Introduction
Problems in engineering often involve the exploration of the relationship(s) between two or more variables. The technique of regression analysis is very useful and well-used in this situation. This Section will look at the basics of regression analysis and should enable you to apply regression techniques to the study of relationships between variables. Just because a relationship exists between two variables does not necessarily imply that the relationship is causal. You might find, for example that there is a relationship between the hours a person spends watching TV and the incidence of lung cancer. This does not necessarily imply that watching TV causes lung cancer.
Assuming that a causal relationship does exist, we can measure the strength of the relationship by means of a correlation coefficient discussed in the next Section. As you might expect, tests of significance exist which allow us to interpret the meaning of a calculated correlation coefficient.
Prerequisites
- have knowledge of Descriptive Statistics ( HELM booklet 36)
- be able to find the expectation and variance of sums of variables ( HELM booklet 39.3)
- understand the terms independent and dependent variables
- understand the terms biased and unbiased estimators
Learning Outcomes
- define the terms regression analysis and regression line
- use the method of least squares for finding a line of best fit
Contents
1 Regression1.1 Scatter diagrams
1.2 Regression lines by eye
1.3 The method of least squares - an elementary view
1.4 The method of least squares - a modelling view
1.5 Adequacy of fit
1.6 The coefficient of determination
1.7 The adjusted coefficient of determination
1.8 Significance testing for regression
1.9 Regression curves
1.10 The quadratic case
1.11 The exponential case