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

question 219

Short Answer

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,what is the value of the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

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Definitions:

Plan Contribution

Money added to a retirement or pension plan, either by individuals or employers, to save for the future.

Actuarially Determined

Calculated using actuaries' methods and assumptions, typically in the context of pension plans and insurance.

Discount Rate

The interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows or investments.

Pension Plan

A retirement plan that requires an employer to make contributions into a pool of funds set aside for a worker's future benefit.