One of the assumptions in fitting a linear regression model

One of the assumptions in fitting a linear regression model is that the variance of the error terms, e_i, is constant. A consequence of this assumption not being met is that the estimated coefficients, beeta, will be biased.

Solution

If the variance of the Y is not constant, then the the error variance will not be constant. The most common form of such heteroscedasticity in Y is that the variance of Y may increase as the mean of Y increases, for data with positive X and Y.

Unless the heteroscedasticity of the Y is pronounced, its effect will not be severe: the least squares estimates will still be unbiased, and the estimates of the slope and intercept will either be normally distributed if the errors are normally distributed, or at least normally distributed asymptotically (as the number of data points becomes large) if the errors are not normally distributed