# 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 σ
^{2} - Test and confidence intervals for the regression parameters
*β*_{0},*β*_{1}, 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:

- 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.
- 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.
- Estimate the expected response, predict future observation values, and find their confidence intervals using the given confidence coefficients.
- Make inferences about the correlation coefficient between the response variable and the predictor variables.
- 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 ...

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