Manuals/calci/MULTIPLEREGRESSIONANALYSIS

MULTIPLEREGRESSIONANALYSIS(yRange,xRange,ConfidenceLevel,LogicalValue)

• $yRange$ is the array of y-values.
• $xrange$ is the array of x-values.
• $ConfidenceLevel$ is the value betwen 0 and 1.
• $LogicalValue$ 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:$(x_{1},Y_{1})(x_{2},Y_{2}).......(x_{n},Y_{n})$.
• 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.

Examples

Spreadsheet

	A	B	C
1	AGE	CHOLESTROL LEVEL	SUGAR LEVEL
2	58	189	136
3	69	235	149
4	43	198	165
5	39	137	140
6	63	178	162
7	52	160	152
8	47	198	142
9	31	183	129