- #1
steven10137
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Homework Statement
I have have a set of data pairs (x, y);
(1, a)
(2, b)
(3, c)
(4, d)
(5, e)
(6, f)
(7, g)
The least squares regression line for the this set is y=3x-12
Determine the new gradient of this line if the original set of scores has been transformed to;
(6, a+3)
(12, b+3)
(18, c+3)
(24, d+3)
(30, e+3)
(36, f+3)
(42, g+3)
i.e. the x scores have been multiplied by 6, and the +3 has been added to the y scores.
Now from my statistical tables book; I have the formula;
[tex]m_{gradient} = \frac{{{\rm{covariance}}}}{{{\rm{variance}}}} = \frac{{S_{xy} }}{{S_{x^2 } }}[/tex]
how can I find the new gradient?
The answer says;
[tex]\begin{array}{l}
m_{gradient} = \frac{{{\rm{covariance}}}}{{{\rm{variance}}}} = \frac{{S_{xy} }}{{S_{x^2 } }} = \frac{{ \times 6}}{{ \times 36}} = \times \frac{1}{6} \\
Hence\;gradient\;is\;now\;3 \times \frac{1}{6} = \frac{1}{2} \\
\end{array}[/tex]
I don't really understand how this process works and don't want to assume anything that is wrong
thanks in advance
Steven