When to use weighted least squares for nonconstant variance?
A plot of the residuals versus the predictor values indicates possible nonconstant variance since there is a very slight “megaphone” pattern: We will turn to weighted least squares to address this possiblity. The weights we will use will be based on regressing the absolute residuals versus the predictor.
What happens when nonconstant variance is too high?
For example, if the residual variance increases with the fitted values, then prediction intervals will tend to be wider than they should be at low fitted values and narrower than they should be at high fitted values. Some remedies for refining a model exhibiting excessive nonconstant variance includes the following:
Which is a generalization of weighted least squares?
A generalization of weighted least squares is to allow the regression errors to be correlated with one another in addition to having different variances. This leads to generalized least squares, in which various forms of nonconstant variance can be modeled.
How are standard deviations related to the weights?
The standard deviations tend to increase as the value of Parent increases, so the weights tend to decrease as the value of Parent increases.
What are the effects of excessive nonconstant variance?
Excessive nonconstant variance can create technical difficulties with a multiple linear regression model. For example, if the residual variance increases with the fitted values, then prediction intervals will tend to be wider than they should be at low fitted values and narrower than they should be at high fitted values.
Which is a smaller residual variance 0 or 1?
From this plot, it is apparent that the values coded as 0 have a smaller residual variance than the values coded as 1. The residual variances for the two separate groups defined by the discount pricing variable are: