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Chapter 6: Regression

This chapter is about making predictions.

The higher the correlation between the independent variable and the dependant variable, the
more accurate the predication will be.
Regression analysis:

Applies to paired data (Xi,Yi) where X is the independent variable w/ values Xi that are selected
in advance and y is the dependant variable with values Yi that are free to vary.

Regression procedures also are applicable when both x and y are free to vary as they are in
correlation.
Multiple Regression:

The simultaneous use of two or more predictors in predicting a dependent variable
Objectives:

How to predict one variable from another

How to determine the line of best fit

The relationship between r and the slopes of the bestfitting regression lines

What the standard error of estimate is and how to interpret it

How to interpret multiple regressions and multiple correlations
An Overview of the Prediction Process:

An example of George’s Statistics class, tracked his grades, made a scatter plot,

Predictions based on small samples tend to be unstable.
They tend to vary markedly from
sample to sample. Improvement can be made by utilizing all the data rather than a small subset
of the data.

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Predictions based on the regression line take into account all the sample data and hence are
more stable than those based on only the mean of the Y scores corresponding to a given X score.
6.2 Criterion for the line of best fit:
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 Spring '08
 kirk
 Correlation, Regression Analysis

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