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CFA Level I · CFA Level I Exam · Applications of Simple Linear Regression in Finance

In a simple linear regression of a stock's monthly returns on a market index's returns, the sum of squares total is 400 and the sum of squares regression is 100. The R-squared of the regression is most likely:

R-squared is 0.25. It is the sum of squares regression divided by the sum of squares total, 100/400, meaning the index explains a quarter of the variation in the stock's returns. The 0.75 figure is the unexplained share.

  1. A0.25Correct
  2. B0.75
  3. C4.00

Explanation

R-squared equals explained variation divided by total variation: SSR/SST = 100/400 = 0.25. The value 0.75 is the unexplained proportion (SSE/SST), which is the wrong ratio. A value of 4.00 inverts the ratio, and R-squared cannot exceed 1.

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