Question

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	112	290
2	60	274
3	104	286
4	90	284
5	100	279
6	91	265
7	106	272
8	96	289

Using games won as the explanatory variable x, do the following:

(a) The correlation coefficient is r= ________

(b) The equation of the least squares line is y^=________

Answer 1

Solution :

X	Y	XY	X^2	Y^2
112	290	32480	12544	84100
60	274	16440	3600	75076
104	286	29744	10816	81796
90	284	25560	8100	80656
100	279	27900	10000	77841
91	265	24115	8281	70225
106	272	28832	11236	73984
96	289	27744	9216	83521

  

n	8
sum(XY)	212815.00
sum(X)	759.00
sum(Y)	2239.00
sum(X^2)	73793.00
sum(Y^2)	627199.00
Numerator	3119.00
Denominator	7985.60
r	0.3906
r square	0.1526
Xbar(mean)	94.8750
Ybar(mean)	279.8750
SD(X)	16.4966
SD(Y)	8.2999
b	0.2187
a	259.1280

a) The correlation coefficient ,

r = 0.3906

The correlation coefficient is r = 0.3906

b) The equation of the least squares line,

= a + bx

= 259.1280 + (0.2187*x)

The equation of the least squares line is   = 259.1280 + (0.2187*x)