What is R Square, F Square, and Q Square in PLS-SEM (SmartPLS)

R square, F square, and Q square are three PLS-SEM metrics that answer different questions about a structural model: how much variance the model explains, how much each predictor matters, and whether the model has predictive relevance. R square quantifies explained variance in an endogenous (dependent) construct. In plain terms, it tells how much change in the dependent variable can be accounted for by one or more independent variables.

In the example used to interpret R square, a dependent variable Y influenced by X1, X2, and X3 has an R square of 0.623. That translates to 62.3% of the variance in Y being explained by those predictors. In SmartPLS, interpretation is guided by the arrows pointing toward the endogenous construct(s): each endogenous construct gets its own R square value.

Thresholds for judging whether an R square is “adequate” vary across researchers. Chin (1998) proposed benchmarks of 0.26 for substantial, 0.13 for moderate, and 0.02 for weak explanatory power. Later, Hair and colleagues suggested higher cutoffs for endogenous latent variables—around 0.25 (substantial), with 0.50 and 0.75 often used as stronger benchmarks in broader SEM practice—framing 0.25 as a minimum for a meaningful level of explained variance. The key takeaway is that R square is not just a number; it’s evaluated against accepted effect-size guidelines.

F square shifts the focus from overall explained variance to the contribution of specific exogenous variables. F square is computed as the change in R square when an exogenous construct is removed from the model. If removing a predictor barely changes R square, that predictor has little practical impact. Common effect-size guidance (Cohen, 1988) treats F square values above 0.02 as small, above 0.15 as medium, and above 0.35 as large. In practice, this helps identify which predictors are worth keeping versus which may be redundant.

Q square addresses a different concern: prediction. Q square (predictive relevance) is assessed via SmartPLS’s blindfolding procedure, which systematically omits data points and checks how well the model reconstructs them. A Q square greater than zero indicates predictive relevance for the endogenous construct. The transcript also notes that blindfolding requires selecting an omission distance D, typically between 5 and 12, with 7 used as a default in the example.

A worked SmartPLS example ties everything together using a loyalty outcome predicted by satisfaction, service quality, Corporate social responsibility (CSR), and image. The model reports an R square of 0.719, meaning 71.9% of the variance in loyalty is explained by those predictors. F square results indicate that removing image has a substantial impact on R square, removing CSR and satisfaction affects it, and removing service quality does not meaningfully change R square—suggesting service quality could be removed to improve parsimony. Finally, blindfolding yields a Q square of 0.410, which is well above zero, indicating substantial predictive relevance. Together, these metrics provide a structured way to judge explanation strength, predictor importance, and out-of-sample predictive usefulness in PLS-SEM.