What does non constant variance mean?

What does non constant variance mean?

What Is Heteroskedasticity? Heteroskedasticity is when the variance of the error term, or the residual variance, is not constant across observations. Graphically, it means the spread of points around the regression line is variable.

What happens if the error variance is not constant?

Heteroscedasticity does not destroy the unbiasedness property of OLS estimators, but these estimators are no longer efficient. In other words, OLS estimators are no longer BLUE. If heteroscedastic variances σi2 are known, then the method of weighted least squares (WLS) provides BLUE estimators.

What is orthogonal polynomial regression?

The orthogonal polynomial regression statistics contain some standard statistics such as a fit equation, polynomial degrees (changed with fit plot properties), and the number of data points used as well as some statistics specific to the orthogonal polynomial such as B[n], Alpha[n], and Beta[n].

What does it mean to have constant variance?

It means that when you plot the individual error against the predicted value, the variance of the error predicted value should be constant. See the red arrows in the picture below, the length of the red lines (a proxy of its variance) are the same.

Which is the best method for polynomial regression?

Polynomial regression models are usually fit using the method of least squares. The least-squares method minimizes the variance of the unbiased estimators of the coefficients, under the conditions of the Gauss–Markov theorem.

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:

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.

https://www.youtube.com/watch?v=Rb8MnMEJTI4