Instruction 13-16
Given Below Are Results from the Regression Analysis

question 203

True/False

Instruction 13-16
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.
$$\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.7035 \\\text { R Square } & 0.4949 \\\text { Adjusted R } & 0.4030 \\\text { Square } & \\\text { Standard } & 18.4861 \\\text { Error } \\\text { Observations } & 40 \\\hline\end{array}$$ ANOVA
$\begin{array}{lrrrrrr} & \text { df } & \text { SS } & {\text { MS }} & \text { F } & \text { Significance F } \\\hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\\text { Residual } & 33 & 11277.2586 & 341.7351 & & \\\text { Total } & 39 & 22325.9 & & &\end{array}$

$\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067& 7.8257 \\\text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 &2.0238\\\text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402\\\text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\\text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\\text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 &1.2618\\\text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303\end{array}$ Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager.The results of the regression analysis are given below:
$$\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.6391 \\\text { R Square } & 0.4085 \\\text { Adjusted R } & 0.3765 \\\text { Square } & \\\text { Standard Error } & 18.8929 \\\text { Observations } & 40\\\hline\end{array}$$ $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l r r r l r } \hline & d f & { S S } & { M S } & F & \text { Significance } F \\\hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\\text { Residual } & 37 & 13206.8103 & 356.9408 & & \\\text { Total } & 39 & 22325.9 & & & \\\hline\end{array}\\\begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \\\hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\\text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\\text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\\hline\end{array}\end{array}$$
-Referring to Instruction 13-16 Model 1,the null hypothesis should be rejected at a 10% level of significance when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables.

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