Chapter 15 (1)

Chapter 15 (1) - Chapter 15 Describing Relationships:...

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Chapter 15 Describing Relationships: Regression, Prediction, and Causation
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Outline Regression lines Regression equations Understanding prediction Correlation vs. Regression
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Regression lines
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Definition A regression line is a line that describes how the response variable (Y) changes as the explanatory variable (X) changes. Can be used to predict values of the response variable using the explanatory variable
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Example Lengths of two bones in fossils of archaeopteryx follow a straight line. (Humerus vs. Femur) Do you think the two measurements would be negative or positively correlated?
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Example continued. How might this regression line be useful to an Archaeologist? Suppose that you find a archaeopteryx femur bone 50 centimeters long. If you find a humerous bone that is 70 centimeters long, do you think it came from the same animal? How long would you expect a humerous bone to be if the femur bone is 50 c.m. long? What if the femur is 70 Regression line
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Regression Equations
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The least squares regression line of y on x is the line that minimizes the sum of the vertical squared deviation from the points to that line. What does this really mean?
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This note was uploaded on 06/15/2011 for the course STAT 110 taught by Professor Johnson during the Fall '07 term at South Carolina.

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Chapter 15 (1) - Chapter 15 Describing Relationships:...

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