How do we calculate ( Predictive R-squared ) using ( SPSS ) to find if Regression Overfitting ??
You seem confused. You may want adjusted R squared or something else even. Why not try googling regression overfitting or look in z-library for Applied Linear Statisical Models 5th ed by Kutner.to see what is going on here. BTW the last time I looked the SPSS regression routine supplied both of those statistics. Best wishes, David Booth BTW The attached may be of some use.
A bit of Googling tells me that Minitab has an option to report the predicted (or predictive) R2. But AFAIK, SPSS does not have that option. However, it does allow you to save the deleted (leave one out) residuals, so you can compute it yourself. Here's an example. I have not compared it to a worked example, so cannot guarantee that I've made no mistakes, but I think I have it right. Notice that I did not multiply (1-PRESS/SStot) by 100 so that the scaling would be the same as for R2 and Adj R2 in the SPSS output. HTH.
*** Start of syntax ***.
* Compute "predictive Rsq" for regression model.
* Use the survey_sample.sav file that comes with SPSS.
NEW FILE.
DATASET CLOSE ALL.
* Change path on next line to folder where the sample datasets are stored.
GET FILE='C:\SPSSdata\survey_sample.sav'.
* Estimate model and save the "deleted" (leave one out) residuals.
REGRESSION
/STATISTICS COEFF OUTS CI(95) R ANOVA
/DEPENDENT age
/METHOD=ENTER educ paeduc maeduc
/SAVE DRESID(LOO_res).
* Keep only records with complete data.
SELECT IF NMISS(age,educ,paeduc,maeduc) EQ 0.
COMPUTE LOO_res_sq = LOO_res**2.
AGGREGATE
/OUTFILE=* MODE=ADDVARIABLES
/BREAK=
/SampSize=NU
/age_sd=SD(age)
/PRESS=SUM(LOO_res_sq).
COMPUTE SStot = age_sd**2*(SampSize-1).
COMPUTE PredRsq = 1 - PRESS / SStot.
FORMATS PRESS SStot PredRsq (F8.4).
LIST PRESS SStot PredRsq /CASES=FROM 1 TO 1.
*** End of syntax ***.
References
- https://rpubs.com/RatherBit/102428
- https://en.wikipedia.org/wiki/PRESS_statistic
- https://blog.minitab.com/en/adventures-in-statistics-2/multiple-regession-analysis-use-adjusted-r-squared-and-predicted-r-squared-to-include-the-correct-number-of-variables
- https://www.ibm.com/support/pages/does-spss-statistics-produce-press-statistic
Bruce Weaver Sorry I didn't connect R**2 With the PRESS statistic. Mea Culpa. Thanks for setting it right. Best, David Booth
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