LO 3.2.2.A

Learning Objective: Interpret the coefficients of multiple linear regression.

Review:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><msub><mi>β</mi><mn>0</mn></msub><mo>+</mo><msub><mi>β</mi><mn>1</mn></msub><msub><mi>X</mi><mn>1</mn></msub><mo>+</mo><msub><mi>β</mi><mn>2</mn></msub><msub><mi>X</mi><mn>2</mn></msub><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><msub><mi>β</mi><mi>p</mi></msub><msub><mi>X</mi><mi>p</mi></msub><mo>+</mo><mi>ε</mi></math>

We interpret the coefficient 𝛽j as the average eﬀect on Y of a unit increase in Xj, holding all other predictors ﬁxed.