A researcher developed the following multiple regression model to explain the variation in hours worked by married women.
H = ?0 + ?1X1 + ?2X2 + ?3X3 + ?4X4 + ?
Where, H = hours worked per month, X1 = age, X2 = education level, X3 = experience, X4 = husband’s wage, ?s = the parameters to be estimate, and ? = the error term.
All the explanatory variables (age, education level, experience, and husband’s wage) are expected to have negative impact on hours of work.
The researcher collected data on H and Xs for a random sample of 428 working women in a given geographical area. Upon estimation of the model, the researcher obtained the following regression output.
Explanatory Variable Coefficient Estimate Standard Error of Estimate
Constant 1817.334 296.445
X1 -16.456 5.365
X2 -38.363 16.067
X3 49.487 13.734
X4 -66.505 12.842
Dependent Variable: Hours
Observation (n) = 428
SSR = 691.8015
SST = 1061.8015
F-ratio = 16.806
a. (8 pts.) Test the statistical significance of the coefficient estimate of each explanatory variable at 5% significance level.
b. (3 pts.) Test the statistical significance of the overall model.
c. (2 pts.) Write the estimatedregression equation using the coefficient estimates givenabove.
d. (2 pts.) Do the experience and the husband’s wage variables have the expected signs?
e. (2 pts.) If the education level increases by 1and all the other variables do not change, what will happen to the number of hours worked according to this model?
f. (2 pts.)What percent of the variation in hours worked is explained by this model