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 | 12345678 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 ˆY6—that is,
ˆ

0

ˆ

1(6)
ˆ

2(36)—is 1.69. Compute a 95% CI for Y6.

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