. Develop a simple linear regression model to predict a person’sincome (INCOME) based upon their years of education (EDUC) using a95% level of confidence.
a. Write the reqression equation.
b. Discuss the statistical significance of the model as a wholeusing the appropriate regression statistic at a 95% level ofconfidence.
c. Discuss the statistical significance of the coefficient forthe independent variable using the appropriate regression statisticat a 95% level of confidence.
d. Interpret the coefficient for the independent variable.
e. What percentage of the observed variation in income isexplained by the model?
f. Predict the value of a person’s income using this regressionmodel with 16 years of education.
2. Develop a simple linear regression model to predict aperson’s income (INCOME) based on their age (AGE) using a 95% levelof confidence.
a. Write the reqression equation.
b. Discuss the statistical significance of the model as wholeusing the appropriate regression statistic at a 95% level ofconfidence.
c. Discuss the statistical significance of the coefficient forthe independent variable using the appropriate regression statisticat a 95% level of confidence.
d. Interpret the coefficient for the independent variable.
What percentage of the observed variation in a person’s incomeis 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 aperson’s income (INCOME) based upon the hours worked per week ofthe respondent (HRS1) using a 95% level of confidence.
a. Write the reqression equation.
b. Discuss the statistical significance of the model as a wholeusing the appropriate regression statistic at a 95% level ofconfidence.
c. Discuss the statistical significance of the coefficient forthe independent variable using the appropriate regression statisticat a 95% level of confidence.
d. Interpret the coefficient for the independent variable.
e. What percentage of the observed variation in income isexplained by the model?
f. Predict the value of a person’s income who works 50 hours aweek, using this regression model.
4. Develop a simple linear regression model to predict aperson’s income (INCOME) based upon the number of children (CHILDS)using a 95% level of confidence. Children are expensive, and mayencourage a parent to earn more to support the family.
a. Write the reqression equation.
b. Discuss the statistical significance of the model as a wholeusing the appropriate regression statistic at a 95% level ofconfidence.
c. Discuss the statistical significance of the coefficient forthe independent variable using the appropriate regression statisticat a 95% level of confidence.
d. Interpret the coefficient for the independent variable.
e. What percentage of the observed variation in income isexplained by the model?
f. Predict the value of a person’s income with 3 children, usingthis regression model..
5. Compare the preceding four simple linear regression models todetermine which model is the preferred model. Use the SignificanceF values, p-values for independent variable coefficients, R-squaredor Adjusted R-squared values (as appropriate), and standard errorsto explain your selection.
6. Calculate the predicted income of a 45 year old, with 18years of education, 2 children, and works 40 hours per week usingyour 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 | | | |
