Which two of the of the following statements are correct regarding R2 as a tool to evaluate a regression model. Multiple answers allowed.a.The R2 is the proportion of the total variation in X that can be explained by the variation in the dependent variable in the model.b. If the R2 value is greater than 1, then it shows that the regression model is a very good fit.c.The R2 value needs to be reported in presenting regression results as it shows the relative precision of the model for the users to consider.d.R2 reflects the model’s improvement of the predicted value over the estimator of the sample mean (Y-bar).
Question
Which two of the of the following statements are correct regarding R2 as a tool to evaluate a regression model. Multiple answers allowed.a.The R2 is the proportion of the total variation in X that can be explained by the variation in the dependent variable in the model.b. If the R2 value is greater than 1, then it shows that the regression model is a very good fit.c.The R2 value needs to be reported in presenting regression results as it shows the relative precision of the model for the users to consider.d.R2 reflects the model’s improvement of the predicted value over the estimator of the sample mean (Y-bar).
Solution
The correct statements regarding R2 as a tool to evaluate a regression model are:
c. The R2 value needs to be reported in presenting regression results as it shows the relative precision of the model for the users to consider.
d. R2 reflects the model’s improvement of the predicted value over the estimator of the sample mean (Y-bar).
Explanation:
a. This statement is incorrect because R2 is the proportion of the total variation in the dependent variable (Y) that can be explained by the independent variable(s) (X) in the model, not the other way around.
b. This statement is incorrect because R2 value ranges from 0 to 1. A value greater than 1 is not possible. If R2 is 1, it means the model perfectly fits the data. If it's 0, it means the model does not explain any variability of the response data around its mean.
c. This statement is correct. The R2 value is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. Therefore, it is important to report it when presenting regression results.
d. This statement is correct. R2 reflects how much better the regression line is as a predictor of the dependent variable values compared to the mean of those values (Y-bar). If R2 is high, the regression line is a good predictor. If R2 is low, the mean of the dependent variable values is a better predictor.
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