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

A trend line fitted by least squares to annual output of a Coimbatore mill is Y = 40 + 6X, where X is in years with origin at 2020 and Y is in thousand units. What is the trend value for 2024 and the annual change in trend?

The trend value for 2024 is 64 thousand units, with output rising 6 thousand units each year. With the origin at 2020, 2024 corresponds to X = 4, so Y = 40 + 6×4 = 64, and the slope of 6 is the yearly change.

  1. A64 thousand units; increase of 6 thousand per yearCorrect
  2. B46 thousand units; increase of 6 thousand per year
  3. C64 thousand units; increase of 40 thousand per year
  4. D70 thousand units; increase of 6 thousand per year

Explanation

For 2024, X = 2024 - 2020 = 4, so Y = 40 + 6×4 = 64. The slope 6 gives the annual change. Option 70 wrongly uses X = 5, which would be 2025.

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