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511_Chapter_10

# 511_Chapter_10 - Inferential Tools for Multiple Regression...

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1 Inferential Tools for Multiple Regression Stat 511 Chapter 10

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2 Profound Quote - Page 267 “Data analysis involves finding a good-fitting model whose parameters relate to the questions of interest.”
3 Outline Case Study 1 Case Study 2 Standard Errors Extra-Sums-of-Squares R-Squared Adjusted

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4 Case Study I -- Galileo controlled experiment from 1608 question: is the relationship a parabola? X = initial height of ball on incline Y = horizontal distance from edge of incline traveled by ball question can be approached by inferring whether the coefficients of X 2 and X 3 are different from 0 if parabola fits, coefficient of X 2 should be different from 0, but the coefficient of X 3 should not be different from 0
5 Case Study I -- Galileo experiment preceded discovery of least squares by 200 years, but Galileo correctly concluded that response curve was a parabola (he must have been a genius)

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6 Case Study I -- Galileo 1000 500 0 550 450 350 250 INITIAL HEIGHT (PUNTI) HORIZONTAL DISTANCE (PUNTI) Pg. 269
7 Case Study I -- Galileo See JMP

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8 Case Study 2 – Echolocation Costs observational study question: does echolocation require additional energy in flight? Y = energy expenditure in flight X 1 = body mass X 2 and X 3 , indicator variables for type of flying organism: birds, echolocating bats, non- echolocating bats
9 Case Study 2 – Echolocation Costs question can be approached by making inferences about the coefficients of X 2 and X 3 , depending on how the indicator variables were chosen if echolocation increases flight energy, and echolocating bats form the reference level, one or both of these coefficients should be different from 0

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10 Case Study 2 – Echolocation Costs 0 0.5 1 1.5 2 2.5 3 3.5 4 logenergy 2 3 4 5 6 7 logmass echolocating bats non-echolocating bats non-echolocating birds
11 Multiple Linear Regression Model μ {Y|X1, X2, …} = β 0 + β 1 X 1 + β 2 X 2 + … σ {Y|X1, X2, …} = σ

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511_Chapter_10 - Inferential Tools for Multiple Regression...

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