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CS Executive · Corporate Accounting and Financial Management · Forecasting Financial Statements

Using the least squares method, the trend equation for a firm's sales (Rs lakh) is Y = a + bX, where X is the year index. For five years with X coded as -2, -1, 0, 1, 2, sales were 20, 24, 28, 32, 36. Using this trend, the forecast for the next year (X = 3) is:

The forecast is Rs 40 lakh. With coded X summing to zero, a equals the mean sales of 28 and b equals the sum of XY (40) over the sum of X squared (10), which is 4. Substituting X = 3 gives 28 + 12 = 40.

  1. ARs 44 lakh
  2. BRs 40 lakhCorrect
  3. CRs 38 lakh
  4. DRs 42 lakh

Explanation

Since sum X = 0, a = sum Y / n = 140/5 = 28. b = sum XY / sum X^2 = (-40 -24 + 0 + 32 + 72)/10 = 40/10 = 4. Y = 28 + 4(3) = Rs 40 lakh. Rs 44 lakh wrongly uses X = 4, and Rs 38 lakh uses X = 2.5.

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