How to determine autocorrelation by using Durbin-watson? Apply formulas if possible.
The Durbin-Watson statistic is a measure of autocorrelation in the residuals of a regression model. It ranges from 0 to 4, with a value of 2 indicating no autocorrelation.
To determine whether there is autocorrelation in the residuals, follow these steps:
1. Estimate the regression model using ordinary least squares (OLS).
2. Obtain the residuals by subtracting the fitted values from the observed values.
3. Calculate the Durbin-Watson statistic using the following formula:
DW = (sum of squared differences between adjacent residuals) / (sum of squared residuals)
4. Compare the calculated value of DW to the critical values for the appropriate significance level and degrees of freedom.
The critical values for Durbin-Watson (DW) statistic depend on the sample size, the number of independent variables, and the significance level. A DW value of 2 is optimal, as it indicates no autocorrelation, while values below and above 2 suggest the presence of positive autocorrelation and negative autocorrelation, respectively.
The formula for the critical values of Durbin-Watson statistic can be looked up in a Durbin Watson table or by using the following formula:
DW_crit = DW_lower + [(DW_upper - DW_lower) x (1 - α)/2],
where DW_crit is the critical value, DW_lower and DW_upper are the lower and upper bounds for the DW, and α is the significance level.
If the calculated value of DW is less than the lower critical value, then there is evidence of positive autocorrelation. If the calculated value of DW is greater than the upper critical value, then there is evidence of negative autocorrelation. If the calculated value lies between the two critical values, then there is no evidence of significant autocorrelation.