Statistics 1 Revision Notes - Mr Barton Maths

⇒ –1 ≤ r ≤ +1
Regression line and coding
The regression line of y on x has equation y = a + bx, where b =
, and a = – b.
Using the coding x = hX + m, y = gY + n, the regression line for Y on X is found by writing
gY + n instead of y, and hX + m instead of x in the equation of the regression line of y on x,
⇒ gY + n = a + b(hX + m)
⇔ Y =
Proof
= h + m, and = g + n
+ bX … … … … … equation I.
⇒ (x – ) = (hX + m) – (h + m) = (hX – h), and similarly (y – ) = (gY – g).
Let the regression line of y on x be y = a + bx, and
let the regression line of Y on X be Y = α + β X.
Then b =
and a = – b
also β =
b =
and α = – β .
= ∑
∑ ∑
∑ ∑
∑ ∑
∑
⇒
⇒
b = β
β =
α = – β =
and so
Y = α + β X ⇔ Y =
which is the same as equation I.
=
+ bX
since a = – b
50 14/04/2013 Statistics 1 SDB