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Section 11

Section 11. Junghoon Moon. Contents. Multiple Regression One-way Anova Two-way Anova. ANOVA table for multiple regression. MSE is estimate of σ 2. Example. ANOVA. I groups Variation within groups Variation between groups Variation within groups < variation between groups

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Section 11

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  1. Section 11 Junghoon Moon

  2. Contents • Multiple Regression • One-way Anova • Two-way Anova

  3. ANOVA table for multiple regression • MSE is estimate of σ2

  4. Example

  5. ANOVA • I groups • Variation within groups • Variation between groups • Variation within groups < variation between groups • Group means are different

  6. One-way ANOVA • Means μ1,μ2,μ3,…..,μI • SD’s σ1,σ2,σ3,….,σI • Hypothesis • H0 : μ1=μ2=μ3=…..=μI • Ha : not all μi are equal. • Assumptions • I independent samples • Populations are normally distributed. • Common SD: σ1=σ2=σ3=….=σI • Xij = μi + εij • S2p=s2w (MS within groups = mean square error)

  7. One-way ANOVA table

  8. Standard Error Bars • http://www.uvm.edu/~jleonard/AGRI85/spring2004/Standard_Error_Bars_in_Excel.html

  9. Contrasts

  10. Two-way ANOVA table

  11. Example

  12. More example • Recycling rate: 36 towns in eastern Massachusetts. • Region (northeast, northwest, southeast or southwest) • “Pay as you throw” program (Pay; Yes or No). • a) Complete ANOVA table

  13. Interaction Qualitative No Interaction Quantitative

  14. Multiple Regression and ANOVA • One-way ANOVA • Multiple Regression (ANOVA table) Analysis of Variance Source DF SS MS F P Regression 3 207.281 69.094 9.24 0.000 Residual Error 74 553.437 7.479 Total 77 760.718

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