Question

Only question 6 please, this is the model referred to in Question 6 from 5.c

c) Estimate the linear model for a state's unemployment rate shown below (i.e. estimate Bo and β1) using OLS. Write the resulting regression equation. unemployment rate-β0 + β|minimum wage + ε 6. The following questions ask you to use the regression model you estimated to predict unemployment rates (ie, the model in 5.c). Use the unemployment and minimum wage data from the table above to answer this question. a) What is the predicted unemployment rate for a state with a minimum wage of 8 dollars? How does this compare to the actual unemployment rate in Arkansas (i.e. what is the regression residual for Arkansas)? b) If a state increases its minimum wage from 10 dollars to 15 dollars, what is the predicted change in the unemployment rate? Be precise about the magnitude, units, and direction of the change. c) Compute the predicted unemployment rate and the prediction error for each state. d) Compute the R-squared for your regression line. Interpret your R-squared in a sentence. State 2018 Minimum Rate (%) Wage $7 $11 $8 Unemployment Alabama Arizona Arkansas California$11 DC 4 4 6 $13

Answer 1

6.

Sol:

Wage V/S Unemployment rate y 0.3364x+0.8455 R 0.4526 4 3 E 2 10 1' 1A 0 4 Minimum Wage (S)

Unemployment rate = 0.3364*wage + 0.8455
A.

For a minimum wage of $10.

Predicted unemployment rate = 0.3364*10 + 0.8455

Predicted unemployment rate = 4.21%

Actual unemployment rate in Colorado = 3%

So, predicted unemployment rate in Colorado is overstated by 1.21%

B.

For a minimum wage of $15.

Predicted unemployment rate = 0.3364*15 + 0.8455 = 5.89%

Change in predicted unemployment rate = 5.89%-4.21% = 1.68%

C.

State	2018 Minimum wage ($)	Unemployment rate %	Predicted unemployment rate (%)	Prediction error
Alabama	7	4	3.20	0.80
Arizona	11	5	4.55	0.45
Arkansas	8	3	3.54	-0.54
California	11	4	4.55	-0.55
DC	13	6	5.22	0.78

D.

R Square = 45.26%

The minimum wage can only explain 45.26% of the change in unemployment rate.