# Assumptions that underlie a regresion model

#### katlego

##### New Member
Are there any statistical tests that i can use to evaluate whether the assumptions for the regression model are being met?

The assumptions i want to test are:

1. The model adequately describes the behaviour of the data.

2. The random error term is an independently and normally distributed random variable.

#### Masteras

##### TS Contributor
(2) There are normality tests, shapiro and kolmogorov for instance.

(1) There are goodness of fit measures, such as the R^2, ranging from 0 to 1. You also check the graph of residuals vs fitted values. if yoy see a cloud, NOT any pattern at all, random points only, then you have indepedence and homoscedastictiy of the data. It is good to have (2) from above.

#### bryangoodrich

##### Probably A Mammal
You can also look at a QQ plot of the residuals to see if there are any significant deviations from normality, but the analytic tests (e.g., Shapiro-Wilks) will give you something more concrete.

#### noetsi

##### Fortran must die
Are there any statistical tests that i can use to evaluate whether the assumptions for the regression model are being met?

The assumptions i want to test are:

1. The model adequately describes the behaviour of the data.

2. The random error term is an independently and normally distributed random variable.
As noted there are many other assumptions. To address these.

1 Statistically one could argue that R squared, which shows the percent of the total variation explained by the model, shows if the model adequately explains the behavior of the data. Some might consider the signficance of the overall model F test also a sign of this. This is a statistical perspective, whether the model adequately explains the data has a substantive meaning, but that is a judgement call by you not something the statistics can address.

2 Independence can never be shown by any statistical test except if you consider autocorrelation to mean this. Other than autocorrelation (which normally only occurs with time series data) independence can only be addressed by gathering your data in a way that insures that observations are not correlated. By your research design.

Among the many ways you can assess normality not already mentioned are histograms with the normal curve superimposed, looking at univariate skewness and kurtosis, or Mardia's multivariate skewness and kurtosis. The last is the best, but no commercial software generates it directly I believe (I know SAS and SPSS does not). There is a SAS macro that will do it, but its complex.