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Manuals/calci/MULTIPLEREGRESSIONANALYSIS (view source)
Revision as of 09:19, 5 May 2014
, 09:19, 5 May 2014→Description
1. Simple Regression.
1. Simple Regression.
2. Multiple Regression.
2. Multiple Regression.
*1.Simple Regression:(x_1,Y_1)(x_2,Y_2).......(x_n,Y_n).
*1.'''Simple Regression''':<math>(x_1,Y_1)(x_2,Y_2).......(x_n,Y_n)</math>.
*2.Multiple regression:((x1)_1,(x2)_1,(x3)_1.....(xK)_1,Y_1)
*2.'''Multiple regression''':<math>({(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)</math>.
*The only difference between Simple Regression and Multiple Regression is there where one preditor or many.
*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.
*i.e., The difference is depending of the x-value.
*The Predictor x is indicated as the "Independent Variable" .
*The Predictor x is indicated as the "Independent Variable" .
*The output of a Regression statistics is of the form :
*The output of a Regression statistics is of the form :
*Simple Regression Y(cap)=b_0+b_1x.
*Simple Regression:<math>\hat Y = b_0+b_1x</math>.
*Multiple Regression Y(cap)=b_0+b_1(x1)+b_2(x2)+......+b_K(xK).
*Multiple Regression:<math>\hat Y = b_0+b_1(x1)+b_2(x2)+......+b_K(xK)</math>.
*This analysis give the result in three table values.
*This analysis give the result in three table values.
1.Regression statistics table.
1.Regression statistics table.
2.ANOVA table.
2.ANOVA table.
3.Residual output.
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.
*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.
*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.
*Standard Error refers to the estimated standard deviation of the error term.
*It is called the standard error of the regression.
*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.
*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.
*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.
*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.
*This table is displaying the values of Predicted data, Standard Residuals and Percentile value of the Y-value.