Quantitative Analysis for Business

Quantitative Analysis for Business
Topic #5 Problem Set

Directions: Submit your final answers using D2L Quizzes.

1. Many countries, especially those in Europe, still have significant gold holdings. Many of these countries also have a large amount of debt. The following is a data set of those two variables for a select number of nations in 2012, alongside the country names. Data come from the websites WordPress and Trading Economics.

Country Gold value ($ billions) Debt (% of GDP)
China 63 17.7
France 146 81.7
Germany 203 83.2
Indonesia 33 69.2
Italy 147 119.0
The Netherlands 36 63.7
Russia 50 9.9
Switzerland 62 55.0
United States 487 93.2

Develop a regression equation for the impact of gold holdings on debt. What is ?
What is ?
Estimate the debt of a country with a gold value of $100 billion.
Create a scatterplot. Does it indicate a positive, negative, or null relationship?
Calculate .
Perform a significance test for . Is it significant at the 95% confidence level?

2. The regional transit authority for Atlanta wants to determine if there is a relationship between the age of a bus and its annual maintenance cost. The following sample of 10 buses was collected in 2010 to answer this question.

Bus number Age (in years) Cost ($)
11 1 350
12 2 370
13 2 480
14 2 520
15 2 590
16 3 550
17 4 750
18 4 800
19 5 790
20 5 950

Develop a regression for the impact of bus age on maintenance cost. What is ?
What is ?
Estimate the maintenance cost of a bus that is brand new (age = 0 years).
Create a scatterplot. Does it indicate a positive, negative, or null relationship?
Calculate .
Perform a significance test for . Is it significant at the 95% confidence level?

3. One of the biggest changes in higher education during the early 21st century was the rise of online schools. The following is a data set from 2009 on some online colleges in the U.S. The two variables shown are the school’s retention rate (the % of students who stayed enrolled from 2008 to 2009) and graduation rate (the % of students who typically graduate).

College Retention rate (%) Graduation rate (%)
Western International University 7 25
South University 51 25
University of Phoenix 4 28
American InterContinential Univ. 29 32
Franklin University 33 33
DeVry University 47 33
Tiffin University 63 34
Post University 45 36
Peirce College 60 36
Everest University 62 36
Upper Iowa University 67 36
Dickinson State University 65 37
Western Governors University 78 37
Kaplan University 75 38
Salem International University 54 39
Ashford University 45 41
ITT Technical Institute 38 44
Berkeley College 51 45
Grand Canyon University 69 46
Nova Southeastern University 60 47
Westwood College 37 48
Everglades University 63 50
Liberty University 73 51
LeTourneau University 78 52
Rasmussen College 48 53
Keiser University 95 55
Herzing College 68 56
National University 100 57
Florida National College 100 61

Develop a regression for the impact of retention on graduation. What is ?
What is ?
Estimate the graduation rate of a college with a 50% retention rate.
Create a scatterplot. Does it indicate a positive, negative, or null relationship?
Calculate .
Perform a significance test for . Is it significant at the 95% confidence level?