When estimating the parameters of a linear regression model, the OLS estimator is a scalar value and the OLS estimate is a random variable. For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable. If the error term in a linear regression model is normally distributed, then the distribution of the OLS estimator, conditional on explanatory variables, is also normal. The value of the coefficient of determination, R2 of Model 1: In a4: (M1)
When estimating the parameters of a linear regression model, the OLS estimator is a scalar value and the OLS estimate is a random variable. For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable. If the error term in a linear regression model is normally distributed, then the distribution of the OLS estimator, conditional on explanatory variables, is also normal. The value of the coefficient of determination, R2 of Model 1: In a4: (M1)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 4E
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Transcribed Image Text:1. When estimating the parameters of a linear regression model, the OLS estimator is a
scalar value and the OLS estimate is a random variable.
2. For a linear regression model including only an intercept, the OLS estimator of that
intercept is equal to the sample mean of the independent variable.
3. If the error term in a linear regression model is normally distributed, then the distribution
of the OLS estimator, conditional on explanatory variables, is also normal.
4. The value of the coefficient of determination, R2 of Model 1:
In yi = a + Bx; + E;
(M1)
is different from the value of R2 of the Model 2:
Yi = a+ Bx; + Ei.
(M2)
5. Consider an earnings function In wage = 0.6 + 0.16 · educ estimated on a sample of
n = 1000 individuals. The standard error of the estimated slope coefficient equals 0.11.
This allows us to interpret the estimated slope coefficient as: ceteris paribus expected
returns to schooling are 16%.
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