Simple Linear Regression - David Dalpiaz Simple Linear Regression STAT 3202 | OSU | Autumn 2018...

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Transcript of Simple Linear Regression - David Dalpiaz Simple Linear Regression STAT 3202 | OSU | Autumn 2018...

  • Simple Linear Regression STAT 3202 | OSU | Autumn 2018

    Dalpiaz

  • These aren’t really “slides,” instead just some visual aids for lecture today….

  • Speed Distance 4 2

    4 10

    7 4

    7 22

    8 16

    … …

    25 85

  • Assumptions and Diagnostics

  • Data and Model #1

  • Data and Model #2

  • Data and Model #3

  • Data and Model #4

  • Model 1: Y = 3 − 5x + ϵ, ϵ ∼ N(0, 1)

  • Model 2: Y = 3 − 5x + ϵ, ϵ ∼ N(0, x2)

  • Model 1: Y = 3 − 5x2 + ϵ, ϵ ∼ N(0, 5)

  • Model 4: Y = 3 − 5x + ϵ, ϵ ∼ Exp(1)

  • Multiple Linear Regression

  • Yi = β0 + β1xi1 + β2xi2 + ⋯ + βp−1xi(p−1) + ϵi, ϵi ∼ N(0,σ2)

    Y ∣ X = x ∼ N(β0 + β1x1 + β2x2 + ⋯ + βp−1x(p−1), σ2)