Statistics and Probability with Applications for Engineers and Scientists, Preliminary Edition

Chapter 15

Simple Linear Regression Analysis

The focus of this chapter is the development of some procedures employed in simple linear regression analysis. The topics covered are:

• Basic concepts of regression analysis
• Fitting a straight line by least-squares
• Unbiased estimation of error variance σ²
• Test and confidence intervals for the regression parameters β₀, β₁, of the simple linear regression model
• Determination of confidence intervals for E(Y | X)
• Determination of a prediction interval for a future observation Y
• Inference about the correlation coefficient ρ
• Residual analysis

Learning Outcomes:

After studying this chapter, the reader will be able to:

1. Fit a simple linear regression model to a given set of data, and perform a residual analysis to check the validity of the model under consideration.
2. Estimate the regression coefficients using the method of least-squares, and carry out hypothesis testing to test whether or not the first-order regression model is an appropriate fit to the given data.
3. Estimate the expected response, predict future observation values, and find their confidence intervals using the given confidence coefficients.
4. Make inferences about the correlation coefficient between the response variable and the predictor variables.
5. Use statistical packages MINITAB, Microsoft Excel, and JMP to perform regression analysis.

15.1 Introduction

In this chapter and the next we deal with aspects of mathematical model building for the purpose of either describing a natural ...