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 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 with 3 children, using this regression model..

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.

INCOME	AGE	EARNRS	EDUC	CHILDS	HRS1
500	27	3	12	0	56			Income =	annual income
500	23	3	12	1	10			Age =	years of age of respondent
500	78	0	16	2	0			Earnrs =	number of family members earning income
500	64	0	17	0	0			Educ =	years of education
500	54	1	14	3	0			Childs = number of children
500	22	2	13	1	0			Hrs1 =	number of hours per week of work

Answer 1

1.

X =Number of years of Education

Y =Annual income

a.

Regression equation is: ​​​​​​.

b.

The regression statistic is the slope of the regession line, b1 =0. So, the 95% confidence interval includes 0 because (0 - MoE, 0+MoE) includes 0. (where MoE =margin of error).

Thus, the model is not significant.

c.

The coefficient for the independent variable X is the slope of the regession line, b1 =0. So, the 95% confidence interval includes 0 because (0 - MoE, 0+MoE) includes 0. (where MoE =margin of error).

Thus, the coefficient for the independent variable is not significant.

d.

Interpretation:

If the years of Education(X) changes by 1 year, the annual income(Y) does not show any change since coefficient of X is b1 =0

e.

The percentage of the observed variation in income that is explained by the model cannot be determined because the coefficient of determination, R² is undefined. (since, Correlation, r is undefined, so is R²).

f.

When X =16 years of Education, then the annual income is =500