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CMA Intermediate · Financial Management and Business Data Analytics · Data Analysis and Modelling

In a simple linear regression of a company's share returns on market returns, the correlation coefficient is 0.8. What proportion of the variation in share returns is explained by the market returns?

The proportion of variation explained is the coefficient of determination, r squared. With r = 0.8, r squared is 0.64, so 64 percent of the variation in share returns is explained by market returns, and the remaining 36 percent is unexplained.

  1. A64%Correct
  2. B80%
  3. C8%
  4. D36%

Explanation

The coefficient of determination is r squared = 0.8 x 0.8 = 0.64, so 64% of the variation is explained. 80% wrongly uses r directly. 36% is the unexplained proportion (1 - 0.64), a different quantity.

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