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:

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.

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.

Example

Spreadsheet

	A	B	C	D
1	3	7	5	65
2	4	3	7	38
3	5	5	8	51
4	6	8	1	38
5	7	9	3	55
6	8	5	4	43
7	2	4	0	25
8	3	2	6	33
9	8	8	7	71
10	9	6	4	51
11	2	9	2	49

• =DURBINWATSONTEST(A1:A11,B1:B11,C1:C11,D1:D11,0.05,true)

DURBIN-WATSON TEST

Y	PREDICTED Y	RESIDUAL
65	54.11461	10.88539
38	42.54638	-4.54638
51	56.06668	-5.06668
38	44.9235	-6.9235
55	57.33098	-2.33098
43	42.08043	0.91957
25	21.06987	3.93013
33	33.82123	-0.82123
71	67.51283	3.48717
51	47.12326	3.87674
49	52.41022	-3.41022

SUMMARY

VARIABLE	RESULT
D	1.37587
DL TABLE	0.595
DU TABLE	1.928
RESULT	TEST IS INCONCLUSIVE

• CONCLUSION: DL TABLE < D < DU TABLE, Test is inconclusive.