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.

a. The prediction equation is = 61.3 + 0.35. Find the predicted number of defects for a car having assembly time (i) 12 hours (the minimum) and (ii) 54 hours (the maximum).

b. The first 11 plants were Japanese facilities and the rest were not. Let ₁ = time to assemble vehicle and ₂ = whether facility is Japanese 11 = yes, 0 = no2. The fit of the multiple regression model is  = 105.0 – 0.78₁  36.0₂. Interpret the coefficients that estimate the effect of ₁ and the effect of ₂.

c. Explain why part a and part b indicate that Simpson’s paradox has occurred.

d. Explain how Simpson’s paradox occurred. To do this, construct a scatterplot between y and ₁ in which points are identified by whether the facility is Japanese. Note that the Japanese facilities tended to have low values for both ₁ and ₂.