12.42 Refer to Exercise 12.7. Portions of the MINITAB printout are shown here.

a. Find a 95% confidence interval for the average value of y when x = 2.

b. Find a 95% prediction interval for some value of y to be observed in the future when x = 2.

c. The last line in the third section of the printout indicates a problem with one of the fitted values. What value of x corresponds to the fitted value =1.5429? What problem has the MINITAB program detected?

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MINITAB output for Exercise 12.42 Regression Analysis: y versus x The regression equation is y 6.00 0.557 x Predictor Constant x Coef 6.0000 SE Coef 0.1759 34.10 0.000 -0.55714 0.04518 -12.33 0.000 Predicted Values for New Observations New Obe 2 Fit SE Fit 95.0% CI 4.8857 0.1027 (4.6006, 5.1708) 95.06 PI (4.2886, 5.4829) 1.5429 0.2174 (0.9392, 2.1466) 10.7430, 2.3427) x x denotes a point that is an outlier in the predictors. Values of Predictors for New Observations New Obs 12 1 2 x 2.00 8.00