1. Regression lines
A line of best fit should:
Go through ( x , y )
Minimise the distances to the line from the points
PROBLEM: Some are + and some are – and when added give 0!!!
Change second to minimise the squares of the distances to the line from the points

2. PROBLEM: Is the distance vertical or horizontal?x
Why not both!!
So we have 2 least-squares regression lines:
y on x (vertical distances squared)
x on y (horizontal distances squared)
X on y IS NOT y on x rearranged!!!!!!!!!

3. REMEMBER Sxx = Σx2 – (Σx)2 n Syy = Σy2 – (Σy)2 n Sxy = Σxy – (Σx)(Σy)

4. x y x2 y2 xy 2 3 4 9 6 16 12 5 25 36 30 7 49 27 28
139
144
Sxx=
17.500
Syy=
13.333
Sxy=
13.000
b= 13/17.5=
a = (28/6) –(0.743)(27/6)
= 1.324
Equation for y on x
y = 0.743x

5. x y x2 y2 xy 2 3 4 9 6 16 12 5 25 36 30 7 49 27 28
139
144
Sxx=
17.500
Syy=
13.333
Sxy=
13.000
d = 13/13.333= 0.975
c = (27/6) –(0.975)(28/6)
= -0.05
Equation of x on y
x = 0.975y – 0.05