Difference between revisions of "Durbin-Watson"

From ZCubes Wiki
Jump to navigation Jump to search
 
(29 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
<div style="font-size:25px">'''DURBINWATSONTEST(DataRange,ConfidenceLevel,NewTableFlag))'''</div><br/>
+
<div style="font-size:25px">'''DURBINWATSONTEST(DataRange,ConfidenceLevel,NewTableFlag)'''</div>
−
*<math>DataRange</math> is the array of x and y values.
+
*'''<math>DataRange</math> is the array of x and y values.
−
*<math>ConfidenceLevel</math> is the value of alpha from 0 to 1.
+
*'''<math>ConfidenceLevel</math> is the value of alpha from 0 to 1.
−
*<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube
+
*'''<math>NewTableFlag</math> is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube.<br></br>
  
−
==Description==
+
==='''DESCRIPTION===
−
*This function gives the test statistic of the Durbin-Watson test.  
+
*'''This function gives the test statistic of the Durbin-Watson test.  
−
* The test is used to detect the presence of autocorrelation in the residuals.
+
*'''The test is used to detect the presence of autocorrelation in the residuals.
−
* Autocorrelation means that adjacent observations are correlated.  
+
*'''Autocorrelation means that adjacent observations are correlated.  
−
* If they are correlated, then least-squares regression underestimates the standard error of the coefficients.
+
*'''If they are correlated, then least-squares regression underestimates the standard error of the coefficients.
  
−
==Assumptions==
+
==='''ASSUMPTIONS===
−
The error terms are independent of each other.
+
'''The error terms are independent of each other.
  
−
*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.
 +
 
 +
==='''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===
 +
{| class="wikitable"
 +
|+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)
 +
 
 +
{| class="wikitable"
 +
|+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
 +
|}
 +
{| class="wikitable"
 +
|+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.

Latest revision as of 09:07, 19 August 2020

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.
  • 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.

Retrieved from "http://wiki.zcubes.com/index.php?title=Durbin-Watson&oldid=215003"