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
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
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
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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