Below is partial Excel output from a multiple regression: $$\begin{array}{|l|r|r|r|r|r|} \hline \multicolumn{2}{|c|}{\mbox{Regression Statistics}} & & & & \\ \hline \mbox{Multiple R} & 0.3844 & & & & \\ \hline \mbox{R Square} & 0.1478 & & & & \\ \hline \mbox{Adjusted R Square} & 0.0805 & & & & \\ \hline \mbox{Standard Error} & 5.75 & & & & \\ \hline \mbox{Observations} & 42 & & & & \\ \hline & & & & & \\ \hline \mbox{ANOVA} & & & & & \\ \hline & \mbox{df} &\mbox{SS} &\mbox{MS} &\mbox{F} &\mbox{Significance F} \\ \hline \mbox{Regression} & 3 & 218 & & & 0.104291\\ \hline \mbox{Residual} & 38 & 1257 & & & \\ \hline \mbox{Total} & 41 & 1475 & & & \\ \hline & & & & & \\ \hline & \mbox{Coefficients} & \mbox{Standard Error} & \mbox{t Stat} & \mbox{P-value} & \\ \hline \mbox{Intercept} & 5.8 & 3.5 & 1.66 & 0.1051 & \\ \hline \mbox{x1} & 0.100000000000001 & 2.8 & 0.04 & 0.9683 & \\ \hline \mbox{x2} & 0.700000000000001 & 3.2 & 0.22 & 0.827 & \\ \hline \mbox{x3} & -5.6 & 2.8 & -2 & 0.0527 & \\ \hline \end{array}$$

Suppose that the hypothesis test below is carried out:

$\displaystyle \begin{array}{rl} H_0: & \beta_1 = \beta_2 = \beta_3 = 0 \\ H_1: & \mbox{At least one nonzero} \\ \end{array}$

Find the test statistic and the corresponding p-value.

Test Statistic =

p-Value =