The Minitab outputs displayed below were obtained from a regression analysis conducted to determine the relationship between income and age.
Retain three decimal places in your calculations.
Analysis of Variance
Source DF SS MS F-Value P-Value
Regression ?? ?? 57575.5 19.80 0.000
Error ?? ?? ??
Lack-of-Fit ?? ?? ?? ?? ??
Pure Error 5 348 ??
Total 21 ??
Coefficients
Term Coef SECoef T-Value P-Value
Constant 652.1 48.1 13.55 0.000
age -3.328 0.748 -4.45 0.000
a. Write down the population regression model equation assumed in this analysis.
b. Write down the estimated regression equation.
c. Fill in the missing numbers (??) in the table above.
d. Test the hypothesis that income decreases linearly with age and state if the null hypothesis of zero slope is to be rejected.
e. Based on your conclusion for (d) above, state the three possible outcomes concerning the slope and/or the relationship between income and age. (Refer to section 2.1 in Lesson 2.)
f. Perform a lack of fit test to determine the adequacy of the linear regression model.
g. Based on part (f) above, which of the three possible outcomes in (e) is most likely?