Transcript Statistics 400 - Simon Fraser University

Statistics 350
Lecture 17
Today
• Last Day: Introduction to Multiple Linear Regression Model
• Today: More Chapter 6
Inference for the General Linear Model
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As before, can construct confidence intervals for the regression parameters:
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Know estimates are unbiased and also have an estimate of the variance for
each parameter
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Formula for standard error:
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Inference for the General Linear Model
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Confidence interval:
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Confidence interval interpretation
Inference for the General Linear Model
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Hypotheses:
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Tests for parameters:
Inference for the General Linear Model
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Often interested in inference about the mean response for a set of explanatory
variables Xh
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Estimate of E(Yh)=
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This is a random variable with mean and variance:
Inference for the General Linear Model
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Estimate of variance:
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T-stat:
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Confidence interval:
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How would you make a prediction interval for a new value?
Diagnostics
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The model assumptions for the multiple regression model are the same as the
simple linear regression model
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Assessment of assumptions done via residual plots
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New property to note:
Diagnostics
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Possible violations for the model:
Diagnostics
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Use plots to verify model assumptions: