Correlation Calculations for Multiple Regression

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Correlation Calculations for Multiple Regression
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After calculating the regression parameters (b
values), we can also calculate the correlation
coefficient.
To get the correlation coefficient (r), we first
need to calculate r2.
Actually, in the multiple-regression case, we
only get the absolute value of the correlation
coefficient (r) the "direction" of the
correlation is determined by the sign of each b
value.
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Before trying multiple regression, let's look
again at the case with one independent variable.
These data points come from test case 4 of lab 3.
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We already know how to calculate the regression
parameters.
200.0
b0 -0.351493739 b1 0.094962426
150.0
100.0
50.0
0.0
0
500
1000
1500
2000
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If we evaluate the regression line equation at
each x value, we get the predicted y values.
ypred 0.094962426 x 0.351493739
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To determine the correlation, we also need to
calculate the mean Y value (yavg).
yavg 60.3 (Mean of original y values)
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Next, we need to sum the squares of two
differences (y yavg) and (ypred yavg).
y yavg
ypred yavg
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Once we have the two sums, we can calculate the
correlation coefficient.
Just in case you are curious, the statisticians
label the sum-square values like this
Sum of squares error (unexplained)
Total sum of squares (variability)
Sum of squares predicted (explained)
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Here is an example using the data points from
test case 4 of lab 3.
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To extend the correlation calculation to handle
multiple independent variables, the only change
is in calculating the predicted y values.
One independent variable("linear regression")
One or more independent variables("multiple
regression")
Obviously, both are forms of "linear" regression,
despite the names.
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Please complete the following assignment before
the start of the next class.

• Read textbook pages 133-202.
• Complete (at least most of) lab 4
• Due Tuesday evening when we return
• Enjoy your break!