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.