![]() ![]() For example, you have two variables, household income and socio-economic status (SES), and they are theoretically related to each other. There may be no cause and effect relationship among the independent variables, but nevertheless they move together. The case where some or more of the independent variables are correlated is not unusual. The model is designed to estimate the effects of independent variables on some dependent variable in accordance with a proposed theory. The independent variables are independent of \(Y\), but are also assumed to be independent of the other \(X\) variables, or other independent variables.This can be seen in Figure 13.6 by the shape of the distributions placed on the predicted line at the expected value of the relevant value of \(Y\). The independent variables are all from a probability distribution that is normally distributed.Figure 13.6 shows the case of homoscedasticity where all three distributions have the same variance around the predicted value of \(Y\) regardless of the magnitude of \(X\). If the assumption fails, then it is called heteroscedasticity. ![]() The assumption is for constant variance with respect to the magnitude of the independent variable called homoscedasticity. It is plausible that as income increases, the variation around the amount purchased will also increase simply because of the flexibility provided with higher levels of income. Consider the relationship between personal income and the quantity of a good purchased, which is an example of a case where the variance is dependent upon the value of the independent variable, income. The meaning of this is that the variances of the independent variables are independent of the value of the variable.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |