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Sum of the OLS coefficients

EasyStatistics~4m

For the data (−2,3), (−1,2), (0,1), (1,1), (2,0.5)(-2,3),\,(-1,2),\,(0,1),\,(1,1),\,(2,0.5), fit Y=β0+β1x+ϵY = \beta_0 + \beta_1 x + \epsilon by least squares. Compute β^0+β^1\hat\beta_0 + \hat\beta_1.

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  1. xˉ=0\bar x=0, so β^0=yˉ\hat\beta_0=\bar y and β^1=∑xiyi∑xi2\hat\beta_1=\tfrac{\sum x_iy_i}{\sum x_i^2}.
  2. β^1=−6/10=−0.6\hat\beta_1=-6/10=-0.6, β^0=1.5\hat\beta_0=1.5.

Answer

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0.9 (± 0.001)

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Asked at: Citadel, Two Sigma

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