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Business Strategy and Accounting Basics

At a fab, the monthly number of wafer starts x (thousand wafers) and electricity cost y (¥ million) were (x, y) = (2, 5), (4, 9), (6, 11) and (8, 15). If the regression line y = ax + b is found by the least squares method and the slope a is taken as the variable cost per thousand wafers and the intercept b as the fixed cost, which combination is correct?

  1. Aa = 1.6, b = 2
  2. Ba ≈ 1.67, b ≈ 1.67
  3. Ca = 2.0, b = 0
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Answer: A. a = 1.6, b = 2

The mean of x is 5 and the mean of y is 10; the sum of the products of deviations is (−3) × (−5) + (−1) × (−1) + 1 × 1 + 3 × 5 = 32, and the sum of squared deviations of x is 9 + 1 + 1 + 9 = 20. The least squares slope is a = 32 ÷ 20 = 1.6 and the intercept is b = 10 − 1.6 × 5 = 2, and the regression line passes through the point of means (5, 10). The correlation coefficient of these data is about 0.99, showing a strong positive correlation between wafer starts and electricity cost. Splitting costs into variable and fixed parts from past results in this way is called cost behavior analysis (cost estimation), and it is used in break-even analysis.

  • A. Correct. These are the least squares slope and intercept.
  • B. These are the values of the line through the highest and lowest points (2, 5) and (8, 15) (the high-low method). They generally differ from the least squares result, which uses all the data.
  • C. This takes the mean of y divided by the mean of x as the slope and sets the intercept to zero, which assumes there are no fixed costs.
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