Please ignore my personal answers Suppose you are interested in studying the rel
ID: 3307093 • Letter: P
Question
Please ignore my personal answers
Suppose you are interested in studying the relationship between education and wage. More specifically, suppose that you believe the relationship to be captured by the following linear regression model, Wage po +B,Education +u Suppose further that the only unobservable that can possibly affect both wage and education is inteligence of the individual OLS assumption (1) The conditional distribution of u, given x, has a mean of zero. Mathematically, E (up :0 Which of the following provides evidence in favor of OLS assumption #17 (Check al that apply) A. E(intelligence!Education:EinteligencelEducatonay) for allx#y B. covanance(Inteligence. Educator) #0 C. com(Inteligence, Education):0 D. corr(Inteligence. Education)20 Which of the following provides evidence against of OLS assumption #1? (Check all that apply) A. B. E(inteligencelEducation3x)-E(InteligencelEducatonay) for all x#y com inteligence. Education):0 com Inteligence. Education)20 co vanance(Inteligence. Education) #0 C. D, OLS assumption (2) (X, Y,)1 n are independently and identically distributed Suppose you would like to draw a sample to study the effect of education on wage wich of the following provides evidence in favor of OLS assumption #2? (Check all that apply) A. A random sample is drawn from a population of college graduates B. A sample consisting of a group of college students is drawn repeatedly each year over the course of their college careers c. co inteligence. Education,-0 D. A sample consisting of all honor students is drawn from a population of college graduates Suppose you would like to draw a sample to study the effect of education on wage which of the following provides evidence against OLS assumption #2? Check all that apply) A. B. corr(Intelligence. Educaton)-0 A sample consisting of all honor students is drawn from a population of colege graduates C. Arandom sample is drawn from a population of college graduates. D. Observations consisting of the same group of college students are drawn repeatedly each year over the course of their college careers OLS assumption (3) Large outliers are unlikely Mathematically Xand Y have nonzero finite fourth moments. 0Explanation / Answer
In the given linear regression, we consider y to be the response, which is wage; x is the predictor, which is education. The unobservable or error variable is intelligence.
Given the 1st OLS assumption, we answer the 1st two questions as follows:
1) Option C is correct as-----
cov(ui, Xj)= E(ui Xj) - E(ui) E(Xj)
=EE(ui I Xj) ( since E(ui)=0)
=0 ( since E(ui I Xj)=0)
Hence corr(ui, Xj)=0
2) Option C is correct because if the assumption holds, then the correlation must be 0.
Given the 2nd OLS assumption, we answer the next questions:
3) Option A is correct as if Xi and Yi are iid random variables, then the sample drawn is random in nature.
4) Option D is correct as if we draw observations from the same group of students over the years then it will not ne a random sample and hence the assumption will be violated.
Given the 3rd OLS assumption, we have the answers to the next questions as:
5) Option B is correct because if the wages are multiplied by 1 million then it will lead to large values for some individuals but we know that large outliers are unlikely so it cannot be possible.
6) Option B is correct as if the years of education are recorded in days rather than years for some individuals, it will lead to unusually high values but we do not have large outliers hence there should not be years of education in days for some individuals.