# Regression Outputs

See Regression for a description of how to generate the outputs described on this page and Regression Troubleshooting for a description of some common difficulties and their solutions.

## p-Values by question

The first table of the output screen contains p-values for significance tests for all of the Independent questions. The word INCLUDED indicates the question is in the final model. EXCLUDED will appear if the question has been excluded by stepwise selection.

```p-values of All Questions (Included and Excluded)
p-Values
INCLUDED Satisfaction with fees (linear)                	    .000
INCLUDED Satisfaction with interest rates (linear)      	    .000
INCLUDED Satisfaction with phone (linear)               	    .000
INCLUDED Satisfaction with branch (linear)              	    .000
INCLUDED Satisfaction with availability of ATMs (linear)	    .000
INCLUDED Satisfaction with online (categorical)         	    .000
```

## Goodness of fit statistics

The R-Squared and Adjusted R-Squared are computed in the traditional way for linear regression models. For the other models, McFadden’s Rho-squared is employed. The AIC, which appears for all the models except linear regression, can be used for comparing different models (all else being equal, a lower AIC indicates a better model).

```Dependent question: Overall satisfaction (Linear)
Standard error of the residuals (model): .14557
R-Squared: .458
Model p-value: .00000
```

## Coefficients and related statistics

The following table of coefficients is interpreted in the standard way (see any book on regression or an econometrics textbook; some are listed below).

```
Coef	S.E.	t-Stat	p-Value	Beta	  VIF
Constant                       (intercept)           	-.288	.034	-8.489	   .000	 NaN	  NaN
fees (linear)                                       	 .353	.027	13.120	   .000	.327	1.008
interest rates (linear)                             	 .303	.026	11.729	   .000	.292	1.003
phone (linear)                                      	 .315	.028	11.256	   .000	.281	1.011
branch (linear)                                     	 .128	.010	13.087	   .000	.326	1.008
availability of ATMs (linear)                       	 .214	.025	 8.420	   .000	.211	1.018
online (categorical)           Very dissatisfied + 2	 .000	 NaN	   NaN	    NaN	 NaN	  NaN
3                    	 .036	.017	 2.191	   .029	.086	2.495
4                    	 .082	.016	 5.046	   .000	.201	2.586
5 + Very satisfied   	 .120	.018	 6.669	   .000	.242	2.140
```

See Ordered Logit and Multinomial Logistic Discriminant Analysis for additional information on the interpretation of outputs from these models.

## Good textbooks describing the interpretation of regression models

### Introductory

Fox, John (1997), Applied Regression Analysis, Linear Models, and Related Methods. Thousand Oaks: SAGE Publications

Kennedy, Peter (2008), A Guide to Econometric: Blackwell, 6th Edition