TEST YOUR KNOWLEDGE! You are a program manager for a welfare agency. You want to
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TEST YOUR KNOWLEDGE!
You are a program manager for a welfare agency. You want to consider variables that migh affect the length of unemployment. The table below lists categories of different factors that are hypothesized to be the most important in affecting the length of unemployment. Which are statistically significant? Interpret and write up the results.
TEST YOUR KNOWLEDGE!
You are a program manager for a welfare agency. You want to consider variables that migh affect the length of unemployment. The table below lists categories of different factors that are hypothesized to be the most important in affecting the length of unemployment. Which are statistically significant? Interpret and write up the results.
Multiple Regression Output Model R R-square Adjusted R2 SEE 0.66 0.435 0.423 0.092 Dependent variable: Unemployment duration Coefficients Model b Std. Err. t P>|t| Constant 0.231 0.03 7.740 0.000 Receives job training -0.010 0.04 -2.579 0.010 Marital status -0.072 0.017 -4.125 0.000 Medical condition 0.013 0.005 2.540 0.012 Number of dependents 0.000 0.001 0.252 0.802 Education -0.003 0.003 -0.834 0.405 Note: SEE = standard error of the estimate; Std. Err. = standard error; P>|t|= significance Marital status: 1 = married; 0 = not marriedExplanation / Answer
Given, the dependent variable is unemployment duration and the independent variables that have been uesd in the multiple linear regression model are receives job training, medical condition, marital status, number of dependents and education.
In the regression output table, we are given the details of the independent variables used in the regression model - their estimated values of regression coeffients (denoted by b), the standard errors of the regression coefficients (denoted by Std. Err.), the test statistic value (denoted by t) that is used to test the significance of the corresponding regressor (independent variable) and the p-value of this significance test (denoted by P>|t|), as well.
In order to determine the most important regressors (independent variables) which might affect the dependent variable, that is, the unemployment duration, we have to observe the p-values corresponding to each of the regressors.
Each of the p-values are calculated for testing the null hypothesis that the corresponding regressor variable is insignificant versus the alternative hypothesis that it is significant.
If the p-value is less than alpha (level of significance), which is taken to 0.05 or 0.01 or even 0.001, then we say that the corresponding regressor variable is significant.
Here, we consider alpha = 0.05.
Now, the p-values of the regressors (independent variables) are given below (denoted by P>|t| in the output table).
Here, we see that the p-values of 2 variables - Education and Number of dependents are greater than alpha=0.05. Hence, we conclude that these 2 variables are not statistically significant variables in the regression model.
The remaining 3 variables - Receives job training, Medical condition and Marital status have p-values less than alpha and, hence, are statistically significant. These variables are likely to affect our dependent variable, that is, unemployment duration.
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