Difference between revisions of "Durbin-Watson"
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*The Durbin-Watson test uses the following statistic: | *The Durbin-Watson test uses the following statistic: | ||
<math>d=\frac{\sum_{i=2}^n (e_i-e_{i-1})^2)}{\sum_{i=1}^n (e_i)^2}</math> | <math>d=\frac{\sum_{i=2}^n (e_i-e_{i-1})^2)}{\sum_{i=1}^n (e_i)^2}</math> | ||
| − | * where the <math>e_i = y_i-\bar{y_i}</math> are the residuals | + | * where the <math>e_i = y_i-\bar{y_i}</math> are the residuals. |
| − | * n is the number of elements in the sample | + | * n is the number of elements in the sample. |
| − | * k is the number of independent variables | + | * k is the number of independent variables. |
| + | |||
| + | * d takes the values between 0 and 4. | ||
| + | * d = 2 means there is no autocorrelation. | ||
| + | * A value substantially below 2 means that the data is positively autocorrelated. | ||
| + | * A value of d substantially above 2 means that the data is negatively autocorrelated. | ||
Revision as of 05:50, 3 May 2017
DURBINWATSONTEST(DataRange,ConfidenceLevel,NewTableFlag))
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle DataRange} is the array of x and y values.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ConfidenceLevel} is the value of alpha from 0 to 1.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle NewTableFlag} is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube
Description
- This function gives the test statistic of the Durbin-Watson test.
- The test is used to detect the presence of autocorrelation in the residuals.
- Autocorrelation means that adjacent observations are correlated.
- If they are correlated, then least-squares regression underestimates the standard error of the coefficients.
Assumptions
The error terms are independent of each other.
- The Durbin-Watson test uses the following statistic:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d=\frac{\sum_{i=2}^n (e_i-e_{i-1})^2)}{\sum_{i=1}^n (e_i)^2}}
- where the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e_i = y_i-\bar{y_i}} are the residuals.
- n is the number of elements in the sample.
- k is the number of independent variables.
- d takes the values between 0 and 4.
- d = 2 means there is no autocorrelation.
- A value substantially below 2 means that the data is positively autocorrelated.
- A value of d substantially above 2 means that the data is negatively autocorrelated.