Regression in Business Analytics

https://www.linkedin.com/in/aykhaled/

Problem 1

The Dow Jones Industrial Average (DJIA) and the Standard & Poor’s 500 (S&P 500) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. The closing price for the DJIA and the S&P 500 for 15 weeks, beginning with January 6, 2012, follow (Barron’s Web site, April 17, 2012).

data : data1.csv

1.a)

Develop an estimated regression equation showing how S&P 500 is related to DJIA. What is the estimated regression model?

1.b)

What is the 95 percent confidence interval for the regression parameter b1? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter b1 is equal to zero?

1.c)

What is the 95 percent confidence interval for the regression parameter b0? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter b0 is equal to zero?

1.d)

Suppose that the closing price for the DJIA is 13,500. Estimate the closing price for the S&P 500.

1.e)

Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value we have just calculated is beyond the range of the DJIA used to develop the estimated regression equation?

Problem 2

Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.

data : data2.csv

2.a)

Develop an estimated regression equation with the amount of television advertising as the independent variable. Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?

2.b)

How much of the variation in the sample values of weekly gross revenue does the model in part a explain?

2.c)

Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. Is the overall regression statistically significant at the 0.05 level of significance? What is the interpretation of this relationship?

2.d)

How much of the variation in the sample values of weekly gross revenue does the model in part c explain?

2.e)

Given the results in parts a and c, what should your next step be? Explain.

2.f)

What are the managerial implications of these results?

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