Assumptions of ordinary least square

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​+β1​X1​+β2​X2​+ε b)Y=β0+β1X12+β2X2+εb)\quad Y={ \beta }_{ 0 }+{ \beta }_{ 1 }{ X }_{ { 1 }^{ 2 } }+{ \beta }_{ 2 }{ X }_{ 2 }+\varepsilonb)Y=β0​+β1​X12​+β2​X2​+ε c)Y=β0+β12X1+β2X2+εc)\quad Y={ \beta }_{ 0 }+{ \beta }_{ { 1 }^{ 2 } }{ X }_{ 1 }+{ \beta }_{ 2 }{ X }_{ 2 }+\varepsilonc)Y=β0​+β12​X1​+β2​X2​+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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