Manuals/calci/MULTIPLEREGRESSIONANALYSIS

MULTIPLEREGRESSIONANALYSIS(yRange,xRange,ConfidenceLevel,LogicalValue)

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: $(x_{1},Y_{1})(x_{2},Y_{2}).......(x_{n},Y_{n})$ .
2.Multiple regression: $({(x1)}_{1},{(x2)}_{1},{(x3)}_{1}.....{(xK)}_{1},Y_{1})({(x1)}_{2},{(x2)}_{2},{(x3)}_{2}....{(xK)}_{2},Y_{2}).......({(x1)}_{n},{(x2)}_{n},{(x3)}_{n}....{(xK)}_{n},Y_{n})$ .
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: ${\hat {Y}}=b_{0}+b_{1}x$ .
Multiple Regression: ${\hat {Y}}=b_{0}+b_{1}(x1)+b_{2}(x2)+......+b_{K}(xK)$ .
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.

REGRESSION ANALYSIS OUTPUT

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