# Statistics

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

[Please refer to the attachment for the data]

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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#### Solution Summary

The solution provides detailed step-by-step method of performing Regression Analysis and Correlation Hypothesis Test in EXCEL. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained and the Regression Analysis has been shown in details.This solution provides students with a clear perspective of the underlying statistical aspects related to Correlation and Regression.