Suppose you fit the second-order model y = b0 + b1 x + b2 x2 + e
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Suppose you fit the second-order model y = b0 + b1 x + b2 x2 + e to n = 30 data points. Your estimate of b2 is b n 2 = .52, and the estimated standard error of the estimate is .18.
a. Test H0: b2 = 0 against Ha: b2 0. Use a = .05.
b. Suppose you want to determine only whether the quadratic curve opens upward; that is, as x increases, the slope of the curve would increase. Give the test statistic and the rejection region for the test for a = .05. Do the data support the theory that the slope of the curve increases as x increases? Explain.
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