This is really a rare case. Please try stratified analysis by variable cso179r and compare the results.

Check for difference in R2 and Adjusted R2 in the model with larger R2 but p value 0.530, the problem may be due to overfitting which is indicated by large difference in R2 and Adjusted R2 values . Theoretically R2 is greater than or equals to R2 adjusted .also check for the condition number of the design matrix associated with the reggresion , multicollinearity can be a problem here.

Dear Bagus,

I did linear regression using R and results indicate that your model is not a good one.

Many variables are not statistical significant:

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 7.0710369 0.7707743 9.174 1.24e-09 ***

NEOB_16Ep -0.0405178 0.0948151 -0.427 0.6727

NEOB_26Ep 0.1218184 0.1410065 0.864 0.3955

NEOB_36En 0.0048615 0.1074088 0.045 0.9642

NEOB_7Np -0.0003444 0.0979849 -0.004 0.9972

NEOB_17Nn -0.1557074 0.1039725 -1.498 0.1463

NEOB_27Nn 0.1207488 0.1073333 1.125 0.2709

NEOB_13Op -0.0183065 0.1608861 -0.114 0.9103

NEOB_23On 0.0523251 0.1036762 0.505 0.6180

NEOB_33Op -0.2133772 0.1124362 -1.898 0.0689 .

NEOB_19Vp 0.0280597 0.1397770 0.201 0.8425

NEOB_49Vn 0.1207761 0.1154743 1.046 0.3052

NEOB_54Vn -0.1374298 0.1194060 -1.151 0.2602

NEOB_15Gp -0.2682287 0.1497143 -1.792 0.0848 .

NEOB_60Gp 0.0383703 0.1288024 0.298 0.7681

NEOB_70Gp 0.0423843 0.1469551 0.288 0.7753

hlmt_150 -0.0677870 0.1028807 -0.659 0.5158

hlmt_115 0.0466131 0.1767453 0.264 0.7941

hlmt_147 0.0545637 0.1735998 0.314 0.7558

hlmt_26 0.0606365 0.1234848 0.491 0.6275

hlmt_122 -0.0618753 0.1224576 -0.505 0.6176

hlmt_54 -0.0258993 0.1143921 -0.226 0.8227

cso45 -0.1440412 0.1166913 -1.234 0.2281

cso75 0.0683229 0.1263918 0.541 0.5934

cso82r -0.0137993 0.1613865 -0.086 0.9325

cso83 0.0423171 0.1905815 0.222 0.8260

cso86 0.3034884 0.1392924 2.179 0.0386 *

cso89 0.0688177 0.1544709 0.446 0.6596

cso179r 0.0075347 0.1359442 0.055 0.9562

cso199 -0.0702202 0.1517985 -0.463 0.6475

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8036 on 26 degrees of freedom

Multiple R-squared: 0.5208, Adjusted R-squared: -0.01377

F-statistic: 0.9742 on 29 and 26 DF, p-value: 0.5298

Please find another model!

PS Regression was:

MEAN_Total ~ NEOB_16Ep + NEOB_26Ep + NEOB_36En + NEOB_7Np + NEOB_17Nn + NEOB_27Nn + NEOB_13Op + NEOB_23On + NEOB_33Op + NEOB_19Vp + NEOB_49Vn + NEOB_54Vn + NEOB_15Gp + NEOB_60Gp + NEOB_70Gp + hlmt_150 + hlmt_115 + hlmt_147 + hlmt_26 + hlmt_122 + hlmt_54 + cso45 + cso75 + cso82r + cso83 + cso86 + cso89 + cso179r + cso199

Bagus -

Are you certain that you are reading your SPSS results correctly?  I haven't used SPSS in many years, but I'm not certain that what you have makes sense. 

First, you do want to use adjusted R, but even that can be misleading.  It may not give you a good idea of model performance.  Using graphical residual analysis with estimated residuals on the y-axis, and predicted y on the x-axis can help determine model fit, and saving test data not used to estimate regression coefficients can help you to avoid overfitting. 

Also, p-values are impacted by sample size, so you need to adjust the threshold accordingly.  In fact p-values  are usually not helpful.  And here, are you sure you are reading from the correct parts of the table?  These are p-values for what, one of the regression coefficients?  You are really interested in predictions, perhaps prediction intervals for predicted y values, not confidence intervals for each regression coefficient.  Because of interactons, such as collinearity, between "independent" variables, such confidence intervals aren't very stable anyway.  The estimated coefficients themselves may even change sign. 

I note that you are looking at "change," as in the change when one independent variable is added or deleted, which might be interesting, but I'm not sure if you are really reading p-values there.  I am more certain regarding the dubious usefulness of p-values. 

Your sample size appears to be rather small, unless you have small variances of prediction errors given such a sample size.  Note that the estimated variance of a prediction error is different for each predicted y, given the natural heteroscedasticity due to different sizes (predicted y) for each member of your population.  Because the estimated variance of the prediction error uses an estimated sigma which is impacted by bias, this estimated variance may be a good overall indicator of accuracy. 

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I suggest that you use your subject matter expertise to pick a few reasonable models, and use graphical residual analyses and test data to compare their performances. 

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You also should make certain that you are using the software correctly and reading the results correctly.  Perhaps you are doing that, but it might be good to check with an SPSS representative online and confirm this. 

As for the very low adjusted R-square values, they would usually be expected to be associated with large variances of prediction errors and regression fits which are not very good, but this is not straightforward.  Also, the perhaps low sample size can cause interpretation problems. 

Cheers - Jim

You are fitting a complex model with a large number of terms to a small data set. The results are correctly warning you that you may get a rather apparently high Rsquared of 0.722 when the true value is zero, 53 times out of 100 just by chance. You are modelling noise not signal and the results strongly suggest that what you have found will not generalize.

As others have advised, much better to have a small set of theoretically justified predictors than this kitchen-sink approach. Regression is really not a discovery tool but a calibration one for the size of the effect and its uncertainty (ie the regression slope and associated standard error) , and of course it requires that a number of assumptions are at least approximately met. Stepwise regression is not a recommended way of developing understanding.

agree with above. simply put: you're under powered. Your confidence interval would probably range down to r=.2-ish.