Questions
1-6 are based on the following scenario:

Question
1:A
consumer products company wants to measure the effectiveness of different types
of advertising media in the promotion of its products. Specifically, the
company is interested in the effectiveness of radio advertising and newspaper
advertising (including the cost of discount coupons). A sample of 22 cities
with approximately equal populations is selected for study during a test period
of one month. Each city is allocated a specific expenditure level both for
radio advertising and for newspaper advertising. The sales of the product (in
thousands of dollars) and also the levels of the media expenditure (in
thousands of dollars) during the test month are recorded, with the following
results in Table 1 and corresponding regression output in Table 2.

Question
1: What is the interpretation of the adjusted R-square value for this problem?
Why is it a better metric than R-square in Multiple Linear Regression.

Question
2: Predict Sales when radio and newspaper advertising are 27,000 and 32,000
dollars respectively.

a.
$890783.4

b.
1047.057
($000)

c.
890.627($000)

d.
Cannot
be determined

Question 3: The appropriate test statistic
and p-value for assessing whether there is evidence that radio advertising aids
in predicting sales are:

a.
F=40.158
p-value = 1.50126E-07

b.
T=1.234
p-value=0.232

c.
T=7.435
p-value=4.88861E-07

d.
T=5.668
p-value=1.83069E-05

Question 4: Based on the sample regression coefficient
newspaper advertising we estimate that:

a.
Holding
mean radio advertising expenditure constant, as the newspaper advertising
expenditure increases by 1 dollar, sales on average increases by 16.795
dollars.

b.
Holding
mean radio advertising expenditure constant, as the newspaper advertising
expenditure increases by 1($000), sales on average increases by 16.795 ($000).

c.
As the
newspaper advertising expenditure increases by 1($000), sales on average
increases by 16.795 ($000)

d.
As the newspaper advertising expenditure
increases by 1 dollar, sales an average increases by 16.795 dollars.

Question
5: Interpret the following plot:

Question
6: Interpret the following plot:

Question
7: A marketing analyst for a major shoe manufacturer is considering the
development of a new brand of running shoes. The marketing analyst wants to
determine which variables can be used in predicting durability (or effect of
long-term impact). Two independent variables are to be considered, X1
(FOREIMP), a measurement of the forefoot shock-absorbing capability, and X2
(MIDSOLE), a measurement of the change in impact properties over time, along
with the dependent variable Y (LTIMP), which is a measure of the long-term
ability to absorb shock after a repeated impact test. A random sample of 20
types of currently manufactured running shoes was selected for testing fill in
the missing values and answer questions a and b.

1.
Complete the ANOVA table and compute the
value of R-square.

2.
At the 0.01 level of significance, What
conclusion can you make about the statistical significance of the overall
model? Show all necessary steps for ANOVA method.

Question
8: When would you use F-test versus t test in linear regression? What
assumptions need to be satisfied for linear regression?

Question
9: What is multicollinearity? What can be used to identify this issue in a
numerical problem and what are the implications if a decision maker ignores to
check for multicollinearity if the independent variables considered in the
modeling specification did suffer from this issue to a significant extent?

Question
10: The computer anxiety rating scale measures an individual’s level of
computer anxiety on a scale from 20 (no anxiety) to 100 (highest level of
anxiety). Researchers at Miami University administered CARS to 200 business
students. One of the objectives of the study was to determine if there are
differences in the amount of computer anxiety experienced by students with
different majors.

1.
Complete the ANOVA table.

2.
At the 0.05 level of significance, is
there evidence of a difference in the average computer anxiety experienced by
different majors? Show all necessary steps for ANOVA

Question 11: The quarterly numbers of applications for home
mortgage loans at a branch office of Chemical Bank Central are recorded in the
table below.

Question 11. Based on what you see in the time series chart
of the data, which of the exponential smoothing models i.e. simple and adjusted
do you believe would be appropriate for forecasting purposes? Support your
answer with appropriate explanation. Using the model you believe is
appropriate, determine the forecast for applications in the first quarter of
year 2002 (Quarter 1-02). To help with forecast computations, you can employ
the following values of alpha and beta: 0.2 and 0.3 respectively.