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Subject:  Statistics

Linear regression for (1, 2), (2, 4), (3, 5), (4, 4), (5, 6)

Fit the least-squares line and report the correlation coefficient r.

Answer y = 0.8x + 1.8 (r = 0.852803)

Solution

  1. Means x̄ = 3, ȳ = 4.2
  2. Sums of squares Sxx = 10, Sxy = 8
  3. Slope b = Sxy / Sxx = 0.8
  4. Intercept a = ȳ − b·x̄ = 1.8
  5. Correlation r = 0.852803, r² = 0.727273
  6. Regression line y = 0.8x + 1.8

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