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- Due on 08 Jul, 2018 12:00:00
- Asked On 07 Jul, 2018 08:21:16
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- Dr.FrapetphD
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Describe the major assumptions of ordinary least squares and define the error term

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- Submitted On 07 Jul, 2018 08:26:48

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- Ptahphil
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The necessary OLS assumptions, which are used to derive the OLS estimators in linear regression models, are discussed below.
OLS Assumption 1: The linear regression model is “linear in parameters.”
When the dependent variable (Y)(Y)(Y) is a linear function of independent variables (X′s)(X's)(X′s) and the error term, the regression is linear in parameters and not necessarily linear in X′sX'sX′s. For example, consider the following:
A1. The linear regression model is “linear in parameters.”
A2. There is a random sampling of observations.
A3. The conditional mean should be zero.
A4. There is no multi-collinearity (or perfect collinearity).
A5. Spherical errors: There is homoscedasticity and no autocorrelation
A6: Optional Assumption: Error terms should be normally distributed.
a)Y=β0+β1X1+β2X2+εa)\quad Y={ \beta }_{ 0 }+{ \beta }_{ 1 }{ X }_{ 1 }+{ \beta }_{ 2 }{ X }_{ 2 }+\varepsilona)Y=β0+β1X1+β2X2+ε
b)Y=β0+β1X12+β2X2+εb)\quad Y={ \beta }_{ 0 }+{ \beta }_{ 1 }{ X }_{ { 1 }^{ 2 } }+{ \beta }_{ 2 }{ X }_{ 2 }+\varepsilonb)Y=β0+β1X12+β2X2+ε
c)Y=β0+β12X1+β2X2+εc)\quad Y={ \beta }_{ 0 }+{ \beta }_{ { 1 }^{ 2 } }{ X }_{ 1 }+{ \beta }_{ 2 }{ X }_{ 2 }+\varepsilonc)Y=β0+β12X1+β2X2+ε
In the above three examples, for a) and b) OLS assumption 1 is satisfied. For c) OLS assumption 1 is not satisfied because it is not linear in parameter β1{ \beta }_{ 1 }β1.
OLS Assumption 2: There is a random sampling of observations
This assumption of OLS regression ...

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