Neither WAGE nor ln(WAGE) appear normally distributed. The distribution for WAGE is
positively skewed and that for ln(WAGE) is too flat at the top. However, ln(WAGE) more closely
resembles a normal distribution.
b) Regression results for linear model:
WAGE = -4.9122 + 1.1385EDUC R = 0.2024
The estimated return to education at the mean = b /2WAGE * 100 = 11.15%
The results for the log-linear model are ln(WAGE) = 0.7884 + 0.1038EDUC R = 0.2146
Estimated return to education = 10.38% c)
The Jarque-Bera test results are JB= 3023 (p-value = 0.0000) for the residuals from the linear
model and JB= 3.48(p-value = 0.1754) for the residuals from the log-linear model.
Both the histograms and the Jarque-Bera test results suggest the residuals from the log-linear
model are more compatible with normality. In the log-linear model a null hypothesis of normality
is not rejected at a 10% level of significance. In the linear regression model it is rejected at a 1%
level of significance.
(d) Linear model: R 0.2024
Log-linear model: R = ([corr(y,y)] )/(var(y)var(y)) = (6.87196 )/(38.9815*5.39435) = 0.2246
Since, R >gR We conclude that the log-linear model fits the data better.
Absolute value of residuals increases in magnitude as EDUC increases.
f) Prediction for simple linear model:
WAGE = -0.9122 + 1.1385 * 16 = 13.30
Prediction for log-linear model: WAGE = exp C0.7884 + 0.1038 * 16 + (0.4902 ) = 13.05 g) log-linear function is preferred because it has higher fit value and its residuals are consistent
with normality. The linear model had a smaller prediction error.
a) (i) t-statistic for1b = 0.476
(ii) Standard error for b 2s se(b )2= 0.00418
(iii) The estimate for β i3 b = 30.0014
(iv) To compute R , we need SSE and SST. From the output, SSE = 5.752896. To find
SST = 1518 * (0.0633) = 6.08246 thus, R = 1 – SSE/SST = 1 –
5.75290/6.08246 = 0.054
(v) The estimated error standard deviation is 0.061622
b) The value b =20.0276 implies that if ln(TOTEXP) increases by 1 unit the alcohol share will
increase by 0.0276. The change in the alcohol share from a 1-unit change in total expenditure
depends on level of tota