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Regression and ANOVA PDF

24 Pages·2015·0.62 MB·English
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Stat 411/511 A & R NOVA EGRESSION Nov 31st 2015 Charlotte Wickham stat511.cwick.co.nz This week Today: Lack of fit F-test Weds: Review…email me topics, otherwise I’ll go over some of last year’s final exam questions. Fri: Office hours instead of lecture. Find me in Weniger 255 10-11am. Finals week Office hours Mon & Wed 10-11am in my office 255 Weniger Randomized experiment Insulating Fluid Case Study Breakdown times for electrical insulating fluid at various voltages. n = 76 I = 7 Randomized experiment Insulating Fluid Case Study Breakdown times for electrical insulating fluid at various voltages. n = 76 I = 7 separate means Insulating Fluid Case Study Breakdown times for electrical insulating fluid at various voltages. n = 76 I = 7 simple linear regression Insulating Fluid Case Study Breakdown times for electrical insulating fluid at various voltages. n = 76 I = 7 equal means Comparing models One way ANOVA Equal means model least complicated Regression ANOVA Regression model Lack of fit F-test most Separate means model complicated (only if there is more than one observation at each value of the explanatory) All three comparisons are made with an Extra SS F-test Review Extra SS F-test Under the null hypothesis (reduced model is true) the F-statistic has an F-distribution with v and v degrees of freedom. 1 2 Sum of squared p- d.f. MSS F residuals value C: subtract A from B F: subtract G: divide C I: divide G D from E by F by H Extra v 1 H: divide A by D Full model v 2 Reduced model Display 8.8 p. 218p. Analysis of variances tables for the insulating fluid data from a simple linear regression analysis and from a separate-means (one-way ANOVA) analysis Review (A): ANALYSIS OF VARIANCE TABLE FROM A SIMPLE LINEAR REGRESSION ANALYSIS One way ANOVA Source Sum of Squares df Mean Square F-Statistic p-value Regression 190.1514 1 190.1514 78.14 <.0001 Residual 180.0745 74 2.4334 Compares separate means model to Total 370.2258 75 equal means model compares Residual sum of 2 σ regression in regression squares, regression and equal- model model means models (B): ANALYSIS OF VARIANCE TABLE FROM A ONE-WAY ANALYSIS OF VARIANCE Source Sum of Squares df Mean Square F-Statistic p-value Between Groups 196.4774 6 32.7462 13.00 <.0001 Within Groups 173.7484 69 2.5181 Total 370.2258 75 compares Residual sum of 2 σ separate-means in separate- squares, separate- and equal- Equal means model Residuals from means model means models means separate means model model New! Regression ANOVA DispClaoy m8.8p ares regression model to p. 218p. equal means model Analysis of variances tables for the insulating fluid data from a simple linear regression analysis and from a separate-means (one-way ANOVA) analysis (A): ANALYSIS OF VARIANCE TABLE FROM A SIMPLE LINEAR REGRESSION ANALYSIS Source Sum of Squares df Mean Square F-Statistic p-value Regression 190.1514 1 190.1514 78.14 <.0001 Residual 180.0745 74 2.4334 Total 370.2258 75 compares Residual sum of 2 σ regression in regression squares, regression and equal- model model means models Equal Residuals from means (B): ANALYSIS OF VARIANCE TABLE regression model d.f. = n - 2 mFoRdOeMl A ONE-WAY ANALYSIS OF VARIANCE Source Sum of Squares df Mean Square F-Statistic p-value Between Groups 196.4774 6 32.7462 13.00 <.0001 Within Groups 173.7484 69 2.5181 Total 370.2258 75 compares Residual sum of 2 σ separate-means in separate- squares, separate- and equal- means model means model means models

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ANOVA. Regression. ANOVA. Lack of fit. F-test least complicated most linear regression analysis and from a separate-means (one-way ANOVA).
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