12. What to Buy? A marketing research experiment was conducted to study the relationship between the length of time necessary for a buyer to reach a decision and the number of alternative package designs of a product presented. The products were identical except for the package design. The length of time necessary to reach a decision was recorded for 15 participants in the marketing research study

a. Find the least-squares line appropriate for these data.

b. Plot the points and graph the line as a check on your calculations.

c. Calculate s2.

d. Do the data present sufficient evidence to indicate that the length of decision time is linearly related to the number of alternative package designs? (Test at the a 5.05 level of significance.)

e. Find the approximate p-value for the test and interpret its value.

f. If they are available, examine the diagnostic plots to check the validity of the regression assumptions.
g. Estimate the average length of time necessary to reach a decision when three alternatives are presented, using a 95% confidence interval.

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Length of Decision Time, y (sec) Number of Alternatives, x 5,8,8,7,9 7, 9, 8, 9, 10 10, 11, 10, 12, 9 2 3 4