RSprimer - Computing Primer for Applied Linear Regression...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Computing Primer for Applied Linear Regression, Third Edition Using R and S-Plus Sanford Weisberg University of Minnesota School of Statistics October 23, 2007 c circlecopyrt 2005, Sanford Weisberg Home Website: www.stat.umn.edu/alr
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Contents Introduction 1 0.1 Organization of this primer 4 0.2 Data files 5 0.2.1 Documentation 5 0.2.2 R data files and a package 6 0.2.3 S-Plus data files and library 6 0.2.4 Getting the data in text files 7 0.2.5 An exceptional file 7 0.3 Scripts 7 0.4 The very basics 8 0.4.1 Reading a data file 8 0.4.2 Reading Excel Files 9 0.4.3 Saving text output and graphs 9 0.4.4 Normal, F , t and χ 2 tables 10 0.5 Abbreviations to remember 11 0.6 Packages/Libraries for R and S-Plus 12 0.7 Copyright and Printing this Primer 12 1 Scatterplots and Regression 13 1.1 Scatterplots 13 v
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
vi CONTENTS 1.2 Mean functions 16 1.3 Variance functions 16 1.4 Summary graph 16 1.5 Tools for looking at scatterplots 16 1.6 Scatterplot matrices 16 2 Simple Linear Regression 19 2.1 Ordinary least squares estimation 19 2.2 Least squares criterion 19 2.3 Estimating σ 2 20 2.4 Properties of least squares estimates 20 2.5 Estimated variances 20 2.6 Comparing models: The analysis of variance 21 2.7 The coefficient of determination, R 2 22 2.8 Confidence intervals and tests 23 2.9 The Residuals 26 3 Multiple Regression 27 3.1 Adding a term to a simple linear regression model 27 3.2 The Multiple Linear Regression Model 27 3.3 Terms and Predictors 27 3.4 Ordinary least squares 28 3.5 The analysis of variance 30 3.6 Predictions and fitted values 31 4 Drawing Conclusions 33 4.1 Understanding parameter estimates 33 4.1.1 Rate of change 34 4.1.2 Sign of estimates 34 4.1.3 Interpretation depends on other terms in the mean function 34 4.1.4 Rank deficient and over-parameterized models 34 4.2 Experimentation versus observation 34 4.3 Sampling from a normal population 34 4.4 More on R 2 34 4.5 Missing data 34 4.6 Computationally intensive methods 36 5 Weights, Lack of Fit, and More 41
Image of page 4
CONTENTS vii 5.1 Weighted Least Squares 41 5.1.1 Applications of weighted least squares 42 5.1.2 Additional comments 42 5.2 Testing for lack of fit, variance known 42 5.3 Testing for lack of fit, variance unknown 43 5.4 General F testing 44 5.5 Joint confidence regions 45 6 Polynomials and Factors 47 6.1 Polynomial regression 47 6.1.1 Polynomials with several predictors 48 6.1.2 Using the delta method to estimate a minimum or a maximum 49 6.1.3 Fractional polynomials 51 6.2 Factors 51 6.2.1 No other predictors 53 6.2.2 Adding a predictor: Comparing regression lines 53 6.3 Many factors 54 6.4 Partial one-dimensional mean functions 54 6.5 Random coefficient models 56 7 Transformations 59 7.1 Transformations and scatterplots 59 7.1.1 Power transformations 59 7.1.2 Transforming only the predictor variable 59 7.1.3 Transforming the response only 63 7.1.4 The Box and Cox method 64 7.2 Transformations and scatterplot matrices 65 7.2.1 The 1D estimation result and linearly related predictors 66 7.2.2 Automatic choice of transformation of the predictors 66 7.3 Transforming the response 68 7.4 Transformations of non-positive variables 68 8 Regression Diagnostics: Residuals 69 8.1 The residuals 69 8.1.1 Difference between ˆ e and
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern