Regression lines A line of best fit should: Go through ( x , y )

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Presentation transcript:

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

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!!!!!!!!!

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

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= 0.7429 a = (28/6) –(0.743)(27/6) = 1.324 Equation for y on x y = 0.743x + 1.324

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