Business statistics

ECON 2110

Dr. Martin Gritsch

Assignment 5

A reminder about Academic Integrity from the syllabus:

Cheating in its various forms will be severely punished. The minimum penalty is a grade of zero on the assignment in question, but it can go up to expulsion from the university. If you have not done so yet, please familiarize yourself with the “Academic Integrity Policy” (available online at http://www.wpunj.edu/dotAsset/230122.pdf). All parts of that Policy are relevant and important, but for the online setting of the class, I especially would like to stress sections II.B. (on plagiarism) and II.C. (on collusion).

Please make sure that you truly understand what all parts of the policy mean. To name a few examples, working together with another student on an assignment, getting help on an assignment from someone else (e.g., a tutor), and copying another student’s work are all violations of the Academic Integrity Policy.

Question 1      (1 point)

A sociologist has data on individuals’ number of children as well as the individual’s number of siblings. In a regression of number of children on number of siblings, the R-squared is 0.1034. If the scientist regressed number of siblings on number of children instead (i.e., switched the dependent and independent variables), what would happen to R-squared? Explain how you found your answer.

*** See p. 2 for Question 2 ***

Question 2      (4 points)
The following table shows output from a regression of individual’s hourly wage (our dependent variable) on two independent variables: the individuals’ years of education and a dummy variable that is one if the individual is an immigrant, zero otherwise.

(A few words about the data source: The U.S. Census of Population and Housing is mandated in the Constitution and gets carried out every ten years. All individuals living in the U.S. are asked a set of basic questions. A subset of individuals used to get the “long form” which collects information on such things as earnings, occupation, and immigrant status. The long form was last used with the 2000 Census and has been replaced by an ongoing survey called the American Community Survey (ACS). The data I used for this estimation are from the ACS. See https://www.census.gov/history/www/programs/demographic/american_community_survey.html and related pages for a wealth of background information.)

SUMMARY OUTPUT
Regression Statistics
R Square	0.0106
Adjusted R Square	0.0106
Standard Error	76.059
Observations	1,380,446
ANOVA
	df	SS	MS	F	Significance F
Regression	2	85,368,506.5	42,684,253.3	7,378.78	0.0000 (rounded)
Residual	1,380,443	7.985,900,000 (rounded)	5,785.0472
Total	1,380,445
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-11.32775	0.28345	-39.964	0.000 (rounded)	-11.8833	-10.7722
Years of education	2.358081	0.0194262	121.386	0.000 (rounded)	2.320007	2.396156
Dummy variable for immigrants	1.605071	0.1900235	8.447	0.000 (rounded)	1.232631	1.97751

Part (a)            (1 point)

Interpret the estimated value of the coefficient on “years of education” (i.e., explain what the number means in this regression).

Part (b)            (1 point)

Interpret the estimated value of the coefficient on the “immigrant” dummy variable (i.e., explain what the number means in this regression).

Part (c)                        (0.5 points)

What is the predicted wage for an individual with 16 years of education who is not an immigrant?

Part (d)            (0.5 points)

What is the predicted wage for an individual with 12 years of education who is an immigrant?

Part (e)                        (1 point)

As you can see, the two included regressors explain a small share of the variation in wages. Name two other variables that could be included in the regression that you think would have a substantial impact on the variation in wages.

Language and ages

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