Correlation Math Example 3

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Example 3

medium
If r=0.92r = 0.92, what is the coefficient of determination r2r^2, and what does it mean?

Solution

  1. 1
    r2=(0.92)2=0.8464r^2 = (0.92)^2 = 0.8464.
  2. 2
    This means approximately 84.6%84.6\% of the variation in yy is explained by the linear relationship with xx.

Answer

r2≈0.846r^2 \approx 0.846
The coefficient of determination r2r^2 tells us the proportion of variance in one variable that is predictable from the other. The remaining 15.4%15.4\% is unexplained variation.

About Correlation

Correlation measures the strength and direction of the linear relationship between two quantitative variables, ranging from −1-1 to +1+1.

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More Correlation Examples

Example 1 medium

Given five data points [formula], compute the Pearson correlation coefficient [formula].

Example 2 easy

A study finds [formula] between hours of TV watched per day and exam scores. Interpret this value.

Example 4 easy

A study finds a correlation coefficient of [formula] between height and arm span. Describe the direc

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