Chapter 15

Chapter 15 - Chapter 15 Describing Relationships:...

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Chapter 15 Describing Relationships: Regression, Prediction, and Causation In this chapter Linear regression Cautions with regression Linear regression Deterministic View – This is the idea that Y is caused by X or that once X has happened, Y will follow. We know the exact value of Y. This is what is done in a typical algebra class. The deterministic view when applied to the behavior of many variables in not possible. Regression – A technique used to predict variables (typically difficult to measure variables) based on a set of other variables (typically easy to measure variables). Linear Regression – Used to predict the value of Y (the response variable), based on X (the explanatory variable). Example Predict reaction time from blood alcohol level. Reaction time is difficult to measure so instead we predict it with blood alcohol level which is easy to measure. The linear regression model expresses Y as a function of X plus random error Random error reflects variation in Y values. Keep in mind we are going to measure X, so assuming we get a good measure there is no error in the X variable. However, when we go to use X to predict Y, out prediction will not be exact. Therefore, there is error in the Y variable. Graphically this error is represented by the vertical distance between the points and the line. The linear regression model follows: x b b Y 1 0 + = Where 0 b is the y-intercept and 1 b is the slope The above formula is the same format as what you should be used to from an algebra class. However, the way we denote the relationship is different. It is important you become familiar with this notation.
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In order to use linear regression, we must first make sure the model is reasonable. The scatter plot and r should indicate a strong relationship. If the model is not reasonable, do not fit a line. It may still be possible to do regression with a more complicated model.
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This note was uploaded on 07/12/2011 for the course STATS 200 taught by Professor Bradley,w during the Fall '10 term at KCTCS.

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Chapter 15 - Chapter 15 Describing Relationships:...

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