Solution Found!
Suppose you fit the second-order modely = ?0 + ?1x + ?2x2
Chapter 12, Problem 50E(choose chapter or problem)
Suppose you fit the second-order model
\(y=\beta_0+\beta_1 x+\beta_2 x^2+\varepsilon\)
to n = 25 data points. Your estimate of \(\beta_2\) is \(\hat{\beta}_2=.47\), and the estimated standard error of the estimate is .5.
a. Test \(H_0: \beta_2=0\) against \(H_{\mathrm{a}}: \beta_2 \neq 0\). Use \(\alpha=.05\).
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 \(\alpha=.05\). Do the data support the theory that the slope of the curve increases as x increases? Explain.
Questions & Answers
QUESTION:
Suppose you fit the second-order model
\(y=\beta_0+\beta_1 x+\beta_2 x^2+\varepsilon\)
to n = 25 data points. Your estimate of \(\beta_2\) is \(\hat{\beta}_2=.47\), and the estimated standard error of the estimate is .5.
a. Test \(H_0: \beta_2=0\) against \(H_{\mathrm{a}}: \beta_2 \neq 0\). Use \(\alpha=.05\).
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 \(\alpha=.05\). Do the data support the theory that the slope of the curve increases as x increases? Explain.
ANSWER:Step 1 of 4
a) The hypotheses of interest concern the parameter 
The test statistic is a t -statistic formed by dividing the sample estimate 
parameter 
These estimates,
The calculated t -value,
Test statistic:
