What Does R-Square Mean? Why Is It a Statistic Every Doctoral Researcher Should Understand?

What Does R-Square Mean? Why Is It a Statistic Every Doctoral Researcher Should Understand?

When running regression analysis or SEM, many doctoral researchers focus primarily on the Path Coefficient or p-value and overlook another important statistic: R-square (R²).

In reality, a model can have statistically significant hypotheses while still having a relatively low R², indicating that its overall explanatory power may be limited.

So, what is R-square?

R-square (Coefficient of Determination) indicates the proportion of variance in the dependent variable that is explained by the predictors in the model.

For example:

• R² = 0.65 means that the model explains 65% of the variance in the variable Purchase Intention.
• The remaining 35% is attributable to other factors not included in the model and unexplained variance.

In other words, R² provides an indication of how well the model explains the variance in an endogenous construct.

An Example in Marketing Research

Suppose you are studying the effects of:

• Service Quality
• Perceived Value
• Brand Trust

→ on Purchase Intention.

After running SEM, you obtain:

R² for Purchase Intention = 0.72

This means that the three predictor variables collectively explain 72% of the variance in Purchase Intention, while the remaining 28% is associated with other factors, such as advertising, previous experiences, individual characteristics, and other variables not included in the model.

This makes R² an important indicator for assessing the explanatory power of a research model, rather than simply looking at whether individual hypotheses are statistically significant.

Does a Higher R² Always Mean a Better Model?

Not necessarily.

In social science research, human behavior is influenced by numerous factors, making a very high R² difficult—and sometimes inappropriate—to achieve.

What matters more is whether:

• The model is grounded in a strong theoretical foundation.
• The selected constructs are theoretically and empirically appropriate.
• The findings provide meaningful academic and practical contributions.

A model with a moderate R² but a strong theoretical foundation may have greater scientific value than a model designed primarily to maximize R².

👉 Understanding R-square correctly not only helps you interpret SEM results accurately, but also enables you to build a more convincing research model for your thesis defense and international publications.

Dr. My Academy supports Master’s and doctoral researchers in developing their expertise in SPSS, AMOS, SmartPLS, and SEM according to international research standards.

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