Question

Question 1: The results of a survey of America's best graduate and professional schools are given below.

School	IQRange	AverageGPA	GMATScore	AcceptanceRate	Salary1
Harvard	135.00	3.44	644.00	15.00	168000.00
Stanford	133.00	3.24	665.00	10.20	165000.00
MIT	130.00	3.33	650.00	21.30	162000.00
Virginia	128.00	3.24	630.00	23.00	160269.00
Chicago	140.00	3.00	632.00	30.00	160269.00
Penn	130.00	3.02	644.00	19.40	160000.00
Northwestern	133.00	2.85	640.00	22.60	159000.00
Duke	132.00	2.75	630.00	18.20	158300.00
NYU	139.00	2.33	610.00	35.00	158161.00
Michigan	140.00	1.60	620.00	32.40	158000.00
CMU	115.00	2.00	630.00	31.20	157050.00
Dartmouth	108.00	2.75	648.00	13.40	157000.00
Columbia	106.00	2.89	645.00	37.10	157000.00
UCLA	105.00	2.32	640.00	20.70	156494.00
UNC	130.00	2.85	625.00	15.40	155800.00
Cornell	125.00	3.86	648.00	14.90	155700.00
Cal-Berkeley	115.00	3.75	634.00	24.70	155000.00
USC	110.00	3.55	610.00	31.90	154080.00
Rochester	108.00	2.98	615.00	35.90	149499.00
Texas	105.00	3.00	612.00	28.10	148985.00
Purdu	102.00	2.80	595.00	26.80	148500.00
Pittsburgh	94.00	2.10	615.00	33.00	148500.00
Maryland	90.00	3.90	593.00	28.10	147925.00

The top 23 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table. For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. (4) IQ Level of typical incoming student (5) GPA of typical graduating student
a) Test whether there is a correlation between these variables and is this significant.
b) The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. Conduct a simple linear regression of SALARY versus GMAT using the dataset provided.

Answer 1

(a) The correlation matrix is:

	IQRange	AverageGPA	GMATScore	AcceptanceRate	Salary1
IQRange	1.000
AverageGPA	-.087	1.000
GMATScore	.452	.123	1.000
AcceptanceRate	-.316	-.346	-.614	1.000
Salary1	.788	.050	.759	-.504	1.000
	23	sample size
	± .413	critical value of r .05 (two-tail)
	± .526	critical value of r .01 (two-tail)

(b) The regression model is:

y = 19,664.5894 + 217.4954*x

	r²	0.576
	r	0.759
	Std. Error	3499.601
	n	23
	k	1
	Dep. Var.	Salary1
ANOVA table
Source	SS	df	MS	F	p-value
Regression	34,97,30,713.8496	1	34,97,30,713.8496	28.56	2.67E-05
Residual	25,71,91,410.7591	21	1,22,47,210.0361
Total	60,69,22,124.6087	22
Regression output				confidence interval
variables	coefficients	std. error	t (df=21)	p-value	95% lower	95% upper
Intercept	19,664.5894
GMATScore	217.4954	40.7007	5.344	2.67E-05	132.8537	302.1372