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# Regression analysis

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1. Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The X column indi-cates the number of client contacts last month, and the Y column shows the value of sales (\$ thou-sands) last month for each client sampled.

Number of contacts
X Sales (\$ thousands)
Y Number of contacts
X Sales (\$ thousands)
Y
14 24 23 30
12 14 48 90
20 28 50 85
16 30 55 120
46 80 50 110

a.Determine the regression equation.

b.Determine the estimated sales if 40 contacts are made.

2. For a sample of 32 large U.S. cities, the correlation between the mean number of square feet per office worker and the mean monthly rental rate in the central business district is .363. At the .05 significance level, can we conclude that there is a negative association in the population between the two variables?

3. The following table gives the annual amount of scrap produced by Machine Products, Inc. Determine the least squares trend equation. Estimate the amount of scrap for the year 2003.

Year Code Scrap (tons)
1997 1 2.0
1998 2 4.0
1999 3 3.0
2000 4 5.0
2001 5 6.0

4. A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:

At the .02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards?

5. A study of 20 worldwide financial institutions showed the correlation between their assets and pretax profit to be .86. At the .05 significance level, can we conclude that there is positive correlation in the population?