Model assumptions

Linear regression models with standard estimation techniques make a number of assumptions about the outcome variable, the predictor variables, and also about their relationship:

1. Y is a continuous variable (not binary, nominal, or ordinal)

2. The errors (the residuals) are statistically independent

3. There is a stochastic linear relationship between Y and each X

4. Y has a normal distribution, holding each X fixed

5. Y has the same variance, regardless of the fixed value of the Xs

A violation of assumption 2 occurs in trend analysis, if we use time as the predictor. Since the consecutive years are not independent, the errors will not be independent from each other. For example, if we have a year with high mortality from a specific illness, then we can expect the mortality for the next year to also be high.

A violation of assumption (3) says that the relationship is not exactly linear, but there is a deviation from the linear trend line. Assumption 4 and 5 require the conditional distribution...