m Q1:A marketing research firm was engaged by an automobile manufacturer to conduct a pilot study investigate the likeli

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M Q1 A Marketing Research Firm Was Engaged By An Automobile Manufacturer To Conduct A Pilot Study Investigate The Likeli 1 (127.43 KiB) Viewed 36 times

m Q1:A marketing research firm was engaged by an automobile manufacturer to conduct a pilot study investigate the likelihood that a family will purchase a new car during the next year. A random sample of 33 suburban families was selecled. Data on annual family income (X1, in thousand dollars) and the current age of the oldest family automobile (X2, in years) were obtained. A follow up interview conducted 12 months later was used to determine whether the family actually purchased a new car (Y = 1) or did not purchase a new car (Y=0) during the year. The following logistic model was fitted: Regression Equation P(1) exp(Y")/(1 + exp(Y)) Y -4.74 +0.0677 X1 ($1000) + 0.599 X2(years) Odds Ratios for Continuous Predictors Odds Ratio 95% CI X1 ($1000) 1.0701 (1.0128, 1.1306) X2(years) 1.8196 (0.8471, 3.9085) a) Explain the meaning of the estimated y-intercept? b) Calculate the predicted P(Y=1) for X1=50 and X2=3? c) Suppose there are 5 families whose income is X2=50 thousands and their oldest automobile is X2=3 years, find the probability that at least 4 of them purchased the new car? d) Discuss the meaning of the partial slope of X1? Is there evidence that this slope is significant? e) Obtain exp(52) and exp(5 * 52). What do these numbers mean? (b2 is the estimated partial slope of X2)? Discuss the significance of X2 in predicting the probability that a family purchases a new car during the next year.