Measuring Autocorrelation Durbin Watson Statistic - YouTube

In this video clip we learn how to use the  Durbin-Watson statistic to measure autocorrelation  

in regression. This method is used when data are  collected over time for detecting autocorrelation.

Autocorrelation exists if residuals in one  time period are related to residuals in another  

time period. So autocorrelation is correlation of  the errors or residuals over time. Here residues  

show a cyclical pattern, not random. Cyclical  patterns are a sign of positive auto correlation.  

Such a pattern violates the regression assumption  that residuals are random and independent.

The Durbin-Watson statistic is used to test  for autocorrelation. Here in H0 null hypothesis  

we have that positive auto correlation does  not exist or residuals are not correlated.  

H1, we have that positive auto correlation  is present or residuals are correlated. So  

we calculate the Durbin-Watson statistic as  follows. The possible range is between 0 and 4.  

The statistic should be close to 2 if H0 is true.  

The statistic is less than 2 when there is  a positive autocorrelation. A greater than  

2 value may signal negativeauto correlation,  which we do not care much in this problem.

So here is the process, we calculate  the Durbin-Watson test statistic  

D, then we find the values Dl and Du from the  Durbin-Watson table. The table is in our textbook.  

For sample size n and number of independent  variable k, we can find the values of Dl and Du.  

The decision rule is to reject H0 if  D is less than Dl and do not reject H0  

is d is greater than Du. If D is between  Dl and Du, then the result is inconclusive.

Here we see one example. We have data collected  over 15 weeks. We have number of customers;  

we have sales. We want to see how  customers affect sales. So here we have  

sample size 15, and only one independent variable  so we can locate Dl and Du from the Durbin-Watson  

table. So we can see we have k equals 1, n equals  

15, assuming alpha, level of significance is 0.05.  We can locate the values here, see, and in here.

Then we can calculate the Durbin-Watson statistic  from PhStat. The value is 0.883, less than Dl. So  

at alpha equals 0.05, there is a positive  autocorrelation among the residuals.

Now we see how to find this D statistic  from PhStat. Okay, we go to regression,  

simple linear regression. Okay,  Y variable cell range, we use  

cells C1 through C16, X variable cell range B1  through B16. Here we need some middle result,  

we check ANOVA and the coefficient tables and  then we check there, Durbin-Watson statistic.  

We click ok, then from here we see the  Durbin-Watson statistic as in here.