Question

The coefficient of determination is mathematically equivalent to the correlation coefficient omega-squared eta-squared both omega-squared and eta-squared

Answer 1

Answer:

The equivalent expression is $\eta^2$, because respect to $\omega^2$ the formula is different.

Step-by-step explanation:

The equivalent expression is $\eta^2$, because respect to $\omega^2$ the formula is different.

$\eta^2$ "describes the ratio of variance explained in the dependent variable by a predictor while controlling for other predictors", similar to the determination coefficient.

One property is that "is a biased estimator of the variance explained by the model in the population" when we are just estimating the size effect.

And other porty is that "measures the variance explained of the sample and not the population" and many times overestimate the effect size.

The formula for is given by:

$\eta^2 = \frac{SSR}{SST}$

Where SST represent the total sum of squares and SSR the sum squares for the regression.

$\omega^2$

This one is a similar estimator to the determination coefficient, but is a estimator with lower bias. And analyze again the variance explained like the determination coefficient and the $\eta^2$

Since have lower bias than $\eta^2$ is prefered, but sometimes is not easy to calculate it. The formula to calculate is given by:

$\omega^2=\frac{SS_{treatment}-(df_{treatment}*MS_{error})}{SS_{total}+MS_{error}}$

There are other estimators like the Cohen's $f^2$ and the Cohen's q who are similar estimators to the variance explained.