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Unformatted text preview: Chapter 10 Inference for Regression Chapter 10 1 Regression One of the most common problems in statistical analysis is the prediction of a response based on one (or more) explanatory variables. The simplest case occurs when there is a linear relationship between a quantitative response variable and a single quantitative explanatory variable. This is what we know as simple linear regression from Chapter 2. Chapter 10 2 Recall - Least Squares Regression In chapter 2, we used scatterplots to examine the relationship between two quantitative variables. When the scatterplot shows a linear relationship between the explanatory and response variables, a least squares regression line fitted to the data can be used to predict the response y for a given value of the explanatory variable x . Usually, the data are a sample from some population of interest. Chapter 10 3 Regression Notation The regression line computed from the sample can be thought of as an estimate for a regression line for the population. This is similar to using x as an estimate of the population mean . The notation for the population regression line is y = + 1 x The notation for the least-squares line fitted to the sample data is y = b + b 1 x Chapter 10 4 Inference for Regression We can use statistical inference to obtain confidence intervals and conduct significance tests for Population Slope 1 Population Intercept We can also compute confidence intervals for the mean response y . We can compute prediction intervals for a new response y (Stat 326). Chapter 10 5 Section 10.1 Inference about the Regression Model Section 10.1 6 Example - Software Training A credit card company hires a substantial number of clerks to enter financial data using the companys database software. Company officials believe that clerks will be more efficient at entering the information if they receive more training on using the software. Section 10.1 7 Example - A Regression Model First, we must define the variables that we will use. Explanatory Variable: Number of hours of software training Response Variable: Number of database entries per hour We can describe the relationship between the two variables with a regression model. y = + 1 x Section 10.1 8 The Regression Model We can think of each value of x as representing a subpopulation of clerks. Each subpopulation has its own mean y that changes as x changes. Individual entries per hour y in each subpopulation vary according to a Normal distribution. The standard deviation for each subpopulation is the same. Section 10.1 9 Graphical View of Regression FIGURE 10.2 The statistical model for linear regression. The mean response is a straight-line function- of the explanatory variable....
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This note was uploaded on 04/02/2008 for the course STAT 226 taught by Professor Abbey during the Spring '08 term at Iowa State.
- Spring '08