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 ($ thousands) last month for each client sampled.
2. Determine the estimated sales if 40 contacts are made.
3. Determine the standard error of estimate.
4. Suppose a large sample is selected (instead of just 10). About 95 percent of the predictions regarding sales would occur between what two values?
Solution: 1.) Using Excel to obtain the regression equation we get the following results:
From the table above we find the regression equation is:
2) We need to evaluate the regression equation at, obtaining
(3) Looking at the Excel table we find that the standard error if the estimate is given by:
(4) For, we get the prediction
For a large sample like this () we have the 95% prediction interval is given by: