ECON 2331: Economic and Business Statistics 2

Assignment 4 (105 marks; 5%)

To receive full marks, you need to show all your work.

1.   A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X1), age of the individuals (X2), and the gender of the individual (X3; zero representing female and one representing male) was performed on a sample of ten students, and the following results were obtained: (19 marks total)

a.   Write the regression equation for the above. (2 marks)

b.   Interpret the meaning of the coefficient of X3. (3 marks)

c.   Compute the coefficient of determination, and state its meaning. (3 marks)

d.  Use the built-in functions in Excel/XLSTAT® to calculate the p-value associated with the coefficient of X1. Is it significant? Use α = 0.05. Now, use the t-Table and interpolate the p-value. (3 marks)

e.   Use the built-in functions in Excel/XLSTAT® to calculate the p-value associated with the coefficient of X2. Is it significant? Use α = 0.05. Now, use the t-Table and interpolate the p-value. (3 marks)

f.    Use the built-in functions in Excel/XLSTAT® to calculate the p-value associated with the coefficient of X3. Is it significant? Use α = 0.05. Now, use the t-Table and interpolate the p-value. (3 marks)

g.   Perform. an F-test, what is your conclusion. (2 marks)

2.   The price of OZ, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of companyʹs stock sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown: (13 marks total)

a.   Use Excel/XLSTAT® to estimate an equation that can be used to predict the price of the stock. (3 marks)

b.   Interpret the coefficients of the estimated regression equation that you found in part (a). (4 marks)

c.   At 95% confidence, determine which variables are significant and which ones are not. (3 marks)

d.  If, in a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be? Use XLSTAT® and construct a prediction interval. (3 marks)

3.   Concern over the number of car thefts grew into a project to determine the relationship between car thefts in provinces and the variables, X1  = Police per  10,000 persons. X2  = Expenditure by local government for police protection, in thousands, and X3  = New passenger car registrations, in thousands. Data from 10 provinces were collected. The Excel/XLSTAT® regression results are: (17 marks total)

a.   Perform. a test to see if the model is significant overall. Use α = 0.01. What is your conclusion? (3 marks)

b.   Perform. a test for each regression coefficient, using both 0.05 and 0.01 significance levels. What are your conclusions? (4 marks)

c.   Do the regression coefficients have the algebraic sign you might expect? (3 marks)

d.  What are the consequences of multicollinearity in multiple regression? Is there any multicollinearity that you detect for this model? (4 marks)

e.   Fully interpret the meaning of the estimated coefficient of X3. (3 marks)

4.   The Consumer Reports Restaurant Customer Satisfaction Survey is based

upon 148,599 visits to full-service restaurant chains (Consumer Reports website, February 11, 2009). Assume the available data on the Portal labelled Restaurant are representative of the results reported. The variable type indicates whether the restaurant is an Italian restaurant or a seafood/steakhouse. Price indicates  the average amount paid per person for dinner and drinks, minus the tip.

Score reflects diners’ overall satisfaction, with higher values indicating greater overall satisfaction. A score of 80 can be interpreted as very satisfied. (31 marks total)

a.   Develop the estimated regression equation to show how overall customer satisfaction is related to the independent variable average meal price. (3 marks)

b.   At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between overall customer satisfaction and average meal price. (2 marks)

c.   Develop a dummy variable that will account for the type of restaurant (Italian or seafood/steakhouse). (2 marks)

d.  Develop the estimated regression equation to show how overall customer satisfaction is related to the average meal price and the type of restaurant. (3 marks)

e.   Is type of restaurant a significant factor in overall customer satisfaction? (3 marks)

f.    Predict the Consumer Reports customer satisfaction score for a seafood/steakhouse that has an average meal price of $20. How much would the predicted score have changed for an Italian restaurant? (3 marks)

g.   Calculate both a Confidence Interval, C.I., and a Prediction Interval, P.I., for the predicted scores in part (f). Show all your results. (6 marks)

h.   Now, redo part (g) for an average meal price of $27. Compare your findings with what you found in part (g). What is your conclusion? (9 marks)

5.   A sample containing years to maturity and yield (%) for 40 corporate bonds is contained in the data file named CorporateBonds (Barron’s, April 2, 2012) available on the portal. (13 marks total)

a.   Use Excel® or XLSTAT® to develop a scatter diagram of the data, using x = years to maturity as the independent variable. Does a simple linear   regression model appear to be appropriate? (3 marks)

b.   Develop an estimated regression equation, with x = years to maturity and x2 as the independent variables. (4 marks)

c.   As an alternative, fit a model using the natural logarithm of years to maturity as the independent variable; that is, = bo  +b1  ln(x). Does the estimated regression using the natural logarithm of x provide a better fit than the estimated regression developed in part (b)?Explain. (6 marks)

6.   A study investigated the relationship between audit delay (Delay), the length of time from a company’s fiscal year-end to the date of the auditor’s report, and variables that describe the client and the auditor. Some of the independent variables that were included in this study follow: (12 marks total)

Industry   A dummy variable coded 1 if the firm was an industrial company or if the firm was a bank, savings and loan, or insurance company

Public        A dummy variable coded 1 if the company was traded on an

organized exchange or over the counter; otherwise coded 0

Quality     A measure of overall quality of internal controls, as judged by

the auditor, on a five-point scale ranging from “virtually none” (1) to “excellent” (5)

Finished   A measure ranging from 1 to 4, as judged by the auditor,

where 1 indicates “all work performed subsequent to year-end” and 4 indicates “most work performed prior to year-end.”

A sample of 40 companies provided the data that is available on the course portal.

a.   Develop the estimated regression equation using all of the independent variables. (3 marks)

b.   Did the estimated regression equation developed in part (a) provide a good fit? Explain. (3 marks)

c.   Develop a scatter diagram showing Delay as a function of Finished. What does this scatter diagram indicate about the relationship between Delay and Finished? (3 marks)

d.  On the basis of your observations about the relationship between Delay and Finished, develop an alternative estimated regression equation to the one developed in (a) to explain as much of the variability in Delay as possible. (3 marks)