Coefficient of Determination Math Example 3

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Example 3

easy
The correlation between study hours and test score is r=0.8r=0.8. Calculate R2R^2 and interpret it.

Solution

  1. 1
    R2=r2=(0.8)2=0.64R^2 = r^2 = (0.8)^2 = 0.64
  2. 2
    Interpretation: 64% of the variation in test scores is explained by variation in study hours

Answer

R2=0.64R^2 = 0.64. Study hours explain 64% of variation in test scores.
For simple linear regression, R2=r2R^2 = r^2 where rr is the correlation coefficient. R2=0.64R^2 = 0.64 means 64% of y's variability is accounted for by x; the remaining 36% is due to other factors not in the model.

About Coefficient of Determination

The proportion of the total variation in the response variable yy that is explained by the linear relationship with the explanatory variable xx. It equals the square of the correlation coefficient: r2r^2.

Learn more about Coefficient of Determination →

More Coefficient of Determination Examples

Example 1 medium

A regression model has [formula] (total variation) and [formula] (unexplained variation). Calculate

Example 2 hard

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Example 4 hard

A model has [formula]. A researcher concludes 'the model is perfect and ready for deployment.' Ident

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