UC Davis - STA 108 Applied Statistical Methods: Regression Analysis - Sample - Q3 Bonferroni or Working-Hotelling Methods
3. In a study on fuel efficiency of cars of old models, 10 pairs of observations are collected. See the table below. Let x represent the weight of the car (unit: 1000 pounds), and Y represent the fuel consumption (unit: gallons/100 miles).
Car Model Weight (x) Fuel Consumption (Y )
AMC Concord 3.4 5.5
Chevy Caprice 3.8 5.9
Ford Country Squire Wagon 4.1 6.5
Chevette 2.2 3.3
Toyota Corona 2.6 3.6
Ford Mustang Ghia 2.9 4.6
Mazda GLC 2.0 2.9
AMC Sprint 2.7 3.6
VW Rabbit 1.9 3.1
Buick Centry 3.4 4.9
Assume that all of the assumptions, including normality, hold for the following simple linear regression model: Y = b0 + b1x + e.
a. Find 90% simultaneous confidence intervals for the mean fuel consumptions of AMC Concord, Chevette, Toyota Corona, Mazda GLC, and Buick Centry using Bonferroni's
method. To save you some time, and least squares estimates for the regression coefficients are b0 = -0.363, b1 = 1.639; also, and the MSE of the regression is 0.084.
b. Find 90% simultaneous confidence intervals for the mean fuel consumptions in part a using Working-Hotelling's method.
c. Which method, Bonferroni or Working-Hotelling, is preferred in this case? and why?
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