**CNLRM (Classical Normal Linear Regression Model)**

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

*Y**i *= β1 + β2*X**i *+ *u**i*

**Assumption 2: ***X *values are fixed in repeated sampling. Values taken by the regressor *X *are considered fixed in repeated samples. More technically, *X *is assumed to be *non- stochastic.*

*X*values are fixed in repeated sampling.

**Assumption 3: Zero mean value of disturbance ***u**i***. **Given the value of *X*, the mean, or expected, value of the random disturbance term *u**i *is zero. Technically, the conditional mean value of *u**i *is zero. Symbolically, we have

*u*

*i*

E(ui |Xi) = 0 .

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

*u*

*i*

var (*u**i *|*X**i*) = *E*[*u**i *− *E*(*u**i *|*X**i*)]2

= *E*(*u**i*2 |*X**i *) because of Assumption 3

** **= σ2

where var stands for variance.

**Assumption 5: No autocorrelation between the disturbances. **Given any two *X *values, *X**i *and *X**j *(*i * *j *), the correlation between any two *u**i *and *u**j *(*i ≠ j *) is zero. Symbolically,

cov(*u**i**,u**j *|*X**i**,X**j*) = *E*{[*u**i *−*E*(*u**i*)]|*X**i*}{[*u**j *−*E*(*u**j*)]|*X**j*}

= *E*(*u**i *| *X**i*)(*u**j *| *X**j*)

=0

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

**Assumption 6: Zero covariance between ***u**i *and *X**i*, or *E*(*u**i**X**i***) = 0.** Formally,

*u*

*i*and

*X*

*i*, or

*E*(

*u*

*i*

*X*

*i*

cov (*u**i*, *X**i*) = *E *[*u**i *− *E*(*u**i*)][*X**i *− *E*(*X**i*)]

= *E *[*u**i *(*X**i *− *E*(*X**i*))] since *E*(*u**i*) = 0

= *E*(*u**i**X**i*) − *E*(*X**i*)*E*(*u**i*) since *E*(*X**i*) is non-stochastic

= *E*(*u**i**X**i*) since *E*(*u**i*) = 0

= 0 by assumption

**Assumption 7: The number of observations ***n *must be greater than the number of parameters to be estimated. Alternatively, the number of observations *n *must be greater than the number of explanatory variables.

*n*must be greater than the number of parameters to be estimated.

**Assumption 8: Variability in ***X *values. The *X *values in a given sample must not all be the same. Technically, var (*X *) must be a finite positive number.

*X*values.

**Assumption 9: The regression model is correctly specified. **Alternatively, there is no **specification bias or error **in the model used in empirical analysis.

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