DURBINWATSONTEST(DataRange,ConfidenceLevel,NewTableFlag)
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: As, DL TABLE < D < DU TABLE, Test is inconclusive.