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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