How to Test Autocorrelation with SPSS 20 Using Durbin Watson Method
How to Test Autocorrelation with SPSS 20 Using Durbin Watson Method
Autocorrelation is a problem that occurs when there is a correlation between the error terms of a regression model. Autocorrelation can cause biased estimates of the regression coefficients and invalid inference tests. Therefore, it is important to detect and correct autocorrelation before performing a regression analysis.
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One of the common methods to test autocorrelation is the Durbin Watson test. The Durbin Watson test is used to test autocorrelation of order one, which means the correlation between the error terms of adjacent observations. The Durbin Watson test requires that the regression model has an intercept term and no lagged variables among the independent variables.
In this article, we will show you how to test autocorrelation with SPSS 20 using the Durbin Watson method. We will use an example dataset of 30 observations with one dependent variable (Y) and three independent variables (X1, X2, and X3). The steps are as follows:
Prepare the data in SPSS 20. Click on Variable View, type the variable names in the Name column. Click on Data View, type the values for each variable.
Run the regression analysis. Click on Analyze, then Regression, then Linear. Select Y as the dependent variable and X1, X2, and X3 as the independent variables. Click on Statistics, check Durbin-Watson under Residuals. Click OK.
Interpret the output. Look at the Durbin-Watson statistic in the Model Summary table. The value ranges from 0 to 4, where 2 indicates no autocorrelation, 0 indicates positive autocorrelation, and 4 indicates negative autocorrelation. Compare the Durbin-Watson statistic with the critical values from a Durbin-Watson table based on the number of observations and the number of independent variables. The critical values define a lower bound (dL) and an upper bound (dU) for testing autocorrelation.
Apply the decision rule. The decision rule for testing autocorrelation using the Durbin Watson test is as follows:
If d < dL, reject the null hypothesis of no autocorrelation and conclude that there is positive autocorrelation.
If d > dU, fail to reject the null hypothesis of no autocorrelation and conclude that there is no evidence of autocorrelation.
If dL < d < dU, the test is inconclusive and further tests are needed.
In our example, the Durbin-Watson statistic is 1.833. Assuming a significance level of 0.05, we can find the critical values from a Durbin-Watson table as follows: dL = 1.38 and dU = 1.69. Since d > dU, we fail to reject the null hypothesis of no autocorrelation and conclude that there is no evidence of autocorrelation in our regression model.
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