Weighted regression is a method that you can use when the least squares assumption of constant variance in the residuals is violated (heteroscedasticity). With the correct weight, this procedure minimizes the sum of weighted squared residuals to produce residuals with a constant variance (homoscedasticity).
Weighted regression is not an appropriate solution if the heteroscedasticity is caused by an omitted variable.
Usually, observations with small variances should have relatively large weights and observations with large variances should have relatively small weights.
Suppose your regression model predicts the annual number of traffic accidents in different cities. Because more populous cities tend to have more accidents, the residuals for larger cities also tend to be larger. One approach for resolving this is to use the reciprocal of each city's population for the weight.
Specifying a column of weights does not affect the degrees of freedom, unless you specify a weight of zero for one or more observations. Giving an observation a weight of zero removes it from the analysis and thus decreases your degrees of freedom.
The graph created with the following steps will not contain the regression equation, s, R-squared, and adjusted R-squared (adj) as the Fitted Line Plot created withdoes. However, Minitab prints this information in the Session window, and you can copy and paste it onto the graph.
Suppose the responses are in C1, predictors are in C2, and weights are in C3:
You can change the color of the line. To make the line blue, double-click it. On the Attributes tab, under Lines, choose Custom, and choose blue from the Color drop-down list. Click OK.