14: Regression — Read — Invisible Network

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Statisticians are often called upon to develop methods to predict one variable from other variables. For example, one might want to predict college grade point average from high school grade point average. Or, one might want to predict income from the number of years of education.

14.1: Introduction to Linear Regression
14.2: Linear Fit Demo
14.3: Partitioning Sums of Squares
One useful aspect of regression is that it can divide the variation in Y into two parts: the variation of the predicted scores and the variation of the errors of prediction. The variation of Y is called the sum of squares Y and is defined as the sum of the squared deviations of Y from the mean of Y.
14.4: Standard Error of the Estimate
The standard error of the estimate is a measure of the accuracy of predictions. Recall that the regression line is the line that minimizes the sum of squared deviations of prediction (also called the sum of squares error). The standard error of the estimate is closely related to this quantity and is defined below:
14.5: Inferential Statistics for b and r
This section shows how to conduct significance tests and compute confidence intervals for the regression slope and Pearson's correlation. As you will see, if the regression slope is significantly different from zero, then the correlation coefficient is also significantly different from zero.
14.6: Influential Observations
It is possible for a single observation to have a great influence on the results of a regression analysis. It is therefore important to be alert to the possibility of influential observations and to take them into consideration when interpreting the results.
14.7: Regression Toward the Mean
14.8: Introduction to Multiple Regression
14.9: Statistical Literacy
14.E: Regression (Exercises)

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