R-Squared (Coefficient of Determination) Statistics Example 1

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

Example 1

hard
A regression model has R2=0.85R^2 = 0.85. Interpret this value.

Solution

  1. 1
    Step 1: R2=0.85R^2 = 0.85 means 85% of the variability in the response variable is explained by the linear relationship with the explanatory variable.
  2. 2
    Step 2: The remaining 15% is due to other factors or random variation.
  3. 3
    Step 3: An R2R^2 of 0.85 indicates a strong linear fit.

Answer

85% of the variation in yy is explained by the linear model.
R2R^2 (coefficient of determination) ranges from 0 to 1. Higher values mean the model explains more variability. It is the square of the correlation coefficient rr.

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 2 hard

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

Example 3 hard

Two models are compared: Model A has [formula] and Model B has [formula]. Which model provides a bet

Example 4 hard

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

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