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

Annual output (in thousand units) of a plant for 5 successive years is 10, 14, 18, 22 and 26. Fitting a straight-line trend by the method of least squares with origin at the middle year, what is the trend value for the year after the last year (the 6th year)?

The trend value is 30 thousand units. The data rise by 4 each year, so the least squares line is Y = 18 + 4x with the middle year as origin. The sixth year is x = 3, giving 18 plus 12, which equals 30.

  1. A30Correct
  2. B28
  3. C34
  4. D32

Explanation

Mean = 90/5 = 18; with the middle year as origin (x = -2 to 2), b = ΣxY/Σx² = (-20-14+0+22+52)/10 = 40/10 = 4. Trend = 18 + 4x. The 6th year has x = 3, so the value is 18 + 12 = 30. Using x = 4 would give 34, a wrong origin shift.

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