SCENARIO 17-10 Given Below Are Results from the Regression Analysis $1 =$

SCENARIO 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: $1 =$ married, $0 =$ otherwise), a dummy variable for head of household (Head: $1 =$ yes, $0 =$ no) and a dummy variable for management position (Manager: $1 =$ yes, $0 =$ no). We shall call this Model 1. The coefficient of partial determination ( $R _ { \mathrm { y } } ^ { 2 }$ (All raiables excopt $j$ ) ) of each of the 6 predictors are, respectively, $0.2807$ , $0.0386,0.0317,0.0141,0.0958$ , and $0.1201$ .

$\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } & \\\text { Observations } & 40 \\\hline\end{array}$
$\text { ANOVA }$



$$\begin{array}{l}\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\\text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\\text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\\text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\\text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \\\hline\end{array}\end{array}$$
-Referring to Scenario 17-10 Model 1, we can conclude that, holding constant the
effect of the other independent variables, there is a difference in the mean number of weeks a
worker is unemployed due to a layoff between a worker who is married and one who is not at a
1% level of significance if all we have is the information of the 95% confidence interval estimate
for $\beta _ { 4 }$ .