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ASSUME THAT THERE IS A POPULATION REGRESSION MODEL

ASSUME THAT THERE IS A POPULATION REGRESSION MODEL

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Author: Christine Farr
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1. Assume that there is a population regression model y = β0 + β1x1 + β2x2 + β3x3 + uand that the model satisfies assumptions MLR1 through MLR5 in the population. Indicate, without explanation, whether the following statements are true or false (each answer is worth 1 point).a. If you take a random sample from the population, and estimate an OLS regression with y as the dependent variable and x1, x2 and x3 as the independent variables, the estimated coefficients of x1, x2 and x3 will be unbiased estimates of β1 , β2, and β3.b. If you take a random sample from the population, and estimate an OLS regression with y as the dependent variable and x1, x2 and x3 as the independent variables, the estimated coefficients of x1, x2 and x3 will be equal to β1 , β2, and β3.c. b. If you take a random sample from the population, and estimate an OLS regression with y as the dependent variable and x1, x2 and x3 as the independent variables, the estimated coefficients of x1, x2 and x3 will be statistically significant.d. If you take two random samples from the same population, and use each of the samples to ^estimate the population model using OLS, you will get the same β estimates from each regression. ^e. If β1 is a positive number, then β1 (the OLS estimate of β1 that you would see on the Stata output after estimating a regression) may be a positive or a negative number. 2. Provide a short answer (one to three sentences) to each of the following questions. (It will sometimes help to think about the meaning and implications of the MLR assumptions for the properties of the OLS estimators, that is, whether the estimated β coefficients are unbiased, how efficient they are, and whether the OLS standard errors are biased or unbiased.) Each part is worth 3 points. 

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