11.42 Suppose you fit the second-order model to data points. Your estimate of ‚ is and the standard error of the estimate is sbN 2 = 0.13.

bN 2 = 0.35, n = 30 b2 Y = b0 + b1x + b2x 2 + e bN 2 = 0.55 sbN 2 = 0.181 bN 1 = 0.62 sNb 1 = 0.273 y = sales for upcoming Christmas x2 = sales for August of current year x1 = previous Christmas sales Y = b0 + b1x1 + b2x2 + e x2 x2 yN = 0, 2, 4, 6, 8

(x1 = 1)

(x1 x2 = 0)

yN a = 0.05 x2 2 sNb 3 = 0.03 yN

= 50 + 5x1 + 5x2 - 0.1x 22 Y = b0 + b1x1 + b2x2 + b3x22

+ e a Test the null hypothesis that the mean value of Y is related to x by the (first-order) linear model Test against the alternative hypothesis that the true relationship is given by the quadratic model (a second-order linear model)
Use .
b Suppose you wanted only to determine whether the quadratic curve opens upward, that is, whether the slope of the curve increases as x increases. Give the test statistic and the rejection region for the test for . Do the data support the theory that the slope of the curve increases as x increases? Explain.
c What is the value of the F statistic for testing the null hypothesis that ?
d Could the F statistic in part

(c) be used to conduct the tests in parts

(a) and (b)? Explain.