Durbin-Watson

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:

$d={\frac {\sum _{i=2}^{n}(e_{i}-e_{i-1})^{2})}{\sum _{i=1}^{n}(e_{i})^{2}}}$

• 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.

Result

* if D > upper bound, no correlation exists.
* if D < lower bound, positive correlation exists.
* if D is in between the two bounds, the test is inconclusive.