2.3 - Lookingatdata:relationships Leastsquaresregression...

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    Looking at data: relationships   Least-squares regression
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Correlation tells us about strength (scatter) and direction of the linear relationship between two quantitative variables. In addition, we would like to have a numerical description of how both variables vary together. And we would like to make predictions based on that numerical description. But which line best describes our data?
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Unlike correlation, this requires that we have an explanatory variable and a response variable.
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A straight line has equation Given observed data , find and that minimize Method of least squares
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The regression line The least-squares regression line is the unique line such that the sum of the squared vertical distances between the data points and the line is the smallest possible.
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Solution: Least squares regression line:
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Software output intercept slope R 2 intercept slope
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Properties of least squares regression line Slope = change in y for each unit increase in x The line need not pass through the observed data points, but it always passes through . An increase of one standard deviation in x corresponds to a change of r standard deviation in y
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The distinction between explanatory and response  variables is crucial in regression. Regression examines  the distance of all points from the line   in the  y  direction  only.  
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This note was uploaded on 09/04/2010 for the course STAT 131 taught by Professor Isber during the Spring '08 term at University of California, Berkeley.

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2.3 - Lookingatdata:relationships Leastsquaresregression...

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