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    Statistics: Stereo Speakers, Auto Speeds and Fuel Consumption for New Cars Sold

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    See attached file for tables.

    Set of problems. Show all essential work.

    Problem 1
    Consider the following prices and accuracy ratings for 27 stereo speakers.
    (a) Make a scatter plot of accuracy rating as a function of price.
    (b) Calculate the correlation coefficient. At ? = .05, does the correlation differ from zero?
    (c) In your own words, describe the scatter plot. (Data are from Consumer Reports 68, no. 11 [November 2003], p. 31.
    (d) Develop the regression equation. Interpret the slope and the Y-intercept

    Problem 2
    A study is conducted concerning automobile speeds and fuel consumption rates. The following data is collected:

    Speed MPG
    44 22
    51 26
    48 21
    60 28
    66 33
    61 32

    a. Plot these data in a scatter diagram.
    b. Compute the coefficient of correlation. Explain
    c. Compute the coefficient of determination. Explain
    d. Determine the regression equation. Interpret the regression equation. Where does the equation cross the Y-axis?

    Problem 3
    Tem Rousos, president of Rousos Ford, believes there is a relationship between the number of new cars sold and the number of sales people on duty. To investigate he selects a sample of eight weeks and determines the number of new cars sold and the number of sales people on duty for that week.

    Week Sales staff Cars sold
    1 5 53
    2 5 47
    3 7 48
    4 4 50
    5 10 58
    6 12 62
    7 3 45
    8 11 60

    a. Plot these data in a scatter diagram.
    b. Compute the coefficient of correlation. Explain
    c. Compute the coefficient of determination. Explain
    d. Determine the regression equation. Interpret the regression equation. Where does the equation cross the Y-axis? How many additional cars can the dealer expect to sell for each additional salesperson employed?

    Problem 4
    Listed below is the net sales in $ million for Home Depot, Inc., and its subsidiaries from 1993 to 2004.

    YEAR NET SALES
    1993 9,240
    1994 12,355
    1995 15,456
    1996 19,873
    1997 24,913
    1998 30,125
    1999 38,423
    2000 45,989
    2001 53,564
    2002 58,654
    2003 64,290
    2004 73,675

    Determine the least squares equation. On the basis of this information, what are the estimated sales for 2005 and 2006?

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    Complete, neat and step-by-step solutions are provided in two attached Excel files.

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