Chapter 10.4 - Math3200 Intermediate Probability and Statistics Prof Nan Lin Department of Mathematics Washington University Outline Regression

# Chapter 10.4 - Math3200 Intermediate Probability and...

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Math3200 Intermediate Probability and Statistics Prof. Nan Lin Department of Mathematics Washington University

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Outline Regression diagnostic for simple linear regression Checking model assumptions Checking for outliers and influential observations Data Transformation Nan Lin, Washington University 2
Linear regression: Assumptions Model: ? ? = 𝛽 0 + 𝛽 1 ? ? + 𝜖 ? , 𝑖 = 1, … , 𝑛, 𝜖 ? ∼ 𝑁(0, 𝜎 2 ) Assumption 1: linearity Assumption 2: errors have equal variances Assumption 3: errors are normally distributed Assumption 4: errors are independent

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Residual plot Fitted value: ? ? = 𝛽 0 + 𝛽 1 ? ? , 𝑖 = 1, … , 𝑛 Residual: 𝑒 ? = ? ? − ? ? = ? ? − (𝛽 0 + 𝛽 1 ? ? ), 𝑖 = 1, … , 𝑛 Plot residuals against fitted values Nan Lin, Washington University 4
Checking for linearity If the linearity assumption is true, residual plot (or plot residual against predictor) should exhibit random scatter around zero.

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