Durbin Watson Statistic

Durbin Watson statistic explained!

The Durbin-Watson statistic is a test statistic used in regression analysis to detect the presence of autocorrelation in the residuals (errors) from a statistical model. Autocorrelation occurs when the residuals are not independent from each other; in other words, the error terms from one observation are correlated with the error terms from another observation.

Key Points About the Durbin-Watson Statistic:

·??????? Value Range: The Durbin-Watson statistic ranges from 0 to 4.

·??????? A value of around 2 suggests no autocorrelation.

·??????? Values less than 2 indicate positive autocorrelation (a tendency for consecutive residuals to have the same sign).

·??????? Values greater than 2 suggest negative autocorrelation (consecutive residuals tend to have opposite signs).

Calculus:

Where,

et-?are residuals from OLS regression.

et-1?are first order differences of residuals.

The DW statistic d lies between 0 and 4. d = 2?means no autocorrelation. 0 ‘ d < 2?means positive autocorrelation 2 < d ‘ 4?means negative autocorrelation

An acceptable range is?between 1.50 - 2.50.

Limitations:

The Durbin-Watson statistic is primarily designed for use with OLS (Ordinary Least Squares) regression.

It may not be appropriate for all datasets and does not provide information on the presence of non-linear autocorrelation.

Usage:

After fitting a regression model, the Durbin-Watson statistic can be calculated to assess the independence of residuals. Depending on the value, further investigation may be warranted, or model adjustments may be necessary.

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Mohammed Hussain Shaikh

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