Leastsquares regression line: The line that makes the sum of the squares of the vertical
distances of the data points from the line as small as possible.
Fact 1. The distinction between explanatory and response variables is essential in regression.
Leastsquares regression makes the distances of the data points from the line small only in the
y direction. If we reverse the roles of the two variables, we get a different leastsquares
regression line.
Fact 2. There is a close connection between correlation and the slope of the leastsquares line.
The slope is
As the correlation grows less strong,
the prediction ŷ moves less in response to changes in x.
Fact 3. The leastsquares regression line always passes through the point (xbar, ybar) on the
graph of y against x.
Fact 4. The correlation r describes the strength of a straightline relationship. In the regression
setting, this description takes a specific form: the square of the correlation, r2, is the fraction
of the variation in the values of y that is explained by the leastsquares regression of y on x.
One of the first principles of data analysis is to look for an overall pattern and also for
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 Winter '11
 PattiColling
 Linear Regression, Regression Analysis, regression line, leastsquares regression, leastsquares regression line

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