lyer Computer, Inc., wishes to know the effect of various variables on labor efficiency. Based on a sample of 64 observations, the following model was estimated by least squares:
$$
\begin{aligned}
\hat{y}= & -16.528+28.729 x_1+.022 x_2-0.023 x_3-0.054 x_4 \\
& -0.077 x_5+0.411 x_6+0.349 x_7+0.028 x_8 \quad R^2=.467
\end{aligned}
$$
where
$\hat{y}=$ index of direct labor efficiency in production plant
$x_1=$ ratio of overtime hours to straight-time hours worked by all production workers
$x_2=$ average number of hourly workers in the plant
$x_3=$ percentage of employees involved in some quality-of-work-life program
$x_4=$ number of grievances filed per 100 workers
$x_5=$ disciplinary action rate
$x_6=$ absenteeism rate for hourly workers
$x_7=$ salaried workers' attitudes, from low (dissatisfied) to high, as measured by questionnaire
$x_8=$ percentage of hourly employees submitting at least one suggestion in a year to the plant's suggestion program
Also obtained by least squares from these data was the fitted model:
$$
\hat{y}=9.062-10944 x_1+0.320 x_2+0.019 x_3 \quad R^2=0.242
$$
The variables $x_4, x_5, x_6, x_7$, and $x_8$ are measures of the performance of a plant's industrial relations system. Test, at the $1 \%$ level, the null hypothesis that they do not contribute to explaining direct labor efficiency, given that $x_1, x_2$ and $x_3$ are also to be used.