least-squares regression line

y-hat = 1.3 + 0.9x

r = 0.9, r² = 0.81: about 81% of the variation in y is explained by the linear relationship with x.

xypredictedresidual
122.2-0.2
233.1-0.1
3541
444.9-0.9
565.80.2

Steps

  1. 1.n = 5; x-bar = 3, y-bar = 4
  2. 2.sx = 1.5811, sy = 1.5811, r = 0.9
  3. 3.slope b = r(sy/sx) = 0.9 x (1.5811/1.5811) = 0.9
  4. 4.intercept a = y-bar - b(x-bar) = 4 - 0.9 x 3 = 1.3

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