Diagnostics – Part II. Using statistical tests to check to see if the assumptions we made about the model are realistic. Diagnostic methods. Some simple (but subjective) plots. (Then) Some formal statistical tests. (Now). Simple linear regression model.
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Using statistical tests to check to see if the assumptions we made about the model are realistic
The response Yi is a function of a systematic linear component and a random error component:
with assumptions that:
Durbin-Watson test statistic
Seasonally adjusted quarterly data, 1988 to 1992.
Reasonable fit, but are the error terms positively auto-correlated?
Levene's Test (any continuous distribution)
Test Statistic: 9.452
P-Value : 0.006
It is highly unlikely (P=0.006) that we’d get such an extreme Levene statistic (L=9.452) if the variances of the two groups were equal.
Reject the null hypothesis at the 0.01 level, and conclude that the error variances are not constant.