Suppose you fit the second order model y 0 1x 2x2 to n 25 data points Your estimate of 2 is 2 47, and the estimated standard error of the estimate is 15 a Test H0 2 0 against Ha 2 0 Use 05 b Suppose you want to determine only whether the quadratic curve opens upward that is as x increases, the slop...

a H 0 2 0 H a 2 0 The test statistic is The rejection region requires 2 05 2 025 in ...

Suppose you fit the second-order model y = 0 + 1x + 2x2 + to n

Question:

Suppose you fit the second-order model
y = β0 + β1x + β2x2 + ε
to n = 25 data points. Your estimate of β2 is 2 = .47, and the estimated standard error of the estimate is .15.
a. Test H0: β2 = 0 against Ha: β2 ≠ 0. Use α = .05.
b. Suppose you want to determine only whether the quadratic curve opens upward; that is. as x increases, the slope of the curve increases. Give the test statistic and the rejection region for the test for α = .05. Do the data support the theory that the slope of the curve increases as x increases? Explain.