Question

Rob found that the coefficient of determination between the length of essays submitted to a teacher x and the score the teacher gave the essay y was about 0.661. What can we conclude?

Answer 1

Answer:

The coefficient of determination is used to measure how well a model fits the real data, or how well it can replicate them. The closer to 1 the value of R ^ 2 the more accurate the model is.

In this case, that R ^ 2 = 0.661 means that the model fits moderately to the variable to be studied.

For a linear regression model, the coefficient of determination is the square of the correlation coefficient r of Pearson. So:

$r =\sqrt{R^2}$

r = 0.813

This value of r close to 1 means that the length of the essays sent to a teacher (x) and the score that the teacher gave to the essay (and) are highly related.