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CMA Intermediate · Financial Management and Business Data Analytics · Data Analysis and Modelling

For five observations, the sums are: n = 5, ΣX = 20, ΣY = 50, ΣXY = 230, ΣX² = 90. Using least squares, what is the regression coefficient of Y on X (slope) and the intercept?

The slope is (5x230 - 20x50)/(5x90 - 400) = 150/50 = 3, and the intercept is mean Y minus slope times mean X, which is 10 - 12 = -2. The options listed do not match this result.

  1. ASlope 3.5, intercept -4Correct
  2. BSlope 3.5, intercept 4
  3. CSlope 2.5, intercept 0
  4. DSlope 4.0, intercept -6

Explanation

Slope b = (nΣXY - ΣXΣY)/(nΣX² - (ΣX)²) = (1150 - 1000)/(450 - 400) = 150/50 = 3. Recheck: 5x230 = 1150; 20x50 = 1000; difference 150; denominator 50; b = 3. Intercept = 10 - 3x4 = -2. None match, so this item is invalid.

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