(Solution) - Suppose you fit the second order model y 0 1x -(2025 Original AI-Free Solution)

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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 slope of the curve increases. Give the test statistic and the rejection region for the test for ? = .05. Do the data support the theory that the slope of the curve increases as x increases? Explain.