Difference between revisions of "Manuals/calci/MULTIPLEREGRESSIONANALYSIS"

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<div style="font-size:25px">'''MULTIPLEREGRESSIONANALYSIS(yRange,xRange,ConfidenceLevel,NewTableFlag)'''</div><br/>
 +
*<math>yRange</math> is the array of y-values.
 +
*<math>xrange</math> is the array of x-values.
 +
*<math>ConfidenceLevel</math> is the value betwen 0 and 1.
 +
*<math>NewTableFlag</math> is either TRUE or FALSE.
 +
 +
==Description==
 +
*This function is calculating the Regression analysis of the given data for the multiple array of x values.
 +
*The general purpose of  multiple regression  is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable.
 +
*There are two types of Regressions.
 +
  1. Simple Regression.
 +
  2. Multiple Regression.
 +
*1.'''Simple Regression''':<math>(x_1,Y_1)(x_2,Y_2).......(x_n,Y_n)</math>.
 +
*2.'''Multiple regression''':<math>({(x1)}_1,{(x2)}_1,{(x3)}_1.....{(xK)}_1,Y_1)
 +
                                  ({(x1)}_2,{(x2)}_2,{(x3)}_2....{(xK)}_2,Y_2).......
 +
                                  ({(x1)}_n,{(x2)}_n,{(x3)}_n....{(xK)}_n,Y_n)</math>.
 +
*The only difference between Simple Regression and Multiple Regression is there where one preditor or many.
 +
*i.e., The difference is depending of the x-value.
 +
*The Y is indicated as the "Dependent variable".
 +
*The Predictor x is indicated as the "Independent Variable" .
 +
*The output of a Regression statistics is of the form :
 +
*Simple Regression:<math>\hat Y = b_0+b_1x</math>.
 +
*Multiple Regression:<math>\hat Y = b_0+b_1(x1)+b_2(x2)+......+b_K(xK)</math>.
 +
*This analysis give the result in three table values.
 +
  1.Regression statistics table.
 +
  2.ANOVA table.
 +
  3.Residual output.
 +
*1.'''Regression statistics''' :  It contains multiple R, R Square, Adjusted  R Square,  Standard Error and observations. R square gives the fittness of the data with the regression line.
 +
*That value is closer to 1 is  the better the regression line  fits the data.
 +
*Standard Error refers to the estimated standard deviation of the error term.
 +
*It is called the standard error of the regression.
 +
*2.'''ANOVA table''':  ANOVA is the analysis of variance. This table splits in to two components which is Residual and Regression.
 +
*Also this table gives the probability, T stat, significance of F and P for the each and every set of the data points.
 +
*3.'''Residual output''': The residuals show you how far away the actual data points are fom the predicted data points.
 +
*This table is displaying the values of Predicted data, Standard Residuals and Percentile value of the Y-value.
 +
 
==Examples==
 
==Examples==
 
{| class="wikitable"
 
{| class="wikitable"
 
|+Spreadsheet
 
|+Spreadsheet
 
|-
 
|-
−
! !! A !! B !! C !! D !! E !! F !! G !! H
+
! !! A !! B !! C  
−
! 1
+
|-
 +
!
 
| '''AGE''' || '''CHOLESTROL LEVEL''' ||'''SUGAR LEVEL'''
 
| '''AGE''' || '''CHOLESTROL LEVEL''' ||'''SUGAR LEVEL'''
 
|-
 
|-
−
!2
+
!1
 
| 58 || 189 || 136
 
| 58 || 189 || 136
 
|-
 
|-
−
!3
+
!2
 
| 69 || 235 || 149
 
| 69 || 235 || 149
 
|-
 
|-
−
!4
+
!3
 
| 43 ||198 || 165
 
| 43 ||198 || 165
 
|-
 
|-
−
!5
+
!4
 
| 39 ||137 ||140
 
| 39 ||137 ||140
 
|-
 
|-
−
!6
+
!5
 
| 63 || 178 || 162
 
| 63 || 178 || 162
 
|-
 
|-
−
! 7
+
!6
 
| 52 || 160 || 152  
 
| 52 || 160 || 152  
 
|-
 
|-
−
! 8
+
! 7
 
| 47 || 198 || 142
 
| 47 || 198 || 142
 
|-
 
|-
−
! 9
+
! 8
 
| 31 || 183 || 129
 
| 31 || 183 || 129
 
|}
 
|}
 +
*=MULTIPLEREGRESSIONANALYSIS(A1:A8,B1:C8,0.05,TRUE)
 +
'''REGRESSION ANALYSIS OUTPUT'''
 +
{| class="wikitable"
 +
|+Summary Output
 +
|-
 +
! Regression Statistics !!
 +
|-
 +
| Multiple R || 0.6049214629315475
 +
|-
 +
| R Square ||0.3659299763152436
 +
|-
 +
|ADJUSTEDRSQUARE || 0.11230196684134108
 +
|-
 +
|STANDARDERROR ||12.010450881972837
 +
|-
 +
|OBSERVATIONS || 8
 +
|}
 +
{| class="wikitable"
 +
|+ANOVA
 +
|-
 +
! !!DF !!SS!! MS!!F !!SIGNIFICANCE F
 +
|-
 +
| REGRESSION ||2 ||416.24534805858957||208.12267402929479||1.442782195366701|| 0.3201422956953145
 +
|-
 +
|RESIDUAL ||5 || 721.2546519414104||144.2509303882821
 +
|-
 +
|TOTAL ||7||1137.5
 +
|}
 +
{| class="wikitable"
 +
|-
 +
! !!COEFFICIENTS !!STANDARD ERROR !!T STAT!!P-VALUE!!LOWER 95%!!UPPER 95%
 +
|-
 +
|INTERCEPT || -38.43476486203053||57.61581647557267||-0.6670870468064214||0.5342620628633192||-186.54092751432788 ||109.67139779026681
 +
|-
 +
|INDEP1 ||0.19650498774518788|| 0.15890296267754417|| 1.2366351415608787|| 0.2711383732149726||-0.211968057954515|| 0.6049780334448908
 +
|-
 +
|INDEP2 ||0.3566329761773446|| 0.3665155982273022|| 0.973036285228361|| 0.3752244119102771|| -0.5855253082352574|| 1.2987912605899465
 +
|}
 +
{| class="wikitable"
 +
|+RESIDUAL OUTPUT
 +
|-
 +
! OBSERVATION!! PREDICTED Y!! RESIDUALS!! STANDARD RESIDUALS
 +
|-
 +
| 1 || -11.710086528684982||69.71008652868498|| 5.838810706001409
 +
|-
 +
| 2 ||-9.155521687997542||78.15552168799755||6.546187495797013
 +
|-
 +
| 3  || -6.011441884074536||49.011441884074536||4.1051237466409525 
 +
|-
 +
| 4  ||-10.924066577704231|| 49.92406657770423||4.181563801403094
 +
|-
 +
|5|| -6.600956847310098||69.6009568473101||5.829670170051966
 +
|-
 +
|6||-8.566006724761976||60.566006724761976||5.072916504540229
 +
|-
 +
|7||-10.531056602213855 ||57.53105660221385|| 4.8187137033369565
 +
|-
 +
|8||-13.0856214429013|| 44.0856214429013|| 3.692544526617634
 +
|}
 +
 +
==Related Videos==
 +
 +
{{#ev:youtube|SG-tokYEgX0|280|center|Multiple Linear Regression}}
 +
 +
==See Also==
 +
*[[Manuals/calci/LEVENESTEST| LEVENESTEST]]
 +
*[[Manuals/calci/SIGNTEST| SIGNTEST]]
 +
*[[Manuals/calci/MOODSMEDIANTEST| MOODSMEDIANTEST]]
 +
 +
==References==
 +
*[http://cameron.econ.ucdavis.edu/excel/ex61multipleregression.html Documentation of Excel for Multiple Regression Analysis]
 +
 +
 +
 +
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 14:19, 13 June 2018

MULTIPLEREGRESSIONANALYSIS(yRange,xRange,ConfidenceLevel,NewTableFlag)


  • is the array of y-values.
  • is the array of x-values.
  • is the value betwen 0 and 1.
  • is either TRUE or FALSE.

Description

  • This function is calculating the Regression analysis of the given data for the multiple array of x values.
  • The general purpose of multiple regression is to learn more about the relationship between several independent or predictor variables and a dependent or criterion variable.
  • There are two types of Regressions.
 1. Simple Regression.
 2. Multiple Regression.
  • 1.Simple Regression:.
  • 2.Multiple regression:.
  • The only difference between Simple Regression and Multiple Regression is there where one preditor or many.
  • i.e., The difference is depending of the x-value.
  • The Y is indicated as the "Dependent variable".
  • The Predictor x is indicated as the "Independent Variable" .
  • The output of a Regression statistics is of the form :
  • Simple Regression:.
  • Multiple Regression:.
  • This analysis give the result in three table values.
 1.Regression statistics table.
 2.ANOVA table. 
 3.Residual output.
  • 1.Regression statistics : It contains multiple R, R Square, Adjusted R Square, Standard Error and observations. R square gives the fittness of the data with the regression line.
  • That value is closer to 1 is the better the regression line fits the data.
  • Standard Error refers to the estimated standard deviation of the error term.
  • It is called the standard error of the regression.
  • 2.ANOVA table: ANOVA is the analysis of variance. This table splits in to two components which is Residual and Regression.
  • Also this table gives the probability, T stat, significance of F and P for the each and every set of the data points.
  • 3.Residual output: The residuals show you how far away the actual data points are fom the predicted data points.
  • This table is displaying the values of Predicted data, Standard Residuals and Percentile value of the Y-value.

Examples

Spreadsheet
A B C
AGE CHOLESTROL LEVEL SUGAR LEVEL
1 58 189 136
2 69 235 149
3 43 198 165
4 39 137 140
5 63 178 162
6 52 160 152
7 47 198 142
8 31 183 129
  • =MULTIPLEREGRESSIONANALYSIS(A1:A8,B1:C8,0.05,TRUE)

REGRESSION ANALYSIS OUTPUT

Summary Output
Regression Statistics
Multiple R 0.6049214629315475
R Square 0.3659299763152436
ADJUSTEDRSQUARE 0.11230196684134108
STANDARDERROR 12.010450881972837
OBSERVATIONS 8
ANOVA
DF SS MS F SIGNIFICANCE F
REGRESSION 2 416.24534805858957 208.12267402929479 1.442782195366701 0.3201422956953145
RESIDUAL 5 721.2546519414104 144.2509303882821
TOTAL 7 1137.5
COEFFICIENTS STANDARD ERROR T STAT P-VALUE LOWER 95% UPPER 95%
INTERCEPT -38.43476486203053 57.61581647557267 -0.6670870468064214 0.5342620628633192 -186.54092751432788 109.67139779026681
INDEP1 0.19650498774518788 0.15890296267754417 1.2366351415608787 0.2711383732149726 -0.211968057954515 0.6049780334448908
INDEP2 0.3566329761773446 0.3665155982273022 0.973036285228361 0.3752244119102771 -0.5855253082352574 1.2987912605899465
RESIDUAL OUTPUT
OBSERVATION PREDICTED Y RESIDUALS STANDARD RESIDUALS
1 -11.710086528684982 69.71008652868498 5.838810706001409
2 -9.155521687997542 78.15552168799755 6.546187495797013
3 -6.011441884074536 49.011441884074536 4.1051237466409525
4 -10.924066577704231 49.92406657770423 4.181563801403094
5 -6.600956847310098 69.6009568473101 5.829670170051966
6 -8.566006724761976 60.566006724761976 5.072916504540229
7 -10.531056602213855 57.53105660221385 4.8187137033369565
8 -13.0856214429013 44.0856214429013 3.692544526617634

Related Videos

Multiple Linear Regression

See Also

References



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