(Solved): (a) Compute the mean square error using equation \( s^{2}= \) MSE \( =\frac{\text { SSE }}{n-2} \). ...

(a) Compute the mean square error using equation \( s^{2}= \) MSE \( =\frac{\text { SSE }}{n-2} \). (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation \( s=\sqrt{\text { MSE }}=\sqrt{\frac{5 S E}{n-2}} \), (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of \( b_{1} \) using equation \( s_{b_{1}}=\frac{s}{\sqrt{\Sigma\left(x_{i}-\bar{x}\right)^{2}}} \). (Round your answer to three decimal places.) (d) Use the \( t \) test to test the following hypotheses \( (\alpha=0.05) \) : \[ \begin{array}{l} H_{0}: \beta_{1}=0 \\ H_{a}: \beta_{1} \neq 0 \end{array} \] Find the value of the test statistic. (Round your answer to three decimal places.) Find the \( D \) value. (Round your answer to four decimal places.) \( p \)-value \( = \) State your conclusion. Reject \( H_{0} \). We cannot conclude that the relationship between \( x \) and \( y \) is significant. Reject \( H_{0} \). We conclude that the relationship between \( x \) and \( y \) is slonillicant. Do not reject \( H_{0} \). We cannot conclude thot the relationship between \( x \) and \( y \) is significant. Do not reject \( H_{0} \). We conclude that the relationship between \( x \) and \( y \) is slgnificant. (e) Use the \( F \) test to test the hypotheses in part (d) at a \( 0.05 \) level of significance. Present the results in the analysis of variance table format. Set up the ANOVA table. (Round your values for MSE and \( F \) to two decimal places, and your \( p \)-value to three decimal places.) Find the value of the test statistic. (Round your answer to two decimal places.) Find the \( p \)-value. (Round your answer to three decimal places.) \( p \) value = State your conclusion. Do not reject \( H_{0} \). We cannot conclude that the relationship between \( x \) and \( y \) is significant. Reject \( H_{0} \). We cannot conclude that the relationship between \( x \) and \( y \) is significant, Reject \( H_{0} \). We conclude that the relationship between \( x \) and \( y \) is significant. Do not reject \( H_{0} \). We conclude that the relationship between \( x \) and \( \gamma \) is significant.