Question

(2 points) is the number of games won by a major league baseball team in a season related to the team batting average? The table below shows the number of games won and the batting average (in thousandths) of 8 teams. Team Games Won Batting Average 1 115 279 2 94 262 3 80 273 4 103 279 5 112 260 6 120 269 7 79 264 В 78 266 Using games won as the explanatory variable r do the following: (a) The correlation coefficient is = (b) The equation of the least squares line is y Note: You can earn partial credit on this problem

Answer 1

Given data:

Game won X	Batting average Y
115	279
94	262
80	273
103	279
119	260
120	269
79	264
78	266

Correlation coefficient ,r

T η(Στy)) - Σ * Σ V[n(Στ2)) – (Στ)2] και [n(Συ2)) - (Σy)2]

	Game won X	Batting average Y	XY	x^2	y^2
	115	279	32085	13225	77841
	94	262	24628	8836	68644
	80	273	21840	6400	74529
	103	279	28737	10609	77841
	119	260	30940	14161	67600
	120	269	32280	14400	72361
	79	264	20856	6241	69696
	78	266	20748	6084	70756
sum	788	2152	212114	79956	579268

$n=8$

$\sum x =788$

$\sum y=2152$

$\sum xy=212114$

$\sum x^2=79956$

$\sum y^2=579268$

T η(Στy)) - Σ * Σ V[n(Στ2)) – (Στ)2] και [n(Συ2)) - (Σy)2]

$r= \frac{8(212114))-788* 2152}{\sqrt{[8(79956))-(788)^2]*[8(579268))-(2152)^2]}}$

r = 0.151

correlation coefficient r =0.151

b)

y =ax+b

sum both side

$\sum y = a*\sum x+ b*n$ -----------(1)

multiply with x in y = ax +b

$\sum xy = a*\sum x^2+ b*\sum x$ ----------(2)

eqn 1 will be.

2152 = a*788 +b*8 -----------(1)

Eqn 2 will be

212114 = a * 79956 + b*788---------(2)

$\hat{y}=0.0607x+263.02$

equation of least squares line is $\hat{y}=0.0607x+263.02$