What to Buy? A marketing researchexperiment was conducted to study the relationshipbetween the length of time necessary for a buyerto reach a decision and the number of alternative packagedesigns of a product presented. Brand names wereeliminated from the packages and the buyers madetheir selections using the manufacturers productdescriptions on the packages as the only buying guide.The length of time necessary to reach a decision was recorded for 15 participants in the marketing researchstudy.Length of DecisionTime, y (sec) 5, 8, 8, 7, 9 7, 9, 8, 9, 10 10, 11, 10, 12, 9Number ofAlternatives, x 23 4a. Find the least-squares line appropriate for these data.b. Plot the points and graph the line as a check onyour calculations.c. Calculate s2.d. Do the data present sufficient evidence to indicatethat the length of decision time is linearly related tothe number of alternative package designs? (Test atthe a .05 level of significance.)e. Find the approximate p-value for the test and interpretits value.f. If they are available, examine the diagnosticplots to check the validity of the regressionassumptions.g. Estimate the average length of time necessary toreach a decision when three alternatives are presented,using a 95% confidence interval.

ST 512 Week Six Notes MaLyn Lawhorn September 18, 2017 and September 20, 2017 Moving on to R 2 Before we move into the mathematical deﬁnition of R , let’s ﬁrst consider the following two mod- els. The question we want to ask looking at these two models is which Y 0 ▯ +1▯ x would yield a better approximation line. The answer is the the model on the...