While not exclusively a time series problem, it is here that we most often see this case. This situation arises from an effect on one error term from another error term. The error terms are uncorrelated with each other.This condition is called multicollinearity, which will be taken up in detail later. The input prices will therefore violate this assumption of regression analysis. There may be multiple inputs that may over time move together from general inflationary pressure. Take the case of a simple supply curve where quantity supplied is theoretically related to the price of the product and the prices of inputs. 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.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 \(Y\). While the independent variables are all fixed values they are 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 as 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.
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