Residual Analysis and Outliers Robb T Koether Homework Review Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Residual Analysis and Outliers Lecture 48 Sections 13 4 13 5 Robb T Koether Hampden Sydney College Assignment Mon Dec 1 2008 Outline Residual Analysis and Outliers Robb T Koether Homework Review 1 Homework Review 2 Introduction 3 Residual Analysis 4 Nonlinear Regression 5 Outliers and Influential Points 6 Assignment Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment Homework Review Residual Analysis and Outliers Robb T Koether Homework Review Exercise 13 4 page 821 The following data represent trends in cigarette consumption per capita in hundreds and lung cancer mortality per 100 000 for Canadian males Introduction Residual Analysis Nonlinear Regression Cigarette Consumption x Mortality Rate y 11 8 10 4 12 5 16 5 15 7 22 9 19 2 26 6 21 9 33 8 23 3 42 8 Outliers and Influential Points b Give the equation of the least squares regression line of y mortality rate on x cigarette consumption Assignment c Interpret the slope of the regression line Be specific d Use the least squares regression equation to predict the lung cancer mortality rate when the cigarette consumption per capita is 2000 Homework Review Residual Analysis and Outliers Robb T Koether Homework Review Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment Solution b Enter the x values into list L1 and the y values into L2 Then use LinReg a bx L1 L2 Y1 to get the regression line The line is y 15 474 2 35x Homework Review Residual Analysis and Outliers Robb T Koether Homework Review Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment Solution c The slope 2 35 means that if x increases by 1 then y increases by 2 35 That is the mortality rate increases by 2 35 deaths per 100 000 for every additional 100 cigarettes consumed d If cigarette consumption were 2000 the model predicts that the mortality rate would be y 20 15 474 2 35 20 31 6 lung cancer deaths per 100 000 Introduction Residual Analysis and Outliers Robb T Koether Homework Review How do we know that a linear regression model is the best choice Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment What other types of regression are there There are many other types How many would you like The linear model is by far the simplest but it is not the only choice Introduction Residual Analysis and Outliers Robb T Koether Homework Review How do we know that a linear regression model is the best choice Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment What other types of regression are there There are many other types How many would you like The linear model is by far the simplest but it is not the only choice Introduction Residual Analysis and Outliers Robb T Koether Homework Review How do we know that a linear regression model is the best choice Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment What other types of regression are there There are many other types How many would you like The linear model is by far the simplest but it is not the only choice Introduction Residual Analysis and Outliers Robb T Koether Homework Review How do we know that a linear regression model is the best choice Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment What other types of regression are there There are many other types How many would you like The linear model is by far the simplest but it is not the only choice Introduction Residual Analysis and Outliers Robb T Koether Homework Review How do we know that a linear regression model is the best choice Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment What other types of regression are there There are many other types How many would you like The linear model is by far the simplest but it is not the only choice The Appropriateness of the Linear Model Residual Analysis and Outliers Robb T Koether Homework Review Introduction We can learn a bit about the nature of the model by examining the residuals Residual Analysis This is called residual analysis Nonlinear Regression First we need to find the residuals Outliers and Influential Points Assignment ei yi y i The Appropriateness of the Linear Model Residual Analysis and Outliers Robb T Koether Homework Review Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment To do this on the TI 83 after finding the equation of the regression line enter L2 Y1 L1 L3 to store the residuals in L3 Then draw a scatterplot of x versus e that is L1 versus L3 The Residual Plot Residual Analysis and Outliers Example Residual Plots Free lunch rate vs graduation rate Robb T Koether Homework Review Introduction 90 Nonlinear Regression Outliers and Influential Points Assignment Graduation Rate Residual Analysis 80 70 60 50 40 0 10 20 30 40 50 60 Free Lunch Rate 70 80 The Residual Plot Residual Analysis and Outliers Example Residual Plots Free lunch rate vs graduation rate Robb T Koether Homework Review Introduction 90 Nonlinear Regression Outliers and Influential Points Assignment Graduation Rate Residual Analysis 80 70 60 50 40 0 10 20 30 40 50 60 Free Lunch Rate 70 80 The Residual Plot Residual Analysis and Outliers Example Residual Plots The residual plot Robb T Koether Homework Review Introduction 20 Nonlinear Regression 10 Outliers and Influential Points Assignment Residuals Residual Analysis 0 10 20 10 20 30 40 50 60 Free Lunch Rate 70 80 The Appropriateness of the Linear Model Residual Analysis and Outliers Robb T Koether Homework Review Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment If the residual plot shows no clear pattern but just a big blob of points then the linear model is appropriate On the other hand if the residual plot shows a distinct curvature then the linear model may not be appropriate A Nonlinear Model Residual Analysis and Outliers Robb T Koether Homework Review Introduction Residual Analysis Nonlinear Regression Outliers and Influential Points Assignment Example A Nonlinear Model Consider the following data x 1 2 2 2 2 3 3 4 4 y 2 2 4 4 5 7 8 9 10 x 5 6 6 7 7 7 8 8 y 12 9 12 7 9 11 9 10 A Nonlinear Model Residual
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