Question

You use the data from the Medical Expenditure Panel Survey to analyse the medical expen- diture of those individuals, who are 65 years and older. This group of people are qualified for health care under the Australian Medicare program. You run a regression of total medi- cal expenditure (totexp:) against a dummy variable private, which takes the value of 1 if individual i has private health insurance and 0, otherwise. The regression model is . totexpi = Bo + B1 x private; + Ui and the regression results are presented as follows Linear regression Number of obs F(2, 3062) Prob > F R-squared Rooc MSE 0.0019 11843 totexp Coef. Robust Scd. Err. P>It (95+ Conf. Interval] 0.014 private cons 1050.864 6420.058 427.2072 312.626 213.2218 5807.08 1888.506 7033.036 The estimated model is totexpi=6420.058 + 1050.864 x private;, R' = 0.002 se (312.626) (427.207) 1. What is the value of the standard error of the residual in this model? (1 point) 2. What is the value of total number of observations? (1 point) 3. What is the value of the F statistic? (1 point) 4. What is the p-value for a two-tail test that the intercept parameter equals to 0? (1 point)
5. What is the difference between B1 and Bı? (1 point) 6. What is the 99% confidence interval for Bi? Do you reject the null hypothesis Ho: B1 = 0 at the 1% significance level? How about at the 5% level? (2 points) 7. Explain what homoscedastic and heteroskedasticity are. (1 point) 8. The Stata command used to generate the output table is regress totexp private, robust Briefly explain what the robust option is for, and what is the consequence if it is not used. (2 points)

Answer 1

Que.1

Standard error of residual = root MSE = 11843

Que.2

Total number of observation = df(residual) + 2 = 3062+2 = 3064

Residual df are obtained from degrees of freedom of F test statistic.

Que.3

F test statistic = (t test statistic for slope )2 = (1050.864 / 427.2072 )2 = 6.0508

Que.4

Test statistic, t = 6420.058 / 312.626 = 20.5359 degrees of freedom = n - 2 = 3062

p-value = 6.63003E-88

P-value is obtained using Excel with function =TDIST(20.5359,3062,2).