Econ 3790           Homework # 3             Dr. Usip

Note: Even though this assignment is worth 14 points,
           it will help you prepare for the final exam.
Part I: Chi-Square Test Problems (Chapters 12)
Please State the H0 and the Ha clearly for each problem.
 1. Test of Goodness-of fit: #7,  p. 464

2. Test of Independence: #11, p. 469 

Part II: One-Way ANOVA Problems: F test (Chapter 13)
1.  # 5, p. 506

2. Family transportation costs are usually higher than most people believe, because they include car payments, insurance, fuel costs, repairs, parking, and public transportation. Twenty randomly selected selected families  in four major cities (Atlanta, New York, Los Angeles, and Chicago) are asked to use their records to estimate a monthly figure for transportation cost. The data matrix is as follows:

ATLANTA NEW YORK LOS ANGELES CHICAGO
$650 $250 $850 $540
  480   525   700   450
  550   300   950   675
  600   175   780    550
  675   500   600   600

1. What is the response variable?
2. What is the factor?
3. What are the Treatments?
4. From the data matrix is the experimental design a balanced or an unbalanced design? Explain.
5. Use Excel to compute the ANOVA table for this problem.
6. At α =.05, use the critical value and the P-value approaches to verify whether there is a significant difference in monthly transportation costs for families living in these cities.
7. At α =.05, use the p-value approach to verify whether there is a significant difference in monthly
    transportation costs for families living in these cities.

Part III: Regression Analysis Problems (Chapters. 14, &15)
 
The owner of Showtime Movie Theaters Inc, Boardman, would like to estimate weekly gross revenue as a function of  advertising expenditure. The company hires you to do the analysis. The following historical data for a sample of eight weeks are given to you:

Weekly Gross Revenue ($1000s) Weekly TV Advertising ($1000s) Weekly Newspaper Adv. ($1000s) 
96 5.0 1.5
90 2.0 2.0
95 4.0 1.5
92 2.5 2.5
95 3.0 3.3
94 3.5 2.3
94 2.5 4.2
94 3.0 2.5

 
1. Develop a simple LRM to predict weekly gross revenue with the amount of TV advertising as the only IV. Please state the expected signs of the regression parameters.
2. Develop a multiple LRM to predict weekly gross revenue with both TV advertising and newspaper advertising as the IVs. Please state the expected signs of the regression parameters.
3. Use Excel to estimate the models in 1 and 2 above. 
(a) Is the estimated coefficient for TV advertising the same in the two models? Which one shows a higher level of precision and why?
(b) Interpret the estimated regression intercept and coefficients in each case. 
(c) Which of the two models do you prefer and why?
4. Interpret the standard error of estimate (Se) in each case
5. Interpret the coefficient of determination (R2) in each case
6. Is the multiple regression model statistically significant at = .05 level? What does this tell you ?
7. Test each of the multiple regression coefficients for statistical significance (use = .05) and interpret the results.
8. For the multiple regression model, which medium of advertising is more important in predicting gross revenue and why? 
9. Suppose the owner plans to spend $3000 a week on TV advertising and $1800 a week on newspaper advertising, how much should the owner expect to gross in revenue for a week (a) using the simple regression model, and (b) using the multiple regression model?

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Last revised: Tuesday, November 17, 2009.