What is the 'Durbin Watson Statistic'
The Durbin Watson statistic is a number that tests for autocorrelation in the residuals from a statistical regression analysis. The DurbinWatson statistic is always between 0 and 4. A value of 2 means that there is no autocorrelation in the sample. Values from 0 to less than 2 indicate positive autocorrelation and values from more than 2 to 4 indicate negative autocorrelation.
BREAKING DOWN 'Durbin Watson Statistic'
Autocorrelation can be a significant problem in analyzing historical data if one does not know to look out for it. For instance, since stock prices tend not to change too radically from one day to another, the prices from one day to the next could potentially be highly correlated, even though there is little useful information in this observation. In order to avoid autocorrelation issues, the easiest solution in finance is to simply convert a series of historical prices into a series of percentageprice changes from day to day.
Durbin Watson Statistic Calculation
The formula for the Durbin Watson statistic is rather complex, but involves the residuals from an ordinary least squares regression on a set of data. The following example illustrates how to calculate this statistic.
Assume the following (x,y) data points:
Pair one = (10, 1,100)
Pair two = (20, 1,200)
Pair three = (35, 985)
Pair four = (40, 750)
Pair five = (50, 1,215)
Pair six = (45, 1,000)
Using the methods of a least squares regression to find the "line of best fit", the equation for the best fit line of this data is:
Y = 2.6268x + 1,129.2
This first step in calculating the Durbin Watson statistic is to calculate the expected "y" values using the line of best fit equation. For this data set, the expected "y" values are:
Expected Y(1) = (2.6268 x 10) + 1,129.2 = 1,102.9
Expected Y(2) = (2.6268 x 20) + 1,129.2 = 1,076.7
Expected Y(3) = (2.6268 x 35) + 1,129.2 = 1,037.3
Expected Y(4) = (2.6268 x 40) + 1,129.2 = 1,024.1
Expected Y(5) = (2.6268 x 50) + 1,129.2 = 997.9
Expected Y(6) = (2.6268 x 45) + 1,129.2 = 1,011
Next, the differences of the actual "y" values versus the expected "y" values, the errors, are calculated:
Error(1) = (1,100  1,102.9) = 2.9
Error(2) = (1,200  1,076.7) = 123.3
Error(3) = (985  1,037.3) = 52.3
Error(4) = (750  1,024.1) = 274.1
Error(5) = (1,215  997.9) = 217.1
Error(6) = (1,000  1,011) = 11
Next these errors must be squared and summed:
Sum of errors squared = (2.9^{2} + 123.3^{2} + 52.3^{2} + 274.1^{2} + 217.1^{2} + 11^{2}) = 140,330.81
Next, the value of the error minus the previous error are calculated and squared:
Difference(1) = (123.3  (2.9)) = 126.2
Difference(2) = (52.3  123.3) = 175.6
Difference(3) = (274.1  (52.3)) = 221.9
Difference(4) = (217.1  (274.1)) = 491.3
Difference(5) = (11  217.1) = 228.1
Sum of differences square = 389,406.71
Finally, the Durbin Watson statistic is the quotient of the squared values:
Durbin Watson = 389,406.71 / 140,330.81 = 2.77
A rule of thumb is that test statistic values in the range of 1.5 to 2.5 are relatively normal. Any value outside this range could be a cause for concern. The Durbin–Watson statistic, while displayed by many regression analysis programs, is not applicable in certain situations. For instance, when lagged dependent variables are included in the explanatory variables, then it is inappropriate to use this test.

Residual Sum Of Squares  RSS
A residual sum of squares is a statistical technique used to ... 
Durbin Amendment
A federal measure called the Durbin Amendment introduced limits ... 
Line Of Best Fit
The line of best fit is an output of regression analysis that ... 
Nonlinear Regression
Nonlinear regression is a form of regression analysis in which ... 
Stepwise Regression
Stepwise regression is the stepbystep iterative construction ... 
Homoskedastic
Homoskedastic refers to a condition in which the variance of ...

Tech
IBM's Watson Spreads Its Wings ... Again
It's been a busy couple of weeks for IBM (NYSE: IBM) in general and its Watson cognitive computing unit in particular. In addition to announcing several more agreements with both large and small ... 
Investing
Regression Basics For Business Analysis
Regression analysis is a quantitative tool that is easy to use and can provide valuable information on financial analysis and forecasting. Find out how. 
Investing
IBM Puts Watson to Work Building Customer Loyalty
Over the past few years, IBM (NYSE: IBM) has taken its Watson artificial intelligence system everywhere, from competing on Jeopardy! to helping provide the brains behind autonomous vehicles. ... 
Tech
IBM Makes Acquisition, Creates New Financial Services for Watson (IBM)
IBM is planning to make its Watson's capabilities available to bankers to deal with increasingly complex regulation. 
Tech
IBM Isn't Worried About Its Stock Tanking. This Is Why.
IBM is experiencing a dearth of revenue growth and earnings performance as its older business channels die on the vine. The company is making a shift though to faster, growing segments and the ... 
Insights
IBM's Watson Meets Salesforce's Einstein in New Partnership
The two tech giants are clubbing IBM’s Watson and Salesforce’s Einstein to bolster sale of dataanalytics and predictive offerings. 
Tech
What is Square, Inc?
Find out how Square helps small businesses accept credit cards, track sales and inventory through their mobile point of sale (POS) systems. 
Investing
IBM's Watson Tackles Cybersecurity Operations
With the scope of its machinelearning wonder only continuing to expand, the latest Watsonrelated announcement isn't surprising: IBM (NYSE: IBM) recently made its new "Watson for Cyber Security" ... 
Trading
When Is A Bull Market Not A Bull Market?
During some bull or bear moves in the stock markets, investors will be going with the trend, but day traders may find they cannot. 
Insights
Can Investors Trust Official Statistics?
The official statistics in some countries need to be taken with a grain of salt. Find out why you should be skeptical.

How can I create a linear regression in Excel?
Learn the steps involved in creating a linear regression chart in Microsoft Excel. A linear regression is a data plot that ... Read Answer >> 
How is residual value of assets taxed?
Find out how and when taxes are assessed on the different kinds of residual value, including the residual value on a leased ... Read Answer >> 
How does the Bureau of Labor Statistics determine the Consumer Price Index (CPI)?
Changes in the average price level of more than 200 goods and services across the U.S. economy are used to determine the ... Read Answer >> 
How do you calculate Rsquared in Excel?
Calculate Rsquared in Microsoft Excel by creating two data ranges to correlate. Use the correlation formula to correlate ... Read Answer >>