Regression Analysis in Stata

Interpretations and Commands for Single Indicator Variables

Task:

1. You are given the following partial Stata output:

. regress y x z

Source | SS df MS Number of obs = 21

-------------+------------------------------ F( 2, 18) =

Model | 810 Prob > F =

Residual | R-squared =

-------------+------------------------------ Adj R-squared =

Total | 1080 Root MSE =

------------------------------------------------------------------------------

y | Coef. Std. Err. t P>|t| [95% Conf. Interval]

------------------------------------------------------------------------------

x | 9 1.5

z | 6 3.0

_cons | -12 3.0

Fill out all the remaining entries in this Stata output.

Note: For F(2, 18) use F =

ExpSS=(k1)

RSS=(nk)

; see p.283 of course notes.

For Prob>F if you do not have access to Stata just give the complete Stata Ftail for this example. 2.-5. The remainder of this assignment uses data from the Rand Health Insurance Experiment. Individuals were randomly assigned to one of Öve di§erent health insurance policies with di§erent coinsurance rates. A coinsurance rate of 25%, for example, means that the individual pays 25% of the bill and the insurance company pays 75% of the bill. Variable outspend is the combined amount paid by the insurance company and the individual.

The end of this assignment gives variable descriptions, summary statistics and output from various regressions. Throughout heteroskedastic-robust standard errors are used. The dependent variable outspend is annual outpatient spending by the individual, where outpatient spending is medical spending outside the hospital.

2. Regression with a single indicator variable (lecture notes 12.2 and 16.2).

(a) For regression 1 output provide an interpretation of the slope coe¢ cient.

(b) For regression 1 output provide an interpretation of the intercept coe¢ cient.

(c) Do the coe¢ cients in (a) and (b) change much when you add age as a regressor?

(d) For regression 3 output provide an interpretation of the e§ect of having free health care compared to not having health care, taking into account the role of age.

(e) Is having free health care statistically signiÖcant at 5%? Explain.

3. Regression with sets of indicator variables (lecture notes 16.3).

(a) For regression 4 output provide an interpretation of the coe¢ cient of coins25.Note: It can be shown that OLS regression of y on a full set of mutually exclusive indicator variables with the intercept included gives coe¢ cients that equal the sample average of y in each category.

(b) For regression 5 output provide an interpretation of the coe¢ cient of coins25.

(c) For regression 6 output give a command in Stata that allows you to test whether the type of health insurance policy has an e§ect on outpatient spending that is statistically signiÖcant at 5%.

4. Regression with quadratic model (lecture notes 12.3 and 16.4).

(a) For regression 7 output give the marginal e§ect on outpatient spending of aging one year, using the calculus method.

(b) Hence compute the average marginal e§ect of aging one year.

(c) Do the regression results support including the quadratic term in age? Explain.

(d) For regression 7 output give a command in Stata that allows you to test whether age has an e§ect on outpatient spending that is statistically signiÖcant at 5%.

5. Regression with natural logarithm (lecture notes 12.4-12.5 and 16.6).

(a) Why have some observations been lost in obtaining the natural logarithm of outspend?

(b) For regression 8 output give an interpretation of the coe¢ cient of age.

(c) For regression 9 output give an interpretation of the coe¢ cient of lnage.

(d) Which model, if any, do you prefer: regression 8 or regression 9? Explain.