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Assignment 1: ECON 2220 A (2020 Late Summer)
Due: 23 July 2020 (to be submitted at cuLearn)
Instructions:
1. You should use STATA software for any calculations. You must paste your log/output onto your
assignment (in a word document) to show your use of STATA; however, this output does not replace any
of the steps outlined below.
2. If you are performing a hypothesis test, make sure you state the hypotheses, the level of significance,
the rejection region, the test statistic (and p-value, if requested), your decision (whether to reject or not to
reject the null hypothesis), and a conclusion in managerial terms that answers the question posed. These
steps must be completed in addition to any STATA output.
3. The required STATA data files can be found in the corresponding folder of cuLearn
4. Please do not forget to write your name and student ID on the cover page of the assignment.
Project 1:
The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds
of an Internal Revenue Service (IRS) audit. The following table shows the average adjusted gross income
reported and the percent of the returns that were audited for 20 selected IRS districts.
District Adjusted Gross Income ($) Percent Audited
Los Angeles 36,664 1.3
Sacramento 38,845 1.1
Atlanta 34,886 1.1
Boise 32,512 1.1
Dallas 34,531 1.0
Providence 35,995 1.0
San Jose 37,799 0.9
Cheyenne 33,876 0.9
Fargo 30,513 0.9
New Orleans 30,174 0.9
Oklahoma City 30,060 0.8
Houston 37,153 0.8
Portland 34,918 0.7
Phoenix 33,291 0.7
Augusta 31,504 0.7
Albuquerque 29,199 0.6
Greensboro 33,072 0.6
Columbia 30,859 0.5
Nashville 32,566 0.5
Buffalo 34,296 0.5
(a) Enter the data in STATA, use STATA to develop the estimated regression equation that could be
used to predict the percent audited given the average adjusted gross income reported. Label your
answers.
(b) At the 0.05 level of significance, determine whether the adjusted gross income and the percent
audited are linearly related.
(c) Did the estimated regression equation provide a good fit? Explain.
(d) Use the estimated regression equation developed in part (a) to calculate a 95% confidence interval
for the expected percent audited for districts with an average adjusted gross income of $35,000.
Project 2:
How much does education affect wage rates? The data file cps4_small.dta contains 1000 observations on
hourly wage rates, education, and other variables from the 2008 Current Population Survey (CPS).
(a) Obtain the summary statistics and histograms for the variables WAGE and EDUC. Discuss the
data characteristics, especially appropriate summary statistics (mean, median) and shape of the
data.
(b) Estimate the linear regression 𝑊𝐴𝐺𝐸 = 𝛽􀬵 + 𝛽􀬶𝐸𝐷𝑈𝐶 + 𝜖 and discuss the results. Interpret the
regression coefficients and comment on the quality of the fit.
(c) Calculate the least squares residuals and plot them against EDUC. Are any patterns evident?
Comment on the assumptions (linearity, normality of errors, and constant variance of errors) of
classical linear regression model.
(d) Estimate the quadratic regression 𝑊𝐴𝐺𝐸 = 𝛼􀬵 + 𝛼􀬶𝐸𝐷𝑈𝐶􀬶 + 𝑒 and discuss the results.
(e) Plot the fitted linear model from part (b) and the fitted values from the quadratic model from part
(d) either in the same or separate graph with the data on WAGE and EDUC. Which model appears
to fit the data better? Compare the sum of squared residuals (RSS) from the models in (b) and (d).
Which model has a lower RSS?
Project 3:
Project 4:
Consider the following model that relates the proportion of a household’s budget spent on alcohol WALC
to total expenditure TOTEXP, age of the household head AGE, and the number of children in the
household NK.
𝑊𝐴𝐿𝐶 = 𝛽􀬵 + 𝛽􀬶𝑙𝑛(𝑇𝑂𝑇𝐸𝑋𝑃) + 𝛽􀬷𝐴𝐺𝐸 + 𝛽􀬸𝑁𝐾 + 𝜖
Note that only households with one or two children are being considered. Thus, NK takes only the values
one or two. Output from estimating this equation appears in the following table.
Dependent Variable: WALC
Included Observations: 1519
Variable Coefficient Std. Error (𝒔𝒃) t-Statistic Prob. (p-value)
C 0.0091 0.0190 ? ?
Ln(TOTEXP) 0.0276 ? 6.6086 ?
AGE ? 0.0002 -6.9624 ?
NK -0.0133 0.0033 -4.0750 ?
R-squared (𝑅􀬶) ? Mean Dependent
Var
0.0606
S.E. of regression
(𝑠∈)
? S.D. Dependent
Var
0.0633
Sum of squared
residual (𝑅𝑆𝑆)
5.752896
(a) Fill in the blank spaces (?) that appear in the table.
(i) The t-statistic for 𝑏􀬵
(ii) The standard error for 𝑏􀬶
(iii) The estimate 𝑏􀬷
(iv) 𝑅􀬶
(v) 𝜎􀷜 (Standard Error of Regression Line or Estimate)
(vi) All p-values
(b) Test the overall significance of the model.
(c) Interpret the coefficients 𝑏􀬷 and 𝑏􀬸.
(d) Compute a 95% confidence interval estimate for 𝛽􀬷. What does this interval tell you?
(e) Test the hypothesis that the budget proportion for alcohol does not depend on the number of
children in the household.
Project 5:
A real estate agent wishes to determine the selling price of residences using the size (square feet) and
whether the residence is a condominium or a single-family home. A sample of 20 residences was obtained
with the following results:
Price ($) Type Square Feet Price ($) Type Square Feet
199,700 Family 1,500 200,600 Condo 1,375
211,800 Condo 2,085 208,000 Condo 1,825
197,100 Family 1,450 210,500 Family 1,650
228,400 Family 1,836 233,300 Family 1,960
215,800 Family 1,730 187,200 Condo 1,360
190,900 Condo 1,726 185,200 Condo 1,200
312,200 Family 2,300 284,100 Family 2,000
313,600 Condo 1,650 207,200 Family 1,755
239,000 Family 1,950 258,200 Family 1,850
184,400 Condo 1,545 203,100 Family 1,630
(a) Produce a regression equation to predict the selling price for residences using a model of the
following form:
𝑦􀯜 = 𝛽􀬴 + 𝛽􀬵𝑥􀬵 + 𝛽􀬶𝑥􀬶 + 𝜖
where:
𝑥􀬵=Square footage and 𝑥􀬶 = 􀵜
1 if a condo
0 if a single-family home
(b) Interpret the estimated parameters 𝛽􀬵 􀷢
and 𝛽􀬶 􀷢
in the model give in part (a).
(c) Produce an equation that describes the relationship between the selling price and the square
footage of (1) condominium and (2) single-family homes.
(d) Conduct a test of hypothesis to determine if the relationship between the selling price and the
square footage is different between the condominiums and single-family homes.
(e) What change would you expect in the estimated regression model if you recode 𝑥􀬶 as the
following? Rerun the regression model with the newly coded 𝑥􀬶 and verify your expectation.
𝑥􀬶 = 􁉄
1 if a single-family home
0 if a condo