Question

Interpreting\({R^2}\)For the multiple regression equation given in Exercise 1, we get \({R^2}\)= 0.928. What does that value tell us?

Short answer

The value \({R^2} = 0.928\) indicates that 92.8% variation in the response variable “weight of bears” is explained by the linear relationship between the variables “weight,” “length,” and “chest size”.

Step-by-step solution

Given information

A regression equation is computed to predict the weight of a bear (in lb) using the linear relationship between the variables “weight,” “length,” and “chest size.”

Interpretation of \({R^2}\)

The value of \({R^2}\) for a regression model implies how good the predicted model is.

In other words, it indicates the percentage of variation explained by the linear relation of the response variables with the predictor variables.

Here, a regression equation is constructed with “weight of bears” as the response variable and “length” and “chest size.”

The value of\({R^2} = 0.928\)indicates that 92.8% variation in the weight of bears can be explained by their lengths and chest sizes.