FStat Practice Problems Set 2015

FStat practice problems

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

Final question below

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.