Contents
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 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.
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.
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 happens when the error terms do not have a constant variance?
One of the assumptions of linear regression is that there should be a constant variance in the error terms and that the confidence intervals and hypothesis tests associated with the model rely on this assumption. What exactly happens when the error terms do not have a constant variance?
Is the variance of a maximum likelihood Estima-Tor negative?
For large sample sizes, the variance of a maximum likelihood estima- tor of a single parameter is approximately the negative of the reciprocal of the the Fisher information I() = E @2. @. lnL(X) : the negative reciprocal of the second derivative, also known as the curvature, of the log-likelihood function.