## 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;
$$m_{gradient} = \frac{{{\rm{covariance}}}}{{{\rm{variance}}}} = \frac{{S_{xy} }}{{S_{x^2 } }}$$

how can I find the new gradient?

$$\begin{array}{l} m_{gradient} = \frac{{{\rm{covariance}}}}{{{\rm{variance}}}} = \frac{{S_{xy} }}{{S_{x^2 } }} = \frac{{ \times 6}}{{ \times 36}} = \times \frac{1}{6} \\ Hence\;gradient\;is\;now\;3 \times \frac{1}{6} = \frac{1}{2} \\ \end{array}$$

I don't really understand how this process works and don't want to assume anything that is wrong

Steven

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HallsofIvy
Homework Helper
I'm no expert on statistics but I know that the "gradient" of a line is just its slope. I would have done this, ignoring all the statistical stuff, by arguing that y is now yold+ 3 and x is now 6xold so that yold= y- 3 and xold= x/6. Since you are told that yold= 3xold- 12, you now have y-3= 3(x/6)- 12 or simply y= x/2- 15. The slope (gradient) of that line is 1/2.

Cheers for that HallsofIvy!

seems like the obvious thing to do looking back lol

thanks!

hi steven10137,
can you please tell me the name of the book from where you read this formula