# Classical Linear Regression Model [CLRM/CNLRM]

### CNLRM (Classical Normal Linear Regression Model)

##### Assumption 1: Linear regression model: The regression model is linear in the parameters, as shown as

Yi = β1 + β2Xi + ui

E(ui |Xi) = 0 .

##### Assumption 4: Homoscedasticity or equal variance of ui. Given the value of X, the variance of ui is the same for all observations. That is, the conditional variances of ui are identical. Symbolically, we have

var (ui |Xi)  = E[ui E(ui |Xi)]2

= E(ui2 |Xi ) because of Assumption 3

= σ2

where var stands for variance.

##### Assumption 5: No autocorrelation between the disturbances. Given any two X values, Xi and Xj (i  j ), the correlation between any two ui and uj (i ≠ j ) is zero. Symbolically,

cov(ui,uj |Xi,Xj) = E{[ui E(ui)]|Xi}{[uj E(uj)]|Xj}
= E(u
i | Xi)(uj | Xj)

=0

where i and j are two different observations and where cov means covariance.

##### Assumption 6: Zero covariance between ui and Xi, or E(uiXi) = 0. Formally,

cov (ui, Xi) = E [ui E(ui)][Xi E(Xi)]
= E [u
i (Xi E(Xi))] since E(ui) = 0

= E(uiXi) − E(Xi)E(ui) since E(Xi) is non-stochastic

= E(uiXi) since E(ui) = 0
= 0 by assumption

##### Assumption 10: There is no perfect multicollinearity. That is, there are no perfect linear relationships among the explanatory variables.
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