86. The following data on y  glucose concentration

(g/L) and x  fermentation time (days) for a particular blend of malt liquor was read from a scatter plot in the article Improving Fermentation Productivity with Reverse Osmosis (Food Tech., 1984: 92—96):

x 1 2 3 4 5 6 7 8 y 74 54 52 51 52 53 58 71

a. Verify that a scatter plot of the data is consistent with the choice of a quadratic regression model.

b. The estimated quadratic regression equation is y  84.482  15.875x  1.7679x2. Predict the value of glucose concentration for a fermentation time of 6 days, and compute the corresponding residual.

c. Using SSE  61.77, what proportion of observed variation can be attributed to the quadratic regression relationship?

d. The n  8 standardized residuals based on the quadratic model are 1.91, 1.95, .25, .58, .90, .04, .66, and .20. Construct a plot of the standardized residuals versus x and a normal probability plot. Do the plots exhibit any troublesome features?

e. The estimated standard deviation of that is, is 1.69. Compute a b ˆ
0  b ˆ 1162  b ˆ 21362 mˆ
Y#6 688 CHAPTER 12 Regression and Correlation Obs Linoleic Kerosene Antiox Betacaro 1 30.00 30.00 10.00 0.7000 2 30.00 30.00 10.00 0.6300 3 30.00 30.00 18.41 0.0130 4 40.00 40.00 5.00 0.0490 5 30.00 30.00 10.00 0.7000 6 13.18 30.00 10.00 0.1000 7 20.00 40.00 5.00 0.0400 8 20.00 40.00 15.00 0.0065 9 40.00 20.00 5.00 0.2020 10 30.00 30.00 10.00 0.6300 11 30.00 30.00 1.59 0.0400 12 40.00 20.00 15.00 0.1320 13 40.00 40.00 15.00 0.1500 14 30.00 30.00 10.00 0.7000 15 30.00 46.82 10.00 0.3460 16 30.00 30.00 10.00 0.6300 17 30.00 13.18 10.00 0.3970 18 20.00 20.00 5.00 0.2690 19 20.00 20.00 15.00 0.0054 20 46.82 30.00 10.00 0.0640 95% CI for mY#6.

f. Compute a 95% PI for a glucose concentration observation made after 6 days of fermentation time.