# Understanding R Square, F Square, and Q Square using SMART-PLS

## R-Square

• R Square statistics explains the variance in the endogenous variable explained by the exogenous variable(s).
• For example, a variable Y influenced by X1, X2, and X3 has a R-Square value of 0.623. This would mean that 62.3% change in Y can be explained by X1, X2, X3.
• In order to make it easier to interpret, look for the arrows that are pointing towards the dependent (endogenous) variable.
• Falk and Miller (1992) recommended that R2 values should be equal to or greater than 0.10 in order for the variance explained of a particular endogenous construct to be deemed adequate.
• Cohen (1988) suggested R2 values for endogenous latent variables are assessed as follows: 0.26 (substantial), 0.13 (moderate), 0.02 (weak).
• Chin (1998) recommended R2 values for endogenous latent variables based on: 0.67 (substantial), 0.33 (moderate), 0.19 (weak).
• Hair et al. (2011) & Hair et al. (2013) suggested in scholarly research that focuses on marketing issues, R2 values of 0.75, 0.50, or 0.25 for endogenous latent variables can, as a rough rule of thumb, be respectively described as substantial, moderate or weak.

## F-Square

• A variable in a structural model may be affected/influenced by a number of different variables.
• Removing an exogenous variable can affect the dependent variable.
• F-Square is the change in R-Square when an exogenous variable is removed from the model.
• f-square is effect size (>=0.02 is small; >= 0.15 is medium;>= 0.35 is large) (Cohen, 1988).

## Q-Square

• Q-square is predictive relevance, measures whether a model has predictive relevance or not (> 0 is good).
• Further, Q2 establishes the predictive relevance of the endogenous constructs.
• Q-square values above zero indicate that your values are well reconstructed and that the model has predictive relevance.
• A Q2 above 0 shows that the model has predictive relevance.
• In order to find out the Q Square value, Run Blindfolding procedure in SMART-PLS.

## References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Ed.). New York: Routledge.
• Chin, W. W. (1998). The partial least squares approach to structural equation modeling. Modern methods for business research, 295(2), 295-336.
• Falk, R. F., & Miller, N. B. (1992). A primer for soft modeling. University of Akron Press.
• Hair, J. F., Ringle, C. M., & Sarstedt, M. (2011). PLS-SEM: Indeed a silver bullet. Journal of Marketing theory and Practice, 19(2), 139-152.
• Hair, J. F., Ringle, C. M., & Sarstedt, M. (2013). Partial least squares structural equation modeling: Rigorous applications, better results and higher acceptance. Long range planning, 46(1-2), 1-12.