Contains data from AED Doctor Visits Data.dta
Observations: 5,190 Data for A. Colin Cameron
(2022), ANALYSIS OF ECONOMIC
DATA, Amazon
Variables: 8 22 Jan 2022 15:50
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Variable Storage Display Value
name type format label Variable label
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female float %9.0g Equals 1 if female and 0
otherwise
freepoor float %9.0g Equals 1 if free government
insurance due to low income
freerepa float %9.0g Equals 1 if free government
insurance due to old-age,
disability or veteran
levyplus float %9.0g Equals 1 if private insurance
age float %9.0g Age in years (midpoint of 10 year
age groups)
income float %9.0g Annual income in tens of
thousands of dollars
illness float %9.0g Number of illnesses in past 2
weeks
visits float %9.0g Number of doctor (or specialist)
visits in past 2 weeks
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Sorted by:
Note: Dataset has changed since last saved.ECN 102: Analysis of Economics Data
Final Exam SQ 2025
This exam consists of 5 short-answer questions (with sub-parts) and 5 multiple choice questions. You will have a maximum of 2 hours to complete this exam. No additional time may be taken without prior accommodation. Show all work to receive full credit. You may use only the calculators provided by the instructor. For questions requiring computation, it suffices to express your final answer with 2 decimal places. There is a formula sheet and scratch paper provided at the end of this exam. You may remove these pages and discard them after the exam. If you plan to use any of these extra pages for your final answers, please write your name and student ID at the top of each scratch page to ensure they are not lost.
This exam is worth 100 points.
Name:
Student ID:
For this exam, we will use a dataset on doctor visits that includes age, sex, income, and health statistics for a group of individuals. The variables present in the dataset are listed here.
Question 1: Summary Statistics [16 points]
- How could we classify the data for variable income in this dataset? Explain three ways. [6 points]
- What is the meaning of an observation with
female==0,freepoor==1in this dataset? [2 points]
- What type of variable is levyplus if we include it in a regression? [2 points]
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
income | 5,190 .5831599 .3689067 0 1.5
illness | 5,190 1.431985 1.384152 0 5
visits | 5,190 .3017341 .7981338 0 9- Which variable above has the greatest dispersion? Which has the least? [3 points]
- What is the standard error of illness? [3 points]
Question 2: Bivariate Regression [16 points]
Suppose we want to run a regression to predict visits using income with OLS:
- Write down the population regression model we are trying to estimate. [2 points]
- What will the independence assumption imply for this regression? [2 points]
- What will the linearity assumption imply for this regression? [2 points]
Source | SS df MS Number of obs = 5,190
-------------+---------------------------------- F(1, 5188) = 81.73
Model | 51.2660961 1 51.2660961 Prob > F = 0.0000
Residual | 3254.2183 5,188 .627258731 R-squared = 0.0155
-------------+---------------------------------- Adj R-squared = 0.0153
Total | 3305.48439 5,189 .637017613 Root MSE = .792
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visits | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
age | .0048538 .0005369 9.04 0.000 .0038013 .0059063
_cons | .1044828 .0244318 4.28 0.000 .0565861 .1523794
------------------------------------------------------------------------------- Suppose we estimate this regression and find that our 95% confidence interval for \(b_2\) is \((.004,.006)\). What conclusion from the test of association for \(\beta_2\) does this imply? [3 points]
- Suppose our R-squared for this regression is 0.0155. What does this mean in words? [2 points]
Suppose instead we estimated a regression of the log of visits on the log of income:
- What would we call this type of regression? [2 points]
- How would we interpret \(b_2\) from this regression in words? [3 points]
Question 3: Multivariate Regression [23 points]
We now estimate \(visits=\beta_1+\beta_2income+\alpha_1freepoor+\alpha_2(income\times freepoor)+\varepsilon\) with OLS:
Source | SS df MS Number of obs = 5,190
-------------+---------------------------------- F(3, 5186) = 15.25
Model | 28.9007111 3 9.63357037 Prob > F = 0.0000
Residual | 3276.58368 5,186 .631813282 R-squared = 0.0087
-------------+---------------------------------- Adj R-squared = 0.0082
Total | 3305.48439 5,189 .637017613 Root MSE = .79487
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visits | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
income | -.1804711 .0305348 -5.91 0.000 -.2403322 -.1206101
freepoor | -.1235766 .0947101 -1.30 0.192 -.3092484 .0620951
incomeXfre~r | -.2656318 .2516047 -1.06 0.291 -.7588831 .2276195
_cons | .4156881 .0214031 19.42 0.000 .373729 .4576472
------------------------------------------------------------------------------(Hint: review variable descriptions on page 2)
- What type of variable is freepoor in this regression? [2 points]
- Which population parameter suggests that those on low-income government insurance have 0.12 fewer doctor visits on average compared to those not on low-income government insurance? [2 points]
- Which population parameter suggests that those on low-income government insurance have 0.265 fewer doctor visits per unit of income compared to those not on low-income government insurance? [2 points]
- Which population parameter suggests that those not on low-income government insurance have 0.18 fewer doctor visits per unit of income? [2 points]
- What conclusion should we draw from the reported F-statistic and its associated p-value? [3 points]
- Which of our coefficients are statistically different from zero at \(\alpha=5\)%? Which are not? [3 points]
- If our four population assumptions hold, how would we expect \(b_2\) to be distributed? Your answer should take the form \(b_2\sim\_\_(\_\_,\_\_)\). Use Greek letters when appropriate. [3 points]
- Find an expression for the marginal effect of income in this regression. [3 points]
- If we want to compare model fit of this regression to that of our previous bivariate model, should we use R-squared or Adj R-squared? Why? [3 points]
Question 4: Multivariate Regression [18 points]
For a multivariate OLS regression with sample size \(n\), \(k-1\) regressors \(x_2,...,x_k\), \(k\) estimated coefficients \(b_1,...,b_k\), and \(j=1,...,k\) as our index of coefficients:
- What is the difference between \(x_j\) and \(\tilde{x}_j\)? [3 points]
- Suppose we add a new regressor \(x_{k+1}\) to our model. What do we expect to happen to the R-squared of our regression? [3 points]
- Suppose we add a new regressor \(x_{k+1}\) to our model and the standard error of \(b_j\) decreases. What might this suggest about our model? [3 points]
- Suppose instead we add a new regressor \(x_{k+1}\) to our model and the standard error of \(b_j\) increases. What might this suggest about our model? [3 points]
- Name the two models that are compared when computing the statistic for the default test of overall significance. Write down the population model for both. [6 points]
Question 5: Miscellaneous [17 points]
- Compute the following sum [3 points]: \[6+\sum_{i=3}^{5}\left(\frac{60}{i}\right)(i-2)\]
- If the default p-values reported for all coefficients from a multivariate regression of \(y\) on \(x_2,...,x_k\) are above 0.05 but we observe
Prob > F = 0.035, what can we conclude about our regressors? [4 points]
- If we choose to use robust standard errors in our model and then find out the homoskedasticity assumption is not violated, should we be concerned? Why or why not? [3 points]
- If we are told to use clustered standard errors in a regression model but know that population assumptions 1, 2, and 4 hold for our data, should we cluster or not? Why? [3 points]
- If to determine the impact a certain variable (not regressor) has on our multivariate regression model we must use an F test/cannot use a t-test, what does this tell us about this variable? [4 points]
Multiple Choice [2 points each]
Only one answer is correct for each question. Read carefully and choose the best possible answer.
MC 1 & 2
Suppose the probability of rejecting \(H_0\) is 0.05 when \(\beta_j=0\) and 0.95 when \(\beta_j\neq0\) for a test on OLS \(b_j\).
The size of this test will be equal to:
5%
95%
100%
0%
The power of this test will be equal to:
5%
95%
100%
0%
MC 3
A trial judge says he believes he made a Type I error when sentencing a defendant. The precedent in court is that individuals are innocent until proven guilty. If the judge is correct, which of the following took place?
The defendant was truly guilty and was found guilty
The defendant was truly guilty but was found innocent
The defendant was truly innocent and was found innocent
The defendant was truly innocent but was found guilty
MC 4
If \(\frac{Q-4}{4}\sim N(0,1)\), it must be true that:
\(E[Q] = 0\)
\(V[Q] = 4\)
\(Q\sim N\)
\(\sigma_Q=16\)
None of the above
MC 5
In which of the following scenarios did we make a mistake?
We claimed that we could not compare the R-squared of a regression of y on x and a regression of ln(y) on x.
We claimed that we could not compare the R-squared of a regression of y on x and a regression of y on ln(x).
We claimed that the critical value approach and p-value approach for a given test would always give us the same answer of whether to reject the null hypothesis or not.
We claimed that the standard error of X will always be smaller than the standard deviation of X for \(n>1\).
None of the above