Mr. James McWhinney, president of Daniel-James Financial Services, believes ther

Question

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 indicates the number of client contacts last month and the Y column shows the value of sales (S thousands) last month for each client sampled. (Round your answers to 3 decimal places.) Number of Contacts, ( thousands), Contacts, ( thousands) Sales Number of Sales 14 12 20 16 46 24 14 28 30 80 23 48 50 30 90 85 120 110 50 a. Determine the .95 confidence interval, in thousands of dollars, for the mean of all sales personnel who make 40 contacts b. Determine the .95 prediction interval, in thousands of dollars, for a particular salesperson who makes 40 contacts

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = -12.201038 + 2.1946418 X
Sample size: 10
R (correlation coefficient) = 0.97536215
R-sq = 0.95133132
Estimate of error standard deviation: 9.3104457

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) 95% confidence interval: (68.289, 82.881)

b) 95% prediction interval: (52.909, 98.260)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -12.201038 6.559576 0 8 -1.8600345 0.0999 Slope 2.1946418 0.17550018 0 8 12.505069 <0.0001

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