Quality Control A manufacturerrecorded the number of defective items (y) producedon a

Chapter 13, Problem 34

(choose chapter or problem)

Quality Control A manufacturerrecorded the number of defective items (y) producedon a given day by each of 10 machine operatorsand also recorded the average output per hour (x1) foreach operator and the time in weeks from the lastmachine service (x2).y x1 x213 20 3.01 15 2.011 23 1.52 10 4.020 30 1.015 21 3.527 38 05 18 2.026 24 5.01 16 1.5The printout that follows resulted when these data wereanalyzed using the MINITAB package using the model:E(y) b0 b1x1 b2x2MINITAB output for Exercise 13.34Regression Analysis: y versus x1, x2The regression equation isy = -28.4 + 1.46 x1 + 3.84 x2Predictor Coef SE Coef T PConstant -28.3906 0.8273 -34.32 0.000x1 1.46306 0.02699 -54.20 0.000x2 3.8446 0.1426 26.97 0.000S = 0.548433 R-Sq = 99.8% R-Sq(adj) = 99.7%Analysis of VarianceSource DF SS MS F PRegression 2 884.79 442.40 1470.84 0.000Residual Error 7 2.11 0.30Total 9 886.90Source DF Seq SSx1 1 666.04x2 1 218.76 a. Interpret R2 and comment on the fit of the model.b. Is there evidence to indicate that the model contributessignificantly to the prediction of y at thea .01 level of significance?c. What is the prediction equation relating y and x1when x2 4?d. Use the fitted prediction equation to predict thenumber of defective items produced for an operatorwhose average output per hour is 25 and whosemachine was serviced 3 weeks ago.e. What do the residual plots tell you about the validityof the regression assumptions?