Econ 3790           Homework # 3             Dr. Usip
                                                                 Fall 2017

Note: Even though this assignment is worth 16 points, doing the problems will help you immensely in preparing for the final exam.

Question 1: One-Way ANOVA Problems: F tests (Chapter 13)
Part I. Problem # 5, p. 561.

Part II. That the starting salaries of new accounting graduates would differ according to geographic regions of the United States seems logical. A random sample of accounting firms is taken from three geographic regions - South, Northeast, and West - and each is asked to state the starting salary for newly employed accounting graduates. The table below contains the salary data (in $000). 



















1. From the above problem description identify the following:
     a. Response variable. 
     b. Factor. 
     c. Treatments. Please list them.
     d. Statistical or experimental units.

2. Is this a case of balanced or unbalanced experimental design? Please explain your answer.

3. Does a significant difference exists in the average starting salaries of the accounting graduates due to regional differences? Please state the null hypothesis and the alternative hypothesis for investigating this question.

4. Is there a significant difference in the average wages of mechanics in the four townships?
    State the correct null and the alternative hypotheses for investigating this question.

5. Use Excel to compute the ANOVA table (attach your Excel output). 
6. From your Excel output, would you reject or fail to reject your null hypothesis in part 3 above at 1% level of significance?  
    a. Use the critical value approach. Please state the decision rules.
    b. Use the p-value approach. Please state the decision rules.

c. Based on your conclusions in parts 'a' and 'b', in which region would you accept a job offer
       and why (assuming you are an accounting graduate)? Please be specific.

Question 3: Simple Regression Problem (Chapter 14)
The following data are the monthly salaries (Salary) and the grade point averages (GPA) for students who obtained a bachelor's degree in business administration. 

GPA Salary
2.6 3600
3.4 3900
3.6 4300
3.2 3800
3.5 4200
2.9 3900

Note: Please attach Excel output with complete results.
. Use the data to construct a scatter diagram that relates Salary to GPA.

. What does the scatter diagram in part 1 above indicate about the type and degree of relationship between the two variables?

. Try to approximate the relationship by drawing a straight line through the data.

. Formulate a simple LRM that represents the true relationship between the two variables. Which one is the DV (Y) and which one is the IV (X)?
  b. On the basis of theory or common sense, what are your expected signs of the regression parameters? 

5. Estimate the model that you have formulated in part 4a. Use the results to answer all the questions as stated in the text.
  a. What is your estimated sample regression line (SRL)? Write it out from the Excel output; show all solutions if you choose to solve the problem manually by using the regression formulas to derive the estimated SRL.
  b. Interpret the estimates for the intercept (or 'a') and the slope (or 'b') of your estimated SRL.
  c. Interpret the estimates for the intercept (or 'a') and the slope (or 'b') of your estimated SRL.
  d. How strong is the relationship between Salary and GPA? 
  e. Are the regression parameters (A, B) statistically significant? Use α = .05 for your test.  
  f. Is the regression parameter (A) economically/practically significant as suggested by your theory in part 4b above? Use α = .05 for your test.    

6. Linda will earn her degree in Business Administration in two weeks with a GPA of 3.0, predict her starting monthly salary?

Question 4: Multiple Regression Problem (Chapters. 15)

The manager of Showtime Movie Theaters Inc, Boardman, would like to estimate the effects of advertising expenditures on weekly gross revenue using regression analysis. The manager hires you to do the analysis for her. 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

Note: Please attach Excel output with complete results.
. Explain to the managers the causal relationship between Weekly Gross Sales, TV Advertising and Newspaper Advertising. In your statement identify the DV (call it Y) and the IVs (call them X1 and X2, respectively).

  b. Formulate a multiple LRM that relates Y to X1 and X2.  
  c. What are your expected signs of the regression parameters?

2a. Use Excel to estimate the model that you have specified in part 1b above.
  b. Are the estimated signs consistent with you expectation on the basis of theory? Please be specific.
. Use the results in your Excel output to answer these questions
   a. Interpret the coefficient of determination estimate in the context of this problem.

   b. Interpret the meaning of the estimates for ‘a’, ‘b1, and ‘b2

   c. Is the multiple LRM you formulated in part 1b statistically significant? Verify at 5% level of significance. 

   d. 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?  

   e. Which medium of advertising is relatively more important in predicting gross revenue and why? 

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Last revised: Saturday, November 18, 2017.