Download 3.2 Getting a Line on the Pattern

3.2 Getting a Line on the Pattern
Using Lines for Prediction
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Find a model that describes the relationship
between the two variables
Use the line to predict the value of y when
you know the value of x
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Variable on x-axis – explanatory variable
Variable on the y-axis – response variable
Predicting value of y when:
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x is inside the range of values –
interpolation
x is outside the range of values -extrapolation
3.2 Getting a Line on the Pattern
Using Lines for Prediction
Residual – difference between
observed and predicted value of y
Residual = observed y – predicted y
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residual  y  yˆ
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D4, pg. 122
3.2 Getting a Line on the Pattern
Least Squares Regression Lines
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Line of best fit is where the sum of squared
errors (SSE) is as small as possible
SSE   (residual )
  ( y  yˆ )
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3.2 Getting a Line on the Pattern
Least Squares Regression Lines
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The sum (and mean) of the residuals is 0.
The line contains the point of averages. ( x , y )
The standard deviation of the residuals is
smaller than for any other line that goes
through the point ( x , y )
The line has slope b1, where
( x  x )( y  y )

b 
 (x  x )
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