1

R²

SSR/SST

Squared multiple correlation coefficient

Goodness of Fit

Large samples

2

R² (adj.)

$1-\left(1-R^2\right)\left(n-1\right)/\left(n-p-1\right)$

Adjusted R²

Goodness of Fit + Parsimony

Large samples

3

RMSE

$\sqrt{\left({\displaystyle {\sum }_i\left({\left({\text{Predicted}}_i-{\text{Actual}}_i\right)}^2/n\right)}\right)}$

Root mean squared error

Goodness of Fit

Large samples

4

MS (LOF)

$\left(\text{RSS}-\text{SSpe}\right)/\left(n-p-\text{dpe}\right)$

Mean Square Lack of Fit

Lack of Fit

Any sample size

5

PRESS

${\displaystyle {\sum }_i\left(r_i/\left(1-H_{ii}\right)\right)}$

Prediction Sum of Squares

Prediction

Any sample size

6

R²-prediction

$\left[1-\left(\text{PRESS}/{\text{SSE}}_{\text{TOT}}\right)\right]\ast 100$

Allen (1971b)

Prediction

Any

sample size

7

Adequate Precision

$\left[\max \left(\widehat{Y}\right)-\min \left(\widehat{Y}\right)\right]/\sqrt{\left({\tilde{V}}_{\widehat{y}}\right)}>4$

This is a signal-to-noise ratio

Prediction

Any sample size

8

Cp

$\left({\text{SSE}}_{\text{p}}/{\sigma }^2\right)-n+2p$

Mallow’s Cp (1973)

Prediction

Large sample size

9

Cp -p

$\left({\text{SSE}}_{\text{p}}/{\sigma }^2\right)-n+p$

Mallow’s Cp (1973)

Prediction

Large sample size

10

AIC

$n\ast \ln \left(\text{SSE}/n\right)+2k$

Akaike (1973)

Goodness of Fit + Parsimony

Large sample size

11

SBC

$n\ast \ln \left(\text{SSE}/n\right)+k\ast \ln \left(n\right)$

Schwarz’s Bayesian Criterion (1978)

Goodness of Fit + Parsimony

Large sample size

12

BIC

$n\ast \ln \left(\text{SSE}/n\right)+\left[2\left(k+2\right)n{\sigma }^2/\text{SSE}\right]-\left[2{\left(n{\sigma }^2\right)}^2/SS{E}^2\right]$

Sawa (1978)

Goodness of Fit + Parsimony

Small sample size

13

APC_p

$\left(n+p\right)\text{SSE}/\left(n\ast \left(n-p\right)\right)$

Amemiya’s Prediction Criterion ()

Prediction

Any size

14

AICc

$\text{AIC}+2k\left(k+1\right)/\left(n-k-1\right)$

Corrected AIC, ugiura (1978)

Goodness of Fit + Parsimony

Small sample size

15

HQ

$n\ast \ln \left(\text{SSE}/n\right)+2p\ast \ln \left(\ln \left(n\right)\right)$

Hannan and Quinn (1979)

Goodness of Fit + Parsimony

Any sample size

16

HQc

$n\ast \ln {\left(\text{SSE}/n\right)}^2+2np\ast \ln \left(\ln \left(n\right)\right)/\left(n-p-1\right)$

Mcquarrie and Tsai (1998)

Goodness of Fit + Parsimony

Small sample size

17

KIC

$n\ast \ln \left(\text{SSE}/n\right)+3\left(k+1\right)$

Cavanaugh J. E. (1999)

Goodness of Fit + Parsimony

Large sample size

18

KICc

$n\ast \ln \left(\text{SSE}/n\right)+\left(k+1\right)\left(3n-k-2\right)/\left(n-k-2\right)+k/\left(n-k\right)$

Bekara M (2004)

Goodness of Fit + Parsimony

Small sample sizes

19

MKIC

$\left[2\left(n-P-2\right){\sigma }^{2}p/{\sigma }^{2}p\right]+2p-2n+4$

Cavanaugh J. E. (2004)

Goodness of Fit + Parsimony

Small sample sizes

20

MAIC

$\text{AICc}+\left[2p\left(n-p\right){\sigma }^{2}x/\left(n-p\right){\sigma }^2-1\right]-2{\left[\left(n-p\right){\sigma }^{2}x/\left(n-p\right){\sigma }^2-1\right]}^2$

Fujikoshi and Satoh (1997)

Goodness of Fit + Parsimony

Small sample sizes

21

TIC

$n\ast \ln \left(\text{SSE}/n\right)+2\left(k+1\right)$

Takeuchi Information Criterion ()

Goodness of Fit + Parsimony

Large sample size

22

S_p

${\text{RMS}}_{\text{p}}/\left(n-p-1\right)$

Hocking (1976)

Prediction

Large sample size

23

J_p

$S_p\ast \left(n-p-1\right)\left(n+p\right)/n$

Hocking (1976), Final Prediction Error

Prediction

Large sample size