Question

LET'S SAY THESE ARE THE NUMBER OF STRIKE-OUTS A PITCHER THROWS IN THE NUMBER OF INNINGS PITCHED (WE HAVE 6 PAIRS OF DATA POINTS SO n = 6)

THE INNINGS PITCHED ARE THE ''X'' VALUES (INDEPENDENT VARIABLE) AND THE STRIKE-OUTS ARE THE ''Y'' VALUES (DEPENDENT VARIABLE)

FOR EXAMPLE WHEN PITCHING 4 INNINGS, THE PITCHER STRUCK OUT 6 BATTERS (4,6) (ETC.)

DATA POINTS (X,Y)	X	Y	X - Mx	(X-Mx)^2	Y - My	(X-Mx)*(Y-My)
(4,6)
(3,7)
(5,12)
(11,17)
(10,10)
(14,14)
MEAN (Mx & My)			TOTAL		TOTAL
SD

SO, USING THIS EQUATION, HOW MANY STRIKE-OUTS WOULD BE PREDICTED FOR THIS PITCHER IN X = 8 INNINGS?

Answer 1

	X	Y	X-Mx	(X-Mx)^2	Y - My	(Y - My)^2	(X - Mx)(Y-My)
	4	6	-3.83333	14.69444	-5	25	19.16667
	3	7	-4.83333	23.36111	-4	16	19.33333
	5	12	-2.83333	8.027778	1	1	-2.83333
	11	17	3.166667	10.02778	6	36	19
	10	10	2.166667	4.694444	-1	1	-2.16667
	14	14	6.166667	38.02778	3	9	18.5
Total	47	66		98.83333		88	71
Mean	7.833333	11
SD	4.445972	4.195235

= 98.33

= 88

= 71

let the simple linear regression equation be y = b₀ + b₁x

b₁ = S_xy/S_xx = 71/98.33 = 0.722

b₀ = M_y - b₁M_x = 11 - 0.722*7.83 = 5.35

Y = 5.35 + 0.722X

for X =8 Y = 5.35 + 0.722*8 = 11.12

Y = 11.