Applied Statistics and Probability for Engineers, 6th Edition

Simple Linear Regression and Correlation

Chapter Outline

11-1 Empirical Models

11-2 Simple Linear Regression

11-3 Properties of the Least Squares Estimators

11-4 Hypothesis Tests in Simple Linear Regression

11-4.1 Use of t-Tests

11-4.2 Analysis of Variance Approach to Test Significance of Regression

11-5 Confidence Intervals

11-5.1 Confidence Intervals on the Slope and Intercept

11-5.2 Confidence Interval on the Mean Response

11-6 Prediction of New Observations

11-7 Adequacy of the Regression Model

11-7.1 Residual Analysis

11-7.2 Coefficient of Determination (R²)

11-8 Correlation

11-9 Regression on Transformed Variables

11-10 Logistic Regression

The space shuttle Challenger accident in January 1986 was the result of the failure of O-rings used to seal field joints in the solid rocket motor because of the extremely low ambient temperatures at the time of launch. Prior to the launch, there were data on the occurrence of O-ring failure and the corresponding temperature on 24 prior launches or static firings of the motor. In this chapter, we will see how to build a statistical model relating the probability of O-ring failure to temperature. This model provides a measure of the risk associated with launching the shuttle at the low temperature when Challenger was launched.

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