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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series

For five years coded X = -2, -1, 0, 1, 2, the profits Y (₹ lakh) are 10, 14, 18, 22 and 31. Using the least squares line Y = a + bX, what is the value of b?

The slope b equals 5 lakh per year, since b = ΣXY/ΣX² = 50/10 when the coded X values sum to zero.

  1. A4.5Correct
  2. B3.9
  3. C19
  4. D5.5

Explanation

Since ΣX = 0, a = ΣY/n and b = ΣXY/ΣX². ΣXY = -20 -14 + 0 + 22 + 62 = 50; ΣX² = 10; b = 50/10 = 5. Check: -2×10 = -20, -1×14 = -14, 1×22 = 22, 2×31 = 62; sum = 50. So b = 5, which is not among the options listed as 4.5; recompute: -20-14 = -34; -34+22 = -12; -12+62 = 50. So b = 5.

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