A manufacturer recorded the number of defective items (y) produced on a given day by each of 10 machine operators and also recorded the average output per hour (x1) for each operator and the time in weeks from the last machine service (x2).

The printout that follows resulted when these data were analyzed using the MINITAB package using the model:
E(y) = β0 + β1x1 + β2x2
MINITAB output for Exercise 13.34
Regression Analysis: y versus x1, x2
The regression equation is
y = -28.4 + 1.46 x1 + 3.84 x2

a. Interpret R2 and comment on the fit of the model.
b. Is there evidence to indicate that the model contributes significantly to the prediction of y at the a = .01 level of significance?
c. What is the prediction equation relating Å· and x1 when x2 = 4?
d. Use the fitted prediction equation to predict the number of defective items produced for an operator whose average output per hour is 25 and whose machine was serviced 3 weeks ago.
e. What do the residual plots tell you about the validity of the regression assumptions? The data were fitted using the quadratic model,

Transcribed Image Text:

0050050005 x-32-413 251 x| 2 1 2 1 3 2 3 1 2 1 20 15 23 10 30 21 38 18 24 16 3112057561 212 Coef red1ctor Constant-28.3906 xl x2 SE Coef 0.8273 0.02699 0.1426 -34.32 0.000 -54.20 0.000 26.97 0.000 I.46306 3.8446 S 0.548433 R-Sq 99.8% R-Sq (adj) 99.7 - - Analysis of Variance DF Source Regression Residual Error 7 Total MS 2 884.79 442.40 1470.84 0.000 2.11 0.30 9 886.90 Source DF Seg SS xl x2 1 666.04 1 218.76 Normal Probability Plot of the Residuals (res ponse is y) -0.5 0.5 99 95 90 70 60 50 40 30 20 05 1 Residuals versus the Fitted Values (response is ) 0050 0.25 0.00 -0.25 -0.50 -0.75- 10 15 Fitted Value 20 25 30