ANSWER ALL QUESTIONS FOR THUMBS UP, ELSE DONT BOTHER. I WILL NOT RATE IF ALL QUE

Question

ANSWER ALL QUESTIONS FOR THUMBS UP, ELSE DONT BOTHER. I WILL NOT RATE IF ALL QUESTIONS ARE NOT ANSWERED

Data set is big, hence I have uploaded it on OneDrive. Please find the file named "injury.xlx". Go to following link:-

https://1drv.ms/x/s!AnCfB5fz9u5Zgfsm5SKOTlmledkPaQ

10. Estimate the following model:

In (duration) = Bo + B1 (weekly disability benefit) + B2 (weekly wages) + B3 (age) + B4(married) + u

Include the regression output.

11.   Interpret B1

12.   Interpret B4

13.   Using the date set, write your own model of how you would test whether disability benefits affect duration of unemployment.

14.   Estimate your model and draw conclusions on whether disability benefits affect duration of unemployment.

Explanation / Answer

10. Save the data in CSV format by adding one extra column "married" assigning 0 if marital status is single and 1 if married.
R code :
data1=read.csv(file.choose(),header=T) #attach the data saved in CSV format
attach(data1)
summary(lm(log(duration)~weekly.wages+weekly.disability.benefit+age+married)) #linear regression

OUTPUT :

Call:
lm(formula = log(duration) ~ weekly.wages + weekly.disability.benefit +
age + married)

Residuals:
Min 1Q Median 3Q Max
-5.0840 -0.7974 0.0513 0.7625 5.9381

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.631e-01 5.654e-02 6.423 1.43e-10 ***
weekly.wages -1.715e-05 1.156e-04 -0.148 0.882
weekly.disability.benefit 4.006e-03 3.394e-04 11.802 < 2e-16 ***
age 8.886e-03 1.256e-03 7.075 1.64e-12 ***
married 2.279e-02 3.390e-02 0.672 0.502
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.279 on 7141 degrees of freedom
(4 observations deleted due to missingness)
Multiple R-squared: 0.04773, Adjusted R-squared: 0.04719
F-statistic: 89.47 on 4 and 7141 DF, p-value: < 2.2e-16

The regression equation is :
In (duration) = 3.631e-01 + 4.006e-03*(weekly disability benefit) -1.715e-05*(weekly wages) + 8.886e-03*(age) +2.279e-02*(married)

11. Since weekly disability benefit is a continuous variable, B1 represents the difference in the predicted value of ln(duration) for each one-unit difference in weekly disability benefit, if other variables remains constant.

12. B4 is interpreted as the difference in the predicted value in ln(duration) for each one-unit difference in (married), if other variables remains constant. However, since (married) is a categorical variable coded as 0 or 1, a one unit difference represents switching from one category to the other.

B4 is then the average difference in ln(duration) between the category for which (married) = 0 (the reference group) and the category for which (married) = 1 (the comparison group).

13. R code :

cor.test(weekly.disability.benefit,duration)

OUTPUT :
Pearson's product-moment correlation

data: weekly.disability.benefit and duration
t = 9.2909, df = 7148, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.08627256 0.13207915
sample estimates:
cor
0.1092338

Since p-value is very small, we reject the null hypothesis of zero correlation and conclude that disability benefits affect the duration of employment significantly.

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