Practical Regression and Anova Using R

By Faraway, Julian J.

Book Id: WPLBN0000659886
Format Type: PDF eBook
File Size: 941.77 KB
Reproduction Date: 2005

Title:	Practical Regression and Anova Using R
Author:	Faraway, Julian J.
Volume:
Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Faraway, J. J. (n.d.). Practical Regression and Anova Using R. Retrieved from http://www.self.gutenberg.org/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: Before you start Statistics starts with a problem, continues with the collection of data, proceeds with the data analysis and finishes with conclusions. It is a common mistake of inexperienced Statisticians to plunge into a complex analysis without paying attention to what the objectives are or even whether the data are appropriate for the proposed analysis. Look before you leap! Formulation The formulation of a problem is often more essential than its solution which may be merely a matter of mathematical or experimental skill. Albert Einstein To formulate the problem correctly, you must...

Table of Contents
Contents 1 Introduction 6 1.1 Before you start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.2 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.3 Initial Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 When to use Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2 Estimation 9 2.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Linear Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Matrix Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Estimating b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.5 Least squares estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6 Examples of calculating ?b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.7 Why is ?b a good estimate? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.8 Gauss-Markov Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.9 Mean and Variance of ?b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.10 Estimating s2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.11 Goodness of Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.12 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Inference 19 3.1 Hypothesis tests to compare models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Test of all predictors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.2 Testing just one predictor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3 Testing a pair of predictors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.4 Testing a subspace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Concerns about Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Confidence Intervals for b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5 Confidence intervals for predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.6 Orthogonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.7 Identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.9 What can go wrong? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.9.1 Source and quality of the data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39