.144399881
	0	2.799999952			14	28	23	23	90	2.67779994
	0	2.339999914			26	29	24	27	82	2.255599976
	1	3.319999933	60	76	29	31	30	30	96	3.444400072
	0	3.369999886	59	63					78	3.400000095
	1	2.819999933	48	41	19	15	23	21	87	2.827300072
	0	3.569999933							98	3.674999952
	1	3.309999943	62	74					96	3.266700029
	0	3.50999999	53	68					94	3.566699982
	1	2.849999905			23	21	16	21	89	2.75
	0	3.380000114			29	26	31	30	92	3.488899946
	0	3.00999999			19	24	20	22	78	3.042900085
	0	2.390000105			21	26	26	26	79	1.933300018
	0	3.00999999							83	2.922199965
	0	3.329999924	48	73	20	33	22	26	93	3.549999952
	0	2.549999952	42	66	22	26	24	25	92	2.529999971
	1	2.940000057			22	28	23	26	94	2.279999971
	0	2.859999895			20	23	15	22	66	2.690900087
	1	3.650000095	68	71					96	3.633300066
	0	2.289999962			20	23	20	22	38	2.099999905
	0	2.950000048			23	34	24	28	77	2.587500095
	0	2.609999895			14	26	18	22	88	2.424999952
	0	2.910000086	60	53					63	2.728600025
	1	3.079999924	56	47	27	23	23	25	76	3.157099962
	0	2.529999971	52	59						2.18569994
	0	2.839999914	48	67					93	2.487499952
	0	2.900000095	65	61	25	30	31	30	69	3.116699934
	0	3.109999895	55	80					95	2.733299971
	0	3.869999886	57	69					99	3.85710001
Ans (a)
		SATverb	EconGPA		ACTeng	EconGPA		SATmath	EconGPA		ACTmath	EconGPA
		50	2.8714			2.8714		63	2.8714			2.8714
		49	2.1429		21	2.1429		57	2.1429		24	2.1429
			2.6364		20	2.6364			2.6364		25	2.6364
			3.6000			3.6000			3.6000			3.6000
		56	3.9500			3.9500		61	3.9500			3.9500
			2.5900		17	2.5900			2.5900		20	2.5900
			2.5500		23	2.5500			2.5500		27	2.5500
		46	2.6750			2.6750		56	2.6750			2.6750
			3.3286			3.3286			3.3286			3.3286
		53	2.9400		22	2.9400		61	2.9400		26	2.9400
		38	2.8600			2.8600		60	2.8600			2.8600
		57	2.9250			2.9250		62	2.9250			2.9250
			3.8250		23	3.8250			3.8250		27	3.8250
			3.1111		19	3.1111			3.1111		25	3.1111
		60	3.2000		25	3.2000		61	3.2000		28	3.2000
			4.0000		27	4.0000			4.0000		31	4.0000
		49	3.1750			3.1750		65	3.1750			3.1750
			3.9000		22	3.9000			3.9000		21	3.9000
		43	3.5300		23	3.5300		61	3.5300		28	3.5300
			3.5714		25	3.5714			3.5714		33	3.5714
		48	3.0111			3.0111		55	3.0111			3.0111
			2.1000		19	2.1000			2.1000		24	2.1000
		69	3.3857		25	3.3857		67	3.3857		33	3.3857
		44	2.7750		18	2.7750		64	2.7750		26	2.7750
		58	3.8625		28	3.8625		75	3.8625		36	3.8625
		57	3.4889		26	3.4889		68	3.4889		31	3.4889
		42	2.2889		22	2.2889		41	2.2889		21	2.2889
		61	2.8600		24	2.8600		60	2.8600		29	2.8600
			1.9143		20	1.9143			1.9143		18	1.9143
			3.6818		26	3.6818			3.6818		34	3.6818
			2.7231		21	2.7231			2.7231		20	2.7231
		52	3.0000			3.0000		66	3.0000			3.0000
		52	3.5000			3.5000		62	3.5000			3.5000
		39	1.8000		22	1.8000		61	1.8000		26	1.8000
		55	2.4200		22	2.4200		52	2.4200		25	2.4200
			2.8833		22	2.8833			2.8833		29	2.8833
		68	3.4000		25	3.4000		54	3.4000		26	3.4000
		42	2.4444			2.4444		59	2.4444			2.4444
			2.5182		20	2.5182			2.5182		23	2.5182
			2.6143		22	2.6143			2.6143		24	2.6143
		55	3.3167		27	3.3167		70	3.3167		29	3.3167
			3.8750		23	3.8750			3.8750		26	3.8750
			2.1167		28	2.1167			2.1167		28	2.1167
		51	3.5500			3.5500		60	3.5500			3.5500
		64	3.6143		22	3.6143		62	3.6143		27	3.6143
			2.1857		24	2.1857			2.1857		27	2.1857
			3.6250			3.6250			3.6250			3.6250
		58	2.7818			2.7818		45	2.7818			2.7818
			3.3286		26	3.3286			3.3286		27	3.3286
		51	3.6000		22	3.6000		60	3.6000		28	3.6000
		44	2.1667			2.1667		49	2.1667			2.1667
		42	3.5000		22	3.5000		57	3.5000		26	3.5000
			2.5286		26	2.5286			2.5286		25	2.5286
		53	2.8700			2.8700		62	2.8700			2.8700
		58	3.4444		23	3.4444		67	3.4444		32	3.4444
		52	3.2667			3.2667		67	3.2667			3.2667
		56	3.0444		23	3.0444		60	3.0444		26	3.0444
		48	2.8571			2.8571		56	2.8571			2.8571
			3.5727		23	3.5727			3.5727		18	3.5727
			2.7714		22	2.7714			2.7714		24	2.7714
			2.1250		18	2.1250			2.1250		22	2.1250
		63	3.7125			3.7125		73	3.7125			3.7125
		59	3.3333			3.3333		66	3.3333			3.3333
		53	3.8700		23	3.8700		59	3.8700		30	3.8700
		31	2.4125		18	2.4125		48	2.4125		27	2.4125		The variable SATverb and SARmath are better predictors because the graphs of
			3.3000		22	3.3000			3.3000		26	3.3000		EconGPA against these two variables are condensed. In the case of other two
		49	2.8455			2.8455		62	2.8455			2.8455		variables, the graphs are more scattered and hence, the varibales- ACTeng and ACTmath
		48	2.5375		21	2.5375		71	2.5375		33	2.5375		are weak predictors.
			2.7273		18	2.7273			2.7273		26	2.7273
		51	3.2500			3.2500		62	3.2500			3.2500
			3.4889		22	3.4889			3.4889		30	3.4889
		49	2.7545			2.7545		60	2.7545			2.7545
		63	2.9500			2.9500		65	2.9500			2.9500
		42	2.6909		19	2.6909		65	2.6909		29	2.6909
		47	3.4750		18	3.4750		56	3.4750		30	3.4750
		44	2.2364			2.2364		35	2.2364			2.2364
		52	3.2818			3.2818		65	3.2818			3.2818
			2.4111			2.4111			2.4111			2.4111
		42	2.4429		23	2.4429		53	2.4429		26	2.4429
			3.8400		27	3.8400			3.8400		24	3.8400
			3.0214		22	3.0214			3.0214		26	3.0214
		50	2.4333		24	2.4333		66	2.4333		29	2.4333
		66	2.5286		25	2.5286		64	2.5286		30	2.5286
		65	3.1444		24	3.1444		62	3.1444		27	3.1444
			2.6778		14	2.6778			2.6778		28	2.6778
			2.2556		26	2.2556			2.2556		29	2.

A college's economics department is attempting to determine if verbal or mathematical proficiency is more important for predicting academic success in the study of economics. The department faculty...

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