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
	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
ADJUSTEDRSQUARE	0.11230196684134108
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

Related Videos

Multiple Linear Regression

See Also

• LEVENESTEST
• SIGNTEST
• MOODSMEDIANTEST

References

• Documentation of Excel for Multiple Regression Analysis

• List of Main Z Functions

• Z3 home