Question

Develop a simple linear regression model to predict a person’s income (INCOME) based upon their years of education (EDUC) using a 95% level of confidence.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income using this regression model with 16 years of education.

2. Develop a simple linear regression model to predict a person’s income (INCOME) based on their age (AGE) using a 95% level of confidence.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

What percentage of the observed variation in a person’s income is explained by the model?

e. Predict the value of a person’s income who is 45 years old, using this regression model.

3. Develop a simple linear regression model to predict a person’s income (INCOME) based upon the hours worked per week of the respondent (HRS1) using a 95% level of confidence.

a. Write the reqression equation.

b. Discuss the statistical significance of the model as a whole using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income who works 50 hours a week, using this regression model.

4. Develop a simple linear regression model to predict a person’s income (INCOME) based upon the number of children (CHILDS) using a 95% level of confidence. Children are expensive and may encourage a parent to earn more to support the family.

a. Write the regression equation.

b. Discuss the statistical significance of the model using the appropriate regression statistic at a 95% level of confidence.

c. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.

d. Interpret the coefficient for the independent variable.

e. What percentage of the observed variation in income is explained by the model?

f. Predict the value of a person’s income with 3 children, using this regression model.

INCOME	AGE	EARNRS	EDUC	CHILDS	HRS1
500	27	3	12	0	56
500	23	3	12	1	10
500	78	0	16	2	0
500	64	0	17	0	0
500	54	1	14	3	0
500	22	2	13	1	0

Please answer only these two parts.

5. Compare the preceding four simple linear regression models to determine which model is the preferred model. Use the Significance F values, p-values for independent variable coefficients, R-squared or Adjusted R-squared values (as appropriate), and standard errors to explain your selection.

6. Calculate the predicted income of a 45-year-old, with 18 years of education, 2 children, and works 40 hours per week using your preferred regression model from part 5.

Answer 1