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Suppose we are interested in the effect of education on salary as expressed in the following model. Salary₁ = Bo + B₁ Education, + €₁ For this problem, we are going to assume that the true model is Salary; = 12,000 + 1,000 Education, + €¡ The model indicates that the salary for each person is $12,000 plus $1,000

Suppose we are interested in the effect of education on salary as expressed in the following model. Salary₁ = Bo + B₁ Education, + €₁ For this problem, we are going to assume that the true model is Salary; = 12,000 + 1,000 Education, + €¡ The model indicates that the salary for each person is $12,000 plus $1,000

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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Suppose we are interested in the effect of education on salary as expressed in the following model. Salary; = Bo + B₁ Education, + €₁ For this problem, we are going to assume that the true model is Salary; = 12,000 + 1,000 Education; + €¡ The model indicates that the salary for each person is $12,000 plus $1,000 times the number of years of education plus the error term for the individual. Our goal is to explore how much our estimate of ₁ varies. The do file salary_simulation.do will simulate a data set with 100 observations (right click to save the do file). Values of education for each observation are between 0 and 16 years. The error term will be a normally distributed error term with a standard deviation of 10,000. What does this simulation show about the least squares estimators? Select one: O a. Unbiasedness O b. Consistency O c. Efficiency O d. Nonlinearity
Transcribed Image Text:Suppose we are interested in the effect of education on salary as expressed in the following model. Salary; = Bo + B₁ Education, + €₁ For this problem, we are going to assume that the true model is Salary; = 12,000 + 1,000 Education; + €¡ The model indicates that the salary for each person is $12,000 plus $1,000 times the number of years of education plus the error term for the individual. Our goal is to explore how much our estimate of ₁ varies. The do file salary_simulation.do will simulate a data set with 100 observations (right click to save the do file). Values of education for each observation are between 0 and 16 years. The error term will be a normally distributed error term with a standard deviation of 10,000. What does this simulation show about the least squares estimators? Select one: O a. Unbiasedness O b. Consistency O c. Efficiency O d. Nonlinearity
/* Overview of simulation code the "simulate" line runs the code 1000 times (as determined in the "reps (1000)" command) Stata will save the beta coefficients for each simulation. - the values of coefficient on Education for each simulation are listed in a variable called "_b_Ed" - the values of the constant for each simulation are listed in a variable called "_b_cons". */¯¯ clear all program OLS_Sim clear set obs 100 gen Ed=16*runiform() scalar SD = 10000 gen Salary = 12000 + 1000* Ed + SD*rnormal() /* Generate salary (dep. variable) */ regress Salary Ed /* Run regression */ /* Set sample size */ /* Generate education (ind. variable) drawn from the uniform distribution between 0 and 16*/ /* Set value of standard deviation of error term */ end simulate _b, reps (1000): OLS_Sim /* Run simulation 1000 times */ summarize /* Summarize coefficient estimates for each simulation */
Transcribed Image Text:/* Overview of simulation code the "simulate" line runs the code 1000 times (as determined in the "reps (1000)" command) Stata will save the beta coefficients for each simulation. - the values of coefficient on Education for each simulation are listed in a variable called "_b_Ed" - the values of the constant for each simulation are listed in a variable called "_b_cons". */¯¯ clear all program OLS_Sim clear set obs 100 gen Ed=16*runiform() scalar SD = 10000 gen Salary = 12000 + 1000* Ed + SD*rnormal() /* Generate salary (dep. variable) */ regress Salary Ed /* Run regression */ /* Set sample size */ /* Generate education (ind. variable) drawn from the uniform distribution between 0 and 16*/ /* Set value of standard deviation of error term */ end simulate _b, reps (1000): OLS_Sim /* Run simulation 1000 times */ summarize /* Summarize coefficient estimates for each simulation */
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