SCENARIO 18-10 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 of each of the 6 predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201. 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:
-Referring to Scenario 18-10 Model 1, which of the following is a correct statement?
A)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager.
B)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager after adjusting for the Number of predictors and sample size.
C)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager after adjusting for the Level of significance
D)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager holding constant the Effect of all the independent variables.

Question

SCENARIO 18-10 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  of each of the 6 predictors are, respectively, 0.2807, 0.0386, 0.0317, 0.0141, 0.0958, and 0.1201.  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:  
-Referring to Scenario 18-10 Model 1, which of the following is a correct statement?
A)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager. 
B)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager after adjusting for the Number of predictors and sample size. 
C)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager after adjusting for the Level of significance 
D)40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker, the number of years of education Received, the number of years at the previous job, marital status, whether the worker Is the head of household and whether the worker is a manager holding constant the Effect of all the independent variables.

Quizplus · Accepted Answer

The coefficient of partial determination for each predictor in Model 1 represents the proportion of variation in the dependent variable that is explained by that predictor while holding constant the effects of all other predictors. Therefore, 40.30% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the predictors Age, Edu, Job Yr, Married, Head, and Manager after adjusting for the number of predictors and sample size. The coefficient of partial determination for each predictor in Model 1 measures the unique contribution of that predictor to the total variation in Unemploy after adjusting for the other predictors in the model. The sum of these coefficients (0.2807 + 0.0386 + 0.0317 + 0.0141 + 0.0958 + 0.1201) equals 0.601. This means that 60.1% of the variation in Unemploy can be explained by the six predictors in Model 1. However, the adjusted coefficient of determination (R-squared) in Model 1 would be a more appropriate measure of the proportion of the total variation in Unemploy that can be explained by the predictors after taking into account the number of predictors and sample size. This information is not provided in the scenario. Therefore, the best choice is B, which correctly states that the proportion of the total variation in Unemploy explained by the predictors in Model 1 is 40.30% after adjusting for the number of predictors and sample size.

SCENARIO 18-10 Given Below Are Results from the Regression Analysis