R-Squared (Coefficient of Determination) Statistics Example 2

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Example 2

hard
If the correlation coefficient is r=−0.9r = -0.9, find R2R^2 and interpret both values.

Solution

  1. 1
    Step 1: R2=(−0.9)2=0.81R^2 = (-0.9)^2 = 0.81.
  2. 2
    Step 2: r=−0.9r = -0.9 tells us there is a strong negative linear relationship.
  3. 3
    Step 3: R2=0.81R^2 = 0.81 tells us 81% of the variation in yy is explained by the linear model.

Answer

R2=0.81R^2 = 0.81. Strong negative linear relationship; 81% of variation explained.
R2R^2 does not indicate direction — only strength. The sign of rr tells us the direction (positive or negative), while R2R^2 tells us the proportion of variation explained.

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 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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