Chapter 13.3, Problem 27E

The following data on y 5 glucose concentration (g/L) and x 5 fermentation time (days) for a particular blend of malt liquor was read from a scatterplot in the article “Improving Fermentation Productivity with Reverse Osmosis” (Food Tech., 1984: 92–96):

X	1	2	3	4	5	6	7	8
V	74	54	52	51	52	53	58	71

a. Verify that a scatterplot 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 ${\hat{\mu }}_{Y\cdot 6}$—that is, ${\hat{\beta }}_0+{\hat{\beta }}_1(6)+{\hat{\beta }}_2(36)$—is 1.69. Compute a 95% CI for ${\mu }_{Y\cdot 6}$

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