# Steps after cross-validation in Linear Regression

After making some variable transformations, I chose this model because I works well with the assumptions and gives the largest R-Squared and the smallest Overall MS in cross-validation between a set of linear models.

> gn<- lm(NA.~ I(PC^0.25) + I(((PI)^2)),data=DSET)
> summary(gn)

Call:
lm(formula = NA. ~ I(PC^0.25) + I(((PI)^2)), data = DSET)

Residuals:
Min      1Q  Median      3Q     Max
-425.22  -87.46   -2.30   79.11  396.14

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.047e+03  1.094e+02  -18.71  < 2e-16 ***
I(PC^0.25)   1.206e+03  4.231e+01   28.52  < 2e-16 ***
I(((PI)^2)) -5.242e-02  1.233e-02   -4.25 2.81e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 127.2 on 319 degrees of freedom
Multiple R-squared:  0.7475,    Adjusted R-squared:  0.746
F-statistic: 472.3 on 2 and 319 DF,  p-value: < 2.2e-16


The output of the cross-validation is the following:

> a<-CVlm(df=DSET,form.lm = gn ,m=5)
Analysis of Variance Table

Response: NA.
Df   Sum Sq  Mean Sq F value  Pr(>F)
I(PC^0.25)    1 14979750 14979750   926.5 < 2e-16 ***
I(((PI)^2))   1   292051   292051    18.1 2.8e-05 ***
Residuals   319  5157489    16168
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

fold 1
Observations in test set: 64

Sum of squares = 1119289    Mean square = 17489    n = 64

fold 2
Observations in test set: 65

Sum of squares = 1072687    Mean square = 16503    n = 65

fold 3
Observations in test set: 65

Sum of squares = 865598    Mean square = 13317    n = 65

fold 4
Observations in test set: 64

Sum of squares = 1178545    Mean square = 18415    n = 64

fold 5
Observations in test set: 64

Sum of squares = 1042335    Mean square = 16286    n = 64

Overall (Sum over all 64 folds)
ms
16393

>


So, my question is, Which steps do you recommend to me after the cross-validation? Should I choose the training set applied to the fold 3(it gives the small mean square error)? Is there a way to improve the coefficients after the cross-validation?