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Unformatted text preview: for nonlinearities.
The key is that y = βo + β1 x + u is linear in the parameters βo and
β1 .
There are no restrictions on how y and x relate to the original dVar
and eVars of interest. Melissa Tartari (Yale) Econometrics 47 / 93 The Meaning of Linear Regression
What does LINEAR mean in SLRM?
We have just seen that we can allow for nonlinearities.
The key is that y = βo + β1 x + u is linear in the parameters βo and
β1 .
There are no restrictions on how y and x relate to the original dVar
and eVars of interest.
However, the interpretation of the coe¢ cients does dependent on
their de…nition. Melissa Tartari (Yale) Econometrics 47 / 93 The Meaning of Linear Regression
What does LINEAR mean in SLRM?
We have just seen that we can allow for nonlinearities.
The key is that y = βo + β1 x + u is linear in the parameters βo and
β1 .
There are no restrictions on how y and x relate to the original dVar
and eVars of interest.
However, the interpretation of the coe¢ cients does dependent on
their de…nition.
Here is an example of a NONLINEAR SRM:
y= Melissa Tartari (Yale) 1
+u
βo + β1 x Econometrics 47 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u . Melissa Tartari (Yale) Econometrics 48 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u .
We now study the statistical properties of OLS: Melissa Tartari (Yale) Econometrics 48 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u .
We now study the statistical properties of OLS:
ˆˆ
we view βo , β1 as estimators of the parameters ( βo , β1 ), i.e. as
random variables, Melissa Tartari (Yale) Econometrics 48 / 93 Statistical Properties of OLS Recall the population model y = βo + β1 x + u .
We now study the statistical properties of OLS:
ˆˆ
we view βo , β1 as estimators of the parameters ( βo , β1 ), i.e. as
random variables,
ˆˆ
we study the properties of the distributions of βo , β1 over
di¤erent random samples from the population. Melissa Tartari (Yale) Econom...
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 Fall '10
 DonaldBrown
 Econometrics

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