R-Squared (Coefficient of Determination) Statistics Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

hard
Two models are compared: Model A has R2=0.72R^2 = 0.72 and Model B has R2=0.58R^2 = 0.58. Which model provides a better fit and why?

Solution

  1. 1
    Step 1: Model A explains 72% of the variation; Model B explains 58%.
  2. 2
    Step 2: Model A provides a better fit because it explains a larger proportion of the variability.

Answer

Model A is the better fit (R2=0.72>0.58R^2 = 0.72 > 0.58).
When comparing models, a higher R2R^2 indicates the model captures more of the variability in the data, though other factors like simplicity also matter.

About R-Squared (Coefficient of Determination)

R-squared (the coefficient of determination) is the proportion of variance in the dependent variable that is explained by the independent variable(s) in a regression model. It ranges from 0 to 1, where 0 means the model explains none of the variability and 1 means it explains all of it.

Learn more about R-Squared (Coefficient of Determination) →

More R-Squared (Coefficient of Determination) Examples

Example 1 hard

A regression model has [formula]. Interpret this value.

Example 2 hard

If the correlation coefficient is [formula], find [formula] and interpret both values.

Example 4 hard

A linear model has [formula]. What percentage of the variation is not explained by the model?

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