Question

The following table shows the unemployment rate for people with various education levels in the United States. Suppose we are interested in predicting the unemployment rate based on the education level.

Years of Education	Unemployment rate
0	20.6
5	17.9
8	19.1
12	13.9
14	12.4
16	6.2
18	8.1

Give the equation of the regression line. (2pts)

Write a sentence interpreting the y-intercept. (2pts)

Write a sentence interpreting the slope. (2pts)

Predict the unemployment rate for the group of people who have 10 years of education. (2pts)

Compute the residual for the group of people who have completed 12 years of education. (2pts)

Compute the residual for the group of people who have completed 5 years of education. (2pts)

Compute the residual for the group of people who have completed 16 years of education. (2pts)

Answer 1

Solution:

Here, we have to predict the dependent variable unemployment by using the regression model which is given as below:

Regression Statistics
Multiple R	0.922392158
R Square	0.850807293
Adjusted R Square	0.820968751
Standard Error	2.336724756
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	155.6928728	155.6928728	28.51370243	0.003089716
Residual	5	27.30141292	5.460282584
Total	6	182.9942857
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	22.29625144	1.782496132	12.5084431	5.79426E-05	17.71419926	26.87830362
Years of Education	-0.792791234	0.148467718	-5.339822322	0.003089716	-1.174439653	-0.411142815

Give the equation of the regression line.

Regression equation is given as below:

Unemployment rate = 22.29625144 - 0.792791234*Years of education

Y = 22.29625144 - 0.792791234*X

Write a sentence interpreting the y-intercept.

Y-intercept is given as 22.29625144.

When there is zero years of education or no education, then employment rate would be 22.29625144.

Write a sentence interpreting the slope.

Slope is given as - 0.792791234.

When there is an increment of one year of education, the unemployment rate would be decreased by 0.792791234.

Predict the unemployment rate for the group of people who have 10 years of education. (2pts)

Unemployment rate = 22.29625144 - 0.792791234*Years of education

Unemployment rate = 22.29625144 - 0.792791234*10

Unemployment rate = 14.3683391

Compute the residual for the group of people who have completed 12 years of education. (2pts)

Predicted Unemployment rate = 22.29625144 - 0.792791234*Years of education

Predicted Unemployment rate = 22.29625144 - 0.792791234*12

Predicted Unemployment rate = 12.7827566

Observed unemployment rate = 13.9

Residual = observed – predicted = 13.9 - 12.7827566 = 1.1172434

Residual = 1.1172434

Compute the residual for the group of people who have completed 5 years of education. (2pts)

Predicted Unemployment rate = 22.29625144 - 0.792791234*Years of education

Predicted Unemployment rate = 22.29625144 - 0.792791234*5

Predicted Unemployment rate = 18.3322953

Observed unemployment rate = 17.9

Residual = observed – predicted = 17.9 - 18.3322953 = -0.4323

Residual = -0.4323

Compute the residual for the group of people who have completed 16 years of education. (2pts)

Predicted Unemployment rate = 22.29625144 - 0.792791234*Years of education

Predicted Unemployment rate = 22.29625144 - 0.792791234*16

Predicted Unemployment rate = 9.61159

Observed unemployment rate = 6.2

Residual = observed – predicted = 6.2 - 9.61159 = -3.41159

Residual = -3.41159