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AMDA-2008-Session 13

# AMDA-2008-Session 13 - Linear Regression Normality of...

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Unformatted text preview: Linear Regression Normality of Errors Assumption plot. y probabilit normal the using assessed is residuals the of normality The residuals. the be will so d distribute normally are errors the If d.f. 2- n on with distributi- a follows ˆ Further, n. any for d distribute normally be to ˆ and ˆ have then we assumed is errors the of normality If d distribute normally ely approximat are ˆ and ˆ large, is n if seen that already have We ). , x N( ~ Y model) x fixed (in the implies This ). N(0, i.i.d. are errors that the assumed often is it model regression linear simple In the 2 2 i i i • • • • • + ∈ • χ σ β α β α σ β α σ Hypothesis Test about Regression Coefficients 2 / , 2 1 | t | if ce significan of level at H reject We . ) ˆ ( e ˆ s ˆ t is statistic test The useful. not is regression linear s, other word In variable. response on the impact any has y variable explanator that the conclude to evidence enough us give not does data that the conclude then we rejected not is H If : H against : H is useful is which hypothesis of test a regression linear simple In α α β β β β- = • • ≠ = • n t Residual Percent 3.0 1.5 0.0-1.5-3.0 99 90 50 10 1 Fitted Value Residual 10.0 7.5 5.0 2 1-1-2 Residual Frequency 2 1-1-2 4.8 3.6 2.4 1.2 0.0 Observation Order Residual 11 10 9 8 7 6 5 4 3 2 1 2 1-1-2 Normal Probabilit y Plot of t he Residuals...
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AMDA-2008-Session 13 - Linear Regression Normality of...

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