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 Y(cap)=b_0+b_1x.
• Multiple Regression Y(cap)=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