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

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

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.

Predicted value of y at x = 47424

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

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

orchestra answered 1 year ago

Next > < Previous

Related Solutions

What will be the major sources of income and expenses that would be associated with the...

What will be the major sources of income and expenses that would be associated with the program you are planning (diabetes program)? Discuss ideas on what expenses you will incur and how you will raise money to pay for this.

The Dean of ASBE School of Business is concerned that grades in the MBA program are...

The Dean of ASBE School of Business is concerned that grades in the MBA program are distributed appropriately. Too many high grades or too many low grades would pose a problem. We wish to test the claim that the mean GPA of ASBE students is smaller than 3.6 at the .01 significance level. The null and alternative hypothesis would be: H0:μ=3.6 Ha:μ<3.6 H0:p=3.64/4 Ha:p≠3.64/4 H0:p=3.6/4 Ha:p>3.6/4 H0:p=3.6/4 Ha:p>3.6/4 H0:μ=3.6 Ha:μ>3.6 H0:p=3.6/4 Ha:p<3.6/4 H0:μ=3.6 Ha:μ≠3.6 The test is: two-tailed right-tailed left-tailed...

The Dean of ASBE School of Business is concerned that grades in the MBA program are...

The Dean of ASBE School of Business is concerned that grades in the MBA program are distributed appropriately. Too many high grades or too many low grades would pose a problem. We wish to test the claim that the mean GPA of ASBE students is smaller than 3.3 at the .005 significance level. The null and alternative hypothesis would be: H0:p=3.34H0:p=3.34 Ha:p>3.34Ha:p>3.34 H0:μ=3.3H0:μ=3.3 Ha:μ≠3.3Ha:μ≠3.3 H0:p=3.34H0:p=3.34 Ha:p<3.34Ha:p<3.34 H0:μ=3.3H0:μ=3.3 Ha:μ<3.3Ha:μ<3.3 H0:p=3.34H0:p=3.34 Ha:p≠3.34Ha:p≠3.34 H0:μ=3.3H0:μ=3.3 Ha:μ>3.3Ha:μ>3.3 The test is: left-tailed two-tailed right-tailed Based on...

If you pay more in tuition to go to a top business school, will it necessarily...

If you pay more in tuition to go to a top business school, will it necessarily result in a higher probability of a job offer at graduation? Let y=percentage of graduates with job offers and x=tuition cost; then fit the simple linearmodel, E(y)=β0+β1x, to the data below. Is there sufficient evidence (α=0.10 of a positive linear relationship between y and x? School Annual tuition ($) % with Job Offer 1 39,738 95 2 39,301 86 3 39,182 92 4 38,731...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 169000 dollars. Assume the standard deviation is 43000 dollars. Suppose you take a simple random sample of 77 graduates. Find the probability that a single randomly selected policy has a mean value between 168019.9 and 175860.4 dollars. P(168019.9 < X < 175860.4) = (Enter your answers as numbers accurate to...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 121000 dollars. Assume the standard deviation is 41000 dollars. Suppose you take a simple random sample of 79 graduates. Find the probability that a single randomly selected salary exceeds 117000 dollars. P(X > 117000) = Find the probability that a sample of size n=79 is randomly selected with a mean...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $156,000. Assume the standard deviation is $42,000. Suppose you take a simple random sample of 49 graduates. Round all answers to four decimal places if necessary. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) For a single randomly selected graduate,...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 160000 dollars. Assume the standard deviation is 42000 dollars. Suppose you take a simple random sample of 100 graduates. Find the probability that a single randomly selected policy has a mean value between 155800 and 157900 dollars. P(155800 < X < 157900) = (Enter your answers as numbers accurate to...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 190000 dollars. Assume the standard deviation is 39000 dollars. Suppose you take a simple random sample of 96 graduates. Find the probability that a single randomly selected salary has a mean value between 184029.4 and 194776.5 dollars. P(184029.4 < X < 194776.5) = (Enter your answers as numbers accurate to...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of...

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $128,000. Assume the standard deviation is $43,000. Suppose you take a simple random sample of 15 graduates. Round all answers to four decimal places if necessary. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯¯¯XX¯? ¯¯¯XX¯ ~ N(,) For a single randomly selected graduate,...

Subjects