Multiple Linear regression paying special attention to the Analytics in Practice on page 253.
Complete exercises 3, 4, 15, 16, 18, and the Performance Lawn Equipment Case on page 272. post your work
3. Using the data in the Excel file Demographics, determine
if a linear relationship exists between unemployment
rates and the cost of living indexes by
constructing a scatter chart. Visually, do there appear
to be any outliers? If so, delete them and then find the best-fitting linear regression line using the Excel
Trendline tool. What would you conclude about the
strength of any relationship? Would you use regression
to make predictions of the unemployment rate
based on the cost of living?
Exercises
4. Using the data in the Excel file Weddings construct
scatter charts to determine whether any linear relationship
appears to exist between (1) the wedding
cost and attendance, (2) the wedding cost and the
value rating, and (3) the couple’s income and wedding
cost only for the weddings paid for by the bride
and groom. Then find the best-fitting linear regression
lines using the Excel Trendline tool for each of
these charts.
Exercises
15. The Excel file Concert Sales provides data on sales
dollars and the number of radio, TV, and newspaper
ads promoting the concerts for a group of cities. Develop
simple linear regression models for predicting
sales as a function of the number of each type of ad.
Compare these results to a multiple linear regression
model using both independent variables. Examine
the residuals of the best model for regression assumptions
and possible outliers.
Exercises
16. Using the data in the Excel file Home Market Value,
develop a multiple linear regression model for estimating
the market value as a function of both the age
and the size of the house. Predict the value of a house
that is 30 years old and has 1,800 square feet, and
one that is 5 years old and has 2,800 square feet.
Exercises
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18. The Excel file Salary Data provides information on
current salary, beginning salary, previous experience
(in months) when hired, and total years of education
for a sample of 100 employees in a firm.
a. Develop a multiple regression model for predicting
current salary as a function of the other
variables.
b. Find the best model for predicting the current salary
using the t-value criterion.
Problem
Performance Lawn Equipment Case, (Page 272).
In reviewing the PLE data, Elizabeth Burke noticed that
defects received from suppliers have decreased (
worksheet
Defects
After Delivery). Upon investigation, she learned
that in 2010, PLE experienced some quality problems
due to an increasing number of defects in materials
received from suppliers. The company instituted an initiative
in August
2011 to work with suppliers to reduce
these defects, to more closely coordinate deliveries, and to
improve
materials quality through reengineering supplier
production policies. Elizabeth noted that the program appeared
to reverse an increasing trend in defects; she would
like to predict what might have happened had the supplier
initiative not been implemented and how the number of
defects might further be reduced in the near future.
In meeting with PLE’s human resources director,
Elizabeth also discovered a concern about the high rate
of turnover in its field service staff. Senior managers have
suggested that the department look closer at its recruiting
policies, particularly to try to identify the characteristics
of individuals that lead to greater retention. However, in
a recent staff meeting, HR managers could not agree on
these characteristics. Some argued that years of education
and grade point averages were good predictors. Others
argued that hiring more mature applicants would lead to
greater retention. To study these factors, the staff agreed
to conduct a statistical study to determine the effect that
years of education, college grade point average, and age
when hired have on retention. A sample of 40 field service
engineers hired 10 years ago was selected to determine
the influence of these variables on how long each individual
stayed with the company. Data are compiled in the
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Employee Retention worksheet.
Finally, as part of its efforts to remain competitive,
PLE tries to keep up with the latest in production technology.
This is especially important in the highly competitive
lawn-mower line, where competitors can gain a real
advantage if they develop more cost-effective means of
production. The lawn-mower division therefore spends a
great deal of effort in testing new technology. When new
production technology is introduced, firms often experience
learning, resulting in a gradual decrease in the time
required to produce successive units. Generally, the rate of
improvement declines until the production time levels off.
One example is the production of a new design for lawnmower
engines. To determine the time required to produce
these engines, PLE produced 50 units on its production
line; test results are given on the worksheet Engines in
the database. Because PLE is continually developing new
technology, understanding the rate of learning can be useful
in estimating future production costs without having to
run extensive prototype trials, and Elizabeth would like a
better handle on this.
Use techniques of regression analysis to assist her in
evaluating the data in these three worksheets and reaching
useful conclusions. Summarize your work in a formal
report
with all appropriate results and analyses.
Note: Complete and post for review and grading the following “Problems and Exercises” starting on page 268,
270, and 272 (all work in Excel).