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11

Simple Linear

Regression and

Correlation

CHAPTER OUTLINE

LEARNING OBJECTIVES

After careful study of this chapter, you should be able to do the following:

1. Use simple linear regression for building empirical models to engineering and scientific data


2. Understand how the method of least squares is used to estimate the parameters in a linear
   regression model


3. Analyze residuals to determine if the regression model is an adequate fit to the data or to see if
   any underlying assumptions are violated


4. Test statistical hypotheses and construct confidence intervals on regression model parameters


5. Use the regression model to make a prediction of a future observation and construct an
   appropriate prediction interval on the future observation


6. Use simple transformations to achieve a linear regression model


7. Apply the correlation model

11-1 EMPIRICAL MODELS

11-2 SIMPLE LINEAR REGRESSION

11-3 PROPERTIES OF THE LEAST

SQUARES ESTIMATORS

11-4 SOME COMMENTS ON USES OF

REGRESSION (CD ONLY)

11-5 HYPOTHESIS TESTS IN SIMPLE

LINEAR REGRESSION

11-5.1 Use of t-Tests

11-5.2Analysis of Variance Approach

to Test Significance of Regression

11-6 CONFIDENCE INTERVALS

11-6.1 Confidence Intervals on the

Slope and Intercept

11-6.2 Confidence Interval on the

Mean Response

11-7 PREDICTION OF NEW

OBSERVATIONS

11-8 ADEQUACY OF THE REGRESSION

MODEL

11-8.1 Residual Analysis

11-8.2 Coefficient of Determination (R^2 )

11-8.3 Lack-of-Fit Test (CD Only)

11-9 TRANSFORMATIONS TO A

STRAIGHT LINE

11-10 MORE ABOUT

TRANSFORMATIONS (CD ONLY)

11-11 CORRELATION

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