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Instruction 13 ANOVA Model 2 Is the Regression Analysis Where the Dependent Variable

question 140

True/False

Instruction 13.25
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.
Model 1
Regression Statistics
 Multiple R 0.7035 R Square 0.4949 Adj. R Square 0.4030 Std. Error 18.4861 Observations 40\begin{array} { l l } \text { Multiple R } & 0.7035 \\ \text { R Square } & 0.4949 \\ \text { Adj. R Square } & 0.4030 \\ \text { Std. Error } & 18.4861 \\ \text { Observations } & 40 \end{array}

ANOVA
df SS  MS F Signiff  Regression 611048.64151841.44025.38850.00057 Residual 3311277.2586341.7351 Total 39223325.9 Coeff  StdError  tStat p value  Lower 95%  Upper95%  Intercept 32.659523.183021.40880.168314.506779.8257 Age 1.29150.35993.58830.00110.55922.0238 Edu 1.35371.17661.15040.25823.74761.0402 Job Yr 0.61710.59401.03890.30640.59141.8257 Married 5.21897.60680.68610.497420.695010.2571 Head 14.29787.64791.86950.070429.85751.2618 Manager 24.820311.69322.12260.041448.61021.0303\begin{array} { l l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } & \\ \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 & \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & & \\ \text { Total } & 39 & 223325.9 & & & & \\ & & & & & & \\ & \text { Coeff } & \text { StdError } & \text { tStat } & p \text { value } & \text { Lower 95\% } & \text { Upper95\% } \\ \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 \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:
Mode 2
Regression Statistics
 Multiple R 0.6391 R Square 0.4085 Adj. R Square 0.3765 Std. Error 18.8929 Observations 40\begin{array} { l l } \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adj. R Square } & 0.3765 \\ \text { Std. Error } & 18.8929 \\ \text { Observations } & 40 \end{array}

ANOVA
df SS  MS F Signiff  Regression 29119.08974559.544812.77400.0000 Residual 3713206.8103356.9408 Total 3922325.9 Coeff  StdError t Stat p value  Intercept 0.214311.57960.01850.9853 Age 1.44480.31604.57170.0000 Manager 22.576111.34881.98930.0541\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } \\ \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \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 & \end{array}
-Referring to Instruction 13.25 Model 1,you 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 5% level of significance if you use only the information of the 95% confidence interval estimate for ?4.

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