$1.$ Exercise $9\mathrm{.}1$

A study of $86$ savings and loan associations in six northwestern states yielded the following cost function.

where $\backslash ($ C$=\backslash )$ average operating expense ratio, expressed as a percentage and defined as total operating expense $(\backslash (\backslash$$ $\backslash )$ million$)$ divided by total assets million$)$ times $100$ percent.

$\backslash ($ Q$=\backslash )$ output; measured by total assets $(\backslash$$ million$)$

$\backslash ($ X$\_\{1\}=\backslash )$ ratio of the number of branches to total assets $(\backslash (\backslash$$ $\backslash )$ million$)$

Note: The number in parentheses below each coefficient is its respective $\backslash ($ t $\backslash )-$statistic.

Which of the variable$($s$)$ is $($are$)$ statistically significant in explaining variations in the average operating expense ratio? $($Hint: $\backslash ($ t$\_\{0\mathrm{.}025,70\}=1\mathrm{.}99\backslash ).)$ Chec all that apply.