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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Correlation and Regression

In a study of 40 shops in Kolkata, the total variation in daily sales is 500 (in squared units) and r = 0.7 between sales and footfall. The unexplained variation in sales is:

The unexplained variation is 255. The coefficient of determination is 0.7 squared, or 0.49, so explained variation is 49 percent of 500, which is 245. Subtracting from the total of 500 leaves 255. Using 0.7 directly instead of its square would give a wrong figure.

  1. A245
  2. B255Correct
  3. C350
  4. D150

Explanation

r² = 0.49, so explained variation = 0.49 x 500 = 245. Unexplained variation = 500 - 245 = 255, equivalently 0.51 x 500. 245 is the explained part, while 350 and 150 wrongly use r (0.7 and 0.3) instead of r².

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