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21 Apr 2019

1. Why does your data need to be a random sample of the population when using OLS to estimate a regression? (Briefly explain)

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Bunny Greenfelder
Bunny GreenfelderLv2
23 Apr 2019

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Related questions

Choose the best answer and breifly explain your reasoning.

1.) Which of the following is valid for R^2 of a linear regression?

A.) A high R^2 means that the regression must be right.

B.) A low R^2 means that the regressors are not strong predictors of the outcome of interest.

C.) R^2 can be any positive number

D.) One can use R^2 to choose between two regressions. The one with a higher R^2 should always be chosen.

2.) To estimate a simple linear regression wage = a + B age + u, using a sample of college graduates, which of the following will cause the estimated B by OLS to be smaller?

A.) Measuring age in months instead of years.

B.) Using yearly wage instead of weekly age.

C.) A smaller sample

D.) A larger sample

3.) To estimate a simple linear regression wage = a + B age + u, using a sample of college graduates, which of the following will tend to cause the t statistic of the OLS estimate `B (Beta hat) to be larger, i.e., more significant estimate `B?

A.) Measuring the age in years instead of months

B.) Measuring the wage in thousands of dollars instead of dollars

C.) A smaller sample

D.) A larger sample

Question 2:

a) Briefly describe the human capital theory of educational attainment. A verbal description is fine, though a figure might help.

b) Consider the following linear regression model for individual earnings: log W_i =alpha + theta S_1 + U_i where Wi is the earnings of individual i and Si are the years of schooling obtained by i. When will the ordinary least squares (OLS) estimate of theta be an unbiased estimate of the "returns to schooling"?

we have a true model

Yt = b0 + b1Xt + b2Yt + Et

where the error term follows a weird serial correlation: Et = Et-1 + Ut. Ut is perfectly well-behaved random variable with 0 mean and constant variance. cov(Ut,Us) = 0 when t is different from s.

a. state the consequences of estimating this model using OLS? what kind of Gauss-Markow assumptions that it happens to violate.

b. find a transformation of the data to be able to use the same data to estimate a model that satisfies the Gauss-Markov assumptions. be clear and explicit about the process. clearly explain why the transformed model meets the Gauss-markov assumption.


* this kind of model is random walk serial correlation.

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