R-Squared (Coefficient of Determination) Statistics Example 4

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

Example 4

hard
A linear model has R2=0.64R^2 = 0.64. What percentage of the variation is not explained by the model?

Solution

  1. 1
    Step 1: R2=0.64R^2 = 0.64 means 64% of the variation is explained by the model.
  2. 2
    Step 2: The unexplained percentage is 100%−64%=36%100\% - 64\% = 36\%.

Answer

36%36\% of the variation is not explained by the model.
R-squared tells us how much variability is explained by a model, but not all of it. The remainder represents noise, omitted variables, or other patterns not captured by the model.

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.

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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 3 hard

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

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