Question

In: Statistics and Probability

Pursuing an MBA is a major personal investment. Tuition and expenses associated with business school programs...

Pursuing an MBA is a major personal investment. Tuition and expenses associated with business school programs are​ costly, but the high costs come with hopes of career advancement and high salaries. A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program​ per-year tuition as a predictor of starting salary. Data were collected for 37 ​full-time MBA programs offered at private universities. The data are stored in the accompanying table. Complete parts​ (a) through​ (e) below.

a. Construct a scatter plot.

b. Assuming a linear​ relationship, use the​ least-squares method to determine the regression coefficients b0 and b1.

c. Interpret the meaning of the​ slope, b1​, in this problem.

d. Predict the mean starting salary upon graduation for a program that has a​ per-year tuition cost of $47,424.

e. What insights can be obtained about the relationship between program​ per-year tuition and starting salary upon​ graduation?

Program Per-Year Tuition ($) Mean Starting Salary Upon Graduation ($)
62525 155817
67451 152357
67749 149035
67666 144735
66779 138899
65528 152385
65695 151892
67655 151383
64351 135432
63923 141959
67172 143153
60574 145089
61936 139567
56822 135936
53789 127037
54703 116149
56016 124588
50732 128107
52677 129467
50944 121455
47172 115002
47340 110982
48454 111045
44833 106917
36539 81620
48766 79609
47016 101254
51112 74476
37992 88178
34391 76630
43591 74766
43030 52071
50032 65298
33704 103286
23853 54156
42047 81971
39597 53127

Solutions

Expert Solution

Ʃx = 1944156
Ʃy = 4214830
Ʃxy = 232985715420
Ʃx² = 106996780762
Ʃy² = 517682716166
Sample size, n = 37
x̅ = Ʃx/n = 1944156/37 = 52544.75676
y̅ = Ʃy/n = 4214830/37 = 113914.3243
SSxx = Ʃx² - (Ʃx)²/n = 106996780762 - (1944156)²/37 = 4841576645
SSyy = Ʃy² - (Ʃy)²/n = 517682716166 - (4214830)²/37 = 37553204574
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 232985715420 - (1944156)(4214830)/37 = 11518498299

a)

b)

Slope, b1 = SSxy/SSxx = 11518498298.9189/4841576644.81081 = 2.37908

y-intercept, b0 = y̅ - b1* x̅ = 113914.32432 - (2.37908)*52544.75676 = -11093.86

Regression equation :

ŷ = -11093.857 + (2.3791) x

c)

As the value of program per-year tuition increases by a unit the value Mean Starting Salary Upon Graduation increases by 2.3791 on average.

d)

Predicted value of y at x = 47424

ŷ = -11093.857 + (2.3791) * 47424 = 101731.6342

e)

Mean starting salaries upon graduation tend to be higher among programs with higher per-year tuitions.

orchestra answered 3 years ago
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