Consider the sample regression function $\widehat { Y } _ { i } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } X _ { i }$
The table below lists estimates for the slope $\left( \widehat { \beta } _ { 1 } \right)$ and the variance of the slope estimator $\left( \widehat { \sigma } _ { \widehat { \beta } _ { 1 } } ^ { 2 } \right)$ In each case calculate the p -value for the null hypothesis of $\beta _ { 1 } = 0$ and a two-tailed alternative hypothesis. Indicate in which case you would reject the null hypothesis at the 5 % significance level.
$\begin{array} { | c | c | c | c | c | }
\hline \widehat { \beta } _ { 1 } & - 1.76 & 0.0025 & 2.85 & - 0.00014 \
\hline \hat { \sigma } _ { \widehat { \beta } _ { 1 } } ^ { 2 } & 0.37 & 0.000003 & 117.5 & 0.0000013 \
\hline
\end{array}$

Question

Consider the sample regression function $\widehat { Y } _ { i } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } X _ { i }$
The table below lists estimates for the slope $\left( \widehat { \beta } _ { 1 } \right)$ and the variance of the slope estimator $\left( \widehat { \sigma } _ { \widehat { \beta } _ { 1 } } ^ { 2 } \right)$ In each case calculate the  p -value for the null hypothesis of $\beta _ { 1 } = 0$ and a two-tailed alternative hypothesis. Indicate in which case you would reject the null hypothesis at the  5 %  significance level.
$\begin{array} { | c | c | c | c | c | } 
\hline \widehat { \beta } _ { 1 } & - 1.76 & 0.0025 & 2.85 & - 0.00014 \
\hline \hat { \sigma } _ { \widehat { \beta } _ { 1 } } ^ { 2 } & 0.37 & 0.000003 & 117.5 & 0.0000013 \
\hline
\end{array}$

Quizplus · Accepted Answer

The Answer of Consider the sample regression function $\widehat { Y } _ { i } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } X _ { i }$
The table below lists estimates for the slope $\left( \widehat { \beta } _ { 1 } \right)$ and the variance of the slope estimator $\left( \widehat { \sigma } _ { \widehat { \beta } _ { 1 } } ^ { 2 } \right)$ In each case calculate the  p -value for the null hypothesis of $\beta _ { 1 } = 0$ and a two-tailed alternative hypothesis. Indicate in which case you would reject the null hypothesis at the  5 %  significance level.
$\begin{array} { | c | c | c | c | c | } 
\hline \widehat { \beta } _ { 1 } & - 1.76 & 0.0025 & 2.85 & - 0.00014 \
\hline \hat { \sigma } _ { \widehat { \beta } _ { 1 } } ^ { 2 } & 0.37 & 0.000003 & 117.5 & 0.0000013 \
\hline
\end{array}$

Consider the Sample Regression Function Y^i=β^0+β^1Xi\widehat { Y } _ { i } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } X _ { i }Yi​=β​0​+β​1​Xi​

Consider the Sample Regression Function $\widehat { Y } _ { i } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 } X _ { i }$