STA 6166 UNIT 4
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Linear Regression

Topics Covered

In the next 300 pages of the book, we present an introduction into regression. Regression is such an important statistical analysis tool that it is typically afforded a full course of its own. In this course you will be provided with enough regression tools to be able to do a regression analysis on your own.

Regression analysis deals with quantifying the relationship between a response variable (here assumed to be a continuous variable, but that is not always the case) and one or more predictor or explanatory variables. We model this relationship in the form of a linear function. The importance of linear models in statistics is not because all statisticians think that all relationships are linear. It is just that to understand how to fit nonlinear relationships you must first understand how to fit linear relationships. In addition, in many situations, the linear model may represent a first order approximation to a nonlinear relationship. Some nonlinear models, such as polynomials (e.g. quadratic or cubic models) can be fit using linear regression techniques. Sometimes a appropriate transformation can make a nonlinear relationship acceptably linear. Be that as it may, there is still plenty of fun to be had playing around with linear regression.

As with any model fitting exercise, the acceptability of the final model will depend to a large extent on whether the assumptions made as part of the analysis (such as that the relationship is linear) are valid. We will spend a good part of our time discussion how to assess the goodness of our assumptions.

While developing a relationship model between one response and one predictor is important, being able to model and examine relationships between one response and a set of predictors is a much more powerful tool. While we cannot explore all the parts of multiple regression analysis, we will develop the basic concepts and practice these in some actual model building exercises.

We will finish the discussion of regression with the development of the general linear model. This regression model will play an important role in the analysis of data from the experimental designs discussed in the next unit.

  1. To understand the underlying structure of simple linear regression.
  2. To develop estimates and tests for model parameters in linear regression.
  3. To develop predictors and associated confidence statements in linear regression.
  4. To develop methods of assessing model assumptions and goodness of fit in regression.
  5. To expand simple linear regression to polynomial regression and on to multiple regression.
  6. To develop a protocol for comparing alternate multiple regression models.
  7. To explore model building strategies in multiple regression.
1 Linear Regression and Correlation
2 Multiple Regression and the General Linear Model
3 Model Selection in Multiple Regression
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