Management Analytics: Linear Regression Assignment

Question One

Linear Regression Assignment Please see attached assignment questions & data sets

The Elysian Mattress Company manufactures high-quality mattresses and accessories at plants in New Brunswick and Manitoba. The mattresses sell for several thousand dollars each and have become something of a status symbol among those who can afford them. Elysian has retail outlets near both of its plants, but otherwise distributes through dealers and representatives located in Canada’s twenty-four largest metropolitan areas.  The company relies on word-of-mouth and dealer advertising for promotion of its products but also places some of its own extra local advertising in each of the cities.

Brad Fellowes, Elysian’s marketing manager, has been reviewing the expenses for advertising across the country.  The company’s reputation is excellent, and he is not convinced that the nearly $900,000 spent on extra advertising last year was worth it.  

1. versus Ad$perCapita.  Brad decides, correctly (he’s a Queen’s grad), that plot 2) gives him the best information about any possible relationship between advertising expenses and revenues.  Explain why Brad made this choice.

2. Perform a simple linear regression of RevPerCapitaversus Ad$perCapita.  Does it appear that there is a statistically significant relationship between revenues and advertising expenses? Explain.

3. How much of the variation in revenues can be ‘explained’ with advertising expenses?

4. Give clear interpretations in words of both the slope and intercept in this regression model.

5. Calculate a prediction for Gross Revenues in London next year if Brad drops his per capita advertising expenditures from the current 7.43 cents to 4 cents.  Also calculate a 95% prediction interval for this estimate.

6. Brad’s assistant (not a Queen’s grad) wants to use the model to predict revenues in Ottawa if per capita advertising expenditures are increased to 12 cents.  What advice would you give him?

7. What advice would you give Brad about stopping all advertising? Be sure to justify your conclusion with calculations.

The “market model” in Finance relates the monthly rate of return, R, on a stock to the monthly rate of return on the market, R_m.  The mathematical model is the linear relationship:

Where the error term  is assumed to satisfy the requirements for linear regression.  For practical purposes,  R_m  is taken to be an index like the NYSE Composite Index.  The coefficient  (called the stock’s beta) measures the sensitivity of the stock to the level of the market.  If  > 1 ( < 1)  the stock is more (less) sensitive to changes in the overall market.  

Question Two

The file HOST contains the monthly rate of return for Host International Inc. over five years, and the corresponding monthly percent return for the NYSE Composite Index.

1. Is Host more or less volatile than the market? (Hint: Ho: = 1 would infer Host and the NYSE are equally volatile)

2. What is the estimated return from Host if the overall market return is 0?

3. What proportion of Host’s return variability is explicable by market swings?

Shoreline Inc. is a high-end outdoor clothing manufacturer with a long history of mail-order catalogue sales.  Since 1995, the company has also maintained a web-site and marketed through online channels.

Shoreline’s catalogues are expensive to produce and have a negative environmental impact; thus the company has offered customers the option to decline catalogue mailings and receive, instead, occasional promotional emails linking to Shoreline’s online catalogue.  Many customers have taken this option, and the company is particularly interested in understanding the factors affecting success in marketing in this way.

Elaine McCormick, a web-services analyst at Shoreline, randomly sampled 120 files from ‘email only’ customers and conducted some background research through Shoreline’s sales history data and the customers’ registration information.  It was not possible to get complete data on the whole sample, but 103 full records were eventually obtained.  The types of data collected are listed in the following table.

Here are selected summary statistics for her sample and an excerpt of the data for the first three and last two customers in the sample.

You have now run a full regression on all of the Shoreline data.  The report and some related questions follow.

 a. How much of the variation in Spending is associated with these variables?

b. Is the overall model statistically significant?  Explain your answer.

Write an interpretation of the intercept coefficient in this model.  Be sure to give an interpretation in the context of this model, not a generic explanation.

c. Write clear interpretations of the slope coefficients for each of the five variables in the model and comment on their statistical significance.  Be sure to give interpretations in the context of this model, not a generic explanation.

d. Is gender of the customer an important factor for spending at Shoreline?  Explain your answer.

e. Write out the equation for the multiple regression model.  Include all variables, whether statistically significant or not.   Now make a prediction of the spending for a male customer who receives 18 emails per year, has been a customer for eight years, and has an estimated income higher than $100,000.  Use the approximate formula to calculate a 95% approximate confidence interval for your prediction.