Chapter12_CN - 1 Chapter 12. Simple Linear Regression and...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Chapter 12. Simple Linear Regression and Correlation 12.1 The Simple Linear Regression Model 12.2 Fitting the Regression Line 12.3 Inferences on the Slope Parameter 1 12.4 Inferences on the Regression Line 12.5 Prediction Intervals for Future Response Values 12.6 The Analysis of Variance Table 12.7 Residual Analysis 12.8 Variable Transformations 12.9 Correlation Analysis 12.10 Supplementary Problems 2 12.1 The Simple Linear Regression Model 12.1.1 Model Definition and Assumptions(1/5) With the simple linear regression model y i = + 1 x i + i the observed value of the dependent variable y i is composed of a linear function + 1 x i of the explanatory variable x i , together with an error term i . The error terms 1 , , n are generally taken to be independent observations from a N(0, 2 ) distribution, for some error variance 2 . This implies that the values y 1 , ,y n are observations from the independent random variables Y i ~ N ( + 1 x i , 2 ) as illustrated in Figure 12.1 3 12.1.1 Model Definition and Assumptions(2/5) 4 12.1.1 Model Definition and Assumptions(3/5) The parameter is known as the intercept parameter, and the parameter is known as the intercept parameter , and the parameter 1 is known as the slope parameter . A third unknown parameter, the error variance 2 , can also be estimated from the data set. As illustrated in Figure 12.2, the data values ( x i , y i ) lie closer to the line y = + 1 x as the error variance 2 decreases. 5 12.1.1 Model Definition and Assumptions(4/5) The slope parameter 1 is of particular interest since it indicates how the expected value of the dependent variable depends upon the explanatory variable x , as shown in Figure 12.3 The data set shown in Figure 12.4 exhibits a quadratic (or at least nonlinear) relationship between the two variables, and it would make no sense to fit a straight line to the data set. 6 12.1.1 Model Definition and Assumptions(5/5) Simple Linear Regression Model The simple linear regression model y i = 0 + 1 x i + i fits a straight line through a set of paired data observations (x 1 ,y 1 ), , (x n , y n ). The error terms 1 , , n are taken to be independent observations from a N(0, 2 ) distribution. The three unknown parameters, the intercept parameter 0 , the slope parameter 1 , and the error variance 2 , are estimated from the data set. 7 12.1.2 Examples(1/2) Example 67 : Car Plant Electricity Usage The manager of a car plant wishes to investigate how the plant s electricity usage depends upon the plant s production. The linear model will allow a month s electrical usage to be estimated as a function of the month s pro- duction....
View Full Document

Page1 / 63

Chapter12_CN - 1 Chapter 12. Simple Linear Regression and...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online