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# Multiple Regression - Essay Example

## Extract of sampleMultiple Regression

They help in assessing the likely value of the regression coefficients in the population.

Model Fit: It provides a statistical test of the models ability to predict the outcome variable and also the value of R, R2 and adjusted R2.

Estimates: They give the estimated coefficients of the regression mode. The test statistics and their significances are also obtained for each regression. Here T-test is used to see whether each b differences significantly from zero.

Durbin Watson: This test statistic tests the assumption of independent errors. If the value is different from value Z, then it is cause of concern.

When this data is run on SPSS taking Satisfaction as dependent variable and functional, Epistemic, Social, Emotional, Conditional as independent variables, we get the following outputs.

The first output is the Descriptive statistics.

Descriptive Statistics

Mean
Std. Deviation
N
Satisfaction
5.1369
1.18900
389
Functional
5.4989
.91570
389
Epistemic
5.3492
.95148
389
Social
5.3209
1.27152
389
Emotional
5.4961
1.04150
389
Conditional
3.4679
1.01706
389

This table gives the mean and standard deviation of each of the variables. This is useful for summary of data.

Correlations

Satisfaction
Functional
Epistemic
Social
Emotional Conditional
Conditional
Pearson Correlation
Satisfaction
1.000
.555
.618
.339
.565
.004

Functional
.555
1.000
.509
.221
.520
.011

Epistemic
.618
.509
1.000
.328
.531
.109

Social
.339
.221
.328
1.000
.338
.148

Emotional
.565
.520
.531
.338
1.000
.154

Conditional
.004
.011
.109
.148
.154
1.000

Sig. (1-tailed)
Satisfaction
.
.000
.000
.000
.000
.471

Functional
.000
.
.000
.000
.000
.415

Epistemic
.000
.000
.
.000
.000
.016...
Once the dependent and independent variable are selected, the method for variables to enter can be selected or to be removed using any of the methods say stepwise, Remove, Backward or Forward. When clicked on the statistics, the estimate confidence intervals and model fit are selected and in the residuals Durbin-Watson is selected. The significance of each of these is as follows.
Estimates: They give the estimated coefficients of the regression mode. The test statistics and their significances are also obtained for each regression. Here T-test is used to see whether each b differences significantly from zero.
The correlation matrix gives the Pearson correlation coefficient between every pair of variables. It also gives the one significance of each correlation. Here we observe that the correlation is significant with p ...Show more

## Summary

The general form of the multiple regression is Y= a +b1X1 +b2X2+b3X3.+bnXn + e which can be estimated by Y= a +b1X1 +b2X2+b3X3.+bnXn, where a is the intercept and bi's are the partial regression coefficients.
Coefficient of Multiple Determination: R2 which gives the % of the variance in the dependent variable that is explained by the variation in the independent variables…
Author : yshanahan
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