Question

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

Answer 1

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.