[statistics] durbin-watson 有什麼用?

簡單來說
考慮你做了一條迴歸方程
y=ax+b+e (e是residuals)
若果你用了n個數據得出這條方程﹐那麼你可以得到n個residuals﹐理論上它們應該是iid (independent and identically distributed) 的﹐不會有自相關(autocorrelation) Durbin-Watson 就是用來test residuals之間有冇autocorrelation. 若果證明到有則條迴歸方程有問題.
而下是詳細說明 (我覺得英文可能好些)
The Durbin-Watson statistic is a test statistic used to detect the presence of autocorrelation in the residuals from a regression analysis. It is named after James Durbin and Geoffrey Watson.
If et is the residual associated with the observation at time t, then the test statistic is
圖片參考：http://upload.wikimedia.org/math/b/6/6/b663612c3de35913556f362d1e678cdf.png
. Its value always lies between 0 and 4.
A value of 2 indicates there appears to be no autocorrelation. Small values of d indicate successive error terms are, on average, close in value to one another, or positively correlated. Large values of d indicate successive error terms are, on average, much different in value to one another, or negatively correlated.
To test for postitive autocorrelation at significance α, the test statistic d is compared to lower and upper critical values (dL,α and dU,α):



If d < dL,α, there is statistical evidence that the error terms are positively autocorrelated.
If d > dU,α, there is statistical evidence that the error terms are not positively autocorrelated.
If dL,α < d < dU,α, the test is inconclusive.
To test for negative autocorrelation at significance α, the test statistic (4 - d) is compared to lower and upper critical values (dL,α and dU,α):



If (4 − d) < dL,α, there is statistical evidence that the error terms are negatively autocorrelated.
If (4 - d) > dU,α, there is statistical evidence that the error terms are not negatively autocorrelated.
If dL,α < (4 − d) < dU,α, the test is inconclusive.
The critical values, dL,α and dU,α, vary by level of significance (α), the number of observations, and the number of predictors in the regression equation.