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NDA 2024 · PYQ · Statistics / Regression · medium

From data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as y = a + bx, then what is the value of 2a + 15b?

  1. A.6
  2. B.11✓ Correct
  3. C.17
  4. D.21

Explanation

For data points (-4,1), (-1,2), (2,7), (3,1): n=4, Σx = 0, Σy = 11, Σxy = -4+(-2)+14+3 = 11, Σx² = 16+1+4+9 = 30. Mean x̄ = 0, ȳ = 11/4. b = (nΣxy - ΣxΣy)/(nΣx² - (Σx)²) = (4·11 - 0)/(4·30 - 0) = 44/120 = 11/30. a = ȳ - b·x̄ = 11/4 - 0 = 11/4. So 2a + 15b = 2(11/4) + 15(11/30) = 11/2 + 11/2 = 11.
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