Question

While exploring MBA programs, a student gathered the following information. What kind of relationship exists between variables and how can this information be used in decision making (i.e. what data would you gather on other schools as you continue your search)

University	Salary	Rank	Tuition	GMAT	Group	Group 1	Group 2	Group 3
1	$105,100	2.8	$72,693	695	1	1	0	0
2	$115,478	3.2	$80,486	708	1	1	0	0
3	$112,318	3.2	$77,003	706	1	1	0	0
4	$102,637	5.8	$70,805	688	1	1	0	0
5	$117,520	6.2	$75,473	721	1	1	0	0
6	$108,975	7.7	$72,890	707	1	1	0	0
7	$105,063	12.7	$59,815	702	2	0	1	0
8	$99,647	13.3	$60,819	685	2	0	1	0
9	$92,316	19.8	$51,130	679	2	0	1	0
10	$91,608	23.2	$64,811	670	2	0	1	0
11	$92,039	29.4	$65,713	667	2	0	1	0
12	$89,678	39.1	$49,710	660	3	0	0	1
13	$86,252	41.1	$40,673	639	3	0	0	1
14	$82,764	45.3	$38,422	655	3	0	0	1
15	$78,080	46.9	$56,697	672	3	0	0	1
16	$83,515	46.9	$32,424	646	3	0	0	1
17	$82,754	49.6	$62,210	658	3	0	0	1
18	$73,748	49.8	$28,986	653	3	0	0	1
19	$83,536	51.8	$55,801	643	3	0	0	1
20	$88,782	67.6	$30,985	512	3	0	0	1

Answer 1

Answer to the question)
This data can be worked through with help of multiple regression

For that any software can be used:

I have made use of excel, and following are the steps for the same:

Enter the data in excel

remove the dollar sign from the salary column

Now click on data tab in excel

in the menu of data tab, click on data analysis

from the data analysis window select regression and click ok

Now the following window appears on screen:

.

.

In the y range input the cell range for salary data

n the x range input the cell range for all the rest of columns

tick mark the check box next to labels

click ok

The following output appears on the screen:

.

.

We ge to the following details from the output obtained:

The P value for the overall model is less than 0.05 hence the overall model is significant

the P values for individual factors is not less than 0.05 , hence individually these factors are not significant

The multiple correlation coefficient of the model is 0.9379 which is an indicator of strong relation

The coefficient of determination (R square) = 0.8797 ~ 87.97%. This tells us that 87.97% of the variation in the dependent variable salary is explained by this model, which indicates that this model is useful in predicting the salary.