Question

Assignment 1 Wage Experience CollGrad 11 2 1 4 3 0 14 7 0 12 3 24 15 0 6 4 0 1
Please explain and write out steps

Answer 1

I have used Excel to run a regression of Experience and CollGrad on Wage.

Hence the model looks like:

Wage = Intercept + A(Experience) + B(CollGrad) + Error term

We get:

Intercept = 0.09944 p value = 0.951257

A = 1.641457 p value = 0.002488

B = 7.296919 p value = 0.021054

Now we need to test whether graduating increases or decreases the wages ceteris paribus. Hence for this we need to check whether B is statistically significant or not.

Since the p value of B = 0.021054 < 0.05 = Significance level, we can say that B is statistically significant and that graduating college does in fact lead to increase in wages(By amount B = 7.296919)

Using Excel, we calculated the covariance of Wages and CollGrad. We get covariance = -0.111111

Hence this suggests that Graduating would slightly decrease the wages (since covariance < 0)

The two answers are not consistent. This is because CollGrad is a 'dummy variable' i.e it only assumes values of 1 and 0 and simply finding out the covariance between wages and CollGrad would lead to a misleading result due to this. Also we need to consider other factors in check too like Experience and hence we have run the regression in the first place using both Experience and CollGrad. This regression is a better model as it has an R² of 0.967743.

Note: If you run the regression of only CollGrad on Wages then you will get the coefficient of CollGrad to be negative, but it is not statistically significant with a p value of 0.945124.