HI 6007 Statistics for Business Decision Making

Q1:

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 website, April 17, 2012). The dataset in Excel file DJIAS&P500.xlsx

Develop a scatter diagram with DJIA as the independent variable.
Develop the estimated regression equation.
Test for a significant relationship. Use α 5 .05.
Did the estimated regression equation provide a good fit? Explain.
Suppose that the closing price for the DJIA is 13,500. Predict the closing price for the S&P 500.
Should we be concerned that the DJIA value of 13,500 used to predict the S&P 500 value in part (e) is beyond the range of the data used to develop the estimated regres- sion equation?

Q2:

Consumers have a wide variety of options when choosing Wi-Fi and Bluetooth speaker systems. However, selecting a speaker system that provides good sound at a reasonable price can be difficult. The following data show the price and overall rating for a sample of 25 portable speaker systems that Consumer Reports tested (Consumer Reports website, January 28, 2014). The overall rating is based upon the sound quality, ease of use, and versatility of the speaker, with higher ratings indicating better overall performance. The dataset in Excel file PortableSpeakers.xlsx

Develop a scatter diagram with Price as the independent variable. Does there appear to be a relationship between the variables?
Develop the estimated regression equation that can be used to predict the rating given the price.
At the .05 level of significance, is there a significant relationship between the two variables?
Did the estimated regression equation provide a good fit?
Use residual analysis to determine if there are any outliers or influential observations. Briefly summarize your findings.
Consumer Reports also tested Wi-Fi and Bluetooth speaker systems developed for home use. One of the models tested is the JBLOnBeat Rumble with a price of $400. Assuming the estimated regression equation developed for the portable speaker sys- tems is also appropriate for home speaker systems, predict the overall rating for the JBLOnBeat Rumble speaker.

Q3:

One of the biggest changes in higher education in recent years has been the growth of online universities. The Online Education Database is an independent organization whose mission is to build a comprehensive list of the top accredited online colleges. The following table shows the retention rate (%) and the graduation rate (%) for 29 online colleges (Online Education Database website, January 2009). The dataset in Excel file OnlineEdu.xlsx.

Develop a scatter diagram with retention rate as the independent variable. What does the scatter diagram indicate about the relationship between the two variables?
Develop the estimated regression equation.
Test for a significant relationship. Use α = .05.
Did the estimated regression equation provide a good fit?
Suppose you were the president of South University. After reviewing the results, would you have any concerns about the performance of your university as compared to other online universities?
Suppose you were the president of the University of Phoenix. After reviewing the results, would you have any concerns about the performance of your university as compared to other online universities?

Q4:

Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance con- tract for its new computer wheel alignment and balancing machine. Managers feel that maintenance expense should be related to usage, and they collected the following information on weekly usage (hours) and annual maintenance expense (in hundreds of dollars). The dataset in Excel file Jensen.xlsx

Develop the estimated regression equation that relates annual maintenance expense to weekly usage.
Test the significance of the relationship in part (a) at a .05 level of significance
Jensen expects to use the new machine 30 hours per week. Develop a 95% prediction interval for the company’s annual maintenance expense.
If the maintenance contract costs $3000 per year, would you recommend purchasing it? Why or why not?

Q5:

The regional transit authority for a major metropolitan area wants to determine whether there is any relationship between the age of a bus and the annual maintenance cost. A sample of 10 buses resulted in the following data.

Develop the least squares estimated regression equation.
Test to see whether the two variables are significantly related with α =.05.
Did the least squares line provide a good fit to the observed data? Explain.
Develop a 95% prediction interval for the maintenance cost for a specific bus that is 4 years old. The dataset in Excel file xlsx.

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