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 }

$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, which of the following is the correct alternative hypothesis 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? a) H _ { 1 } : All \beta _ { j } \neq 0 for j = 0,1,2,3,4,5,6 b) H _ { 1 } : All \beta _ { j } \neq 0 for j = 1,2,3,4,5,6 c) H _ { 1 } : At least one of \beta _ { j } \neq 0 for j = 0,1,2,3,4,5,6 d) H _ { 1 } : At least one of \beta _ { j } \neq 0 for j = 1,2,3,4,5,6$

\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, which of the following is the correct alternative hypothesis 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? a)

H _ { 1 }

: All

\beta _ { j } \neq 0

for

j = 0,1,2,3,4,5,6

H _ { 1 }

: All

\beta _ { j } \neq 0

for

j = 1,2,3,4,5,6

H _ { 1 }

: At least one of

\beta _ { j } \neq 0

for

j = 0,1,2,3,4,5,6

H _ { 1 }

: At least one of

\beta _ { j } \neq 0

for

j = 1,2,3,4,5,6

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