Manuals/calci/MULTIPLEREGRESSIONANALYSIS

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

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
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

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