Chapter 13.5, Problem 44PB

Quality and productivity The table shows data from 27 automotive plants on y = number of assembly defects per 100 cars and x = time (in hours) to assemble each vehicle. The data are in the Quality and Productivity file on the book’s website.

Number of defects in assembling 100 cars and time to assemble each vehicle

Source: Data from S. Chatterjee, M. Handcock, and J. Simonoff, A Casebook for a First Course in Statistics and Data Analysis (Wiley, 1995); based on graph in The Machine That Changed the World, by J. Womack, D. Jones, and D. Roos (Macmillan, 1990).

1. a. The prediction equation is $\hat{y}$ = 61.3 + 0.35x. Find the predicted number of defects for a car having assembly time (i) 12 hours (the minimum) and (ii) 54 hours (the maximum).
2. b. The first 11 plants were Japanese facilities and the rest were not. Let x₁ = time to assemble vehicle and x₂ = whether facility is Japanese (1 = yes, 0 = no). The fit of the multiple regression model is $\hat{y}$ = 105.0 − 0.78x₁ − 36.0x₂. Interpret the coefficients that estimate the effect of x₁ and the effect of x₂.
3. c. Explain why part a and part b indicate that Simpson’s paradox has occurred.
4. d. Explain how Simpson’s paradox occurred. To do this, construct a scatterplot between y and x₁ in which points are identified by whether the facility is Japanese. Note that the Japanese facilities tended to have low values for both x₁ and x₂.