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	114	275
2	79	278
3	73	289
4	91	268
5	102	262
6	100	263
7	79	278
8	103	279

sing games won as the explanatory variable xx, do the following:

(a) The correlation coefficient is r= __________

(b) The equation of the least squares line is y^= ______ + ______*x

Answer 1

a)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
114	275	456.89	1.00	21.38
79	278	185.64	16.00	-54.50
73	289	385.14	225.00	-294.38
91	268	2.64	36.00	9.75
102	262	87.89	144.00	-112.50
100	263	54.39	121.00	-81.13
79	278	185.64	16.00	-54.50
103	279	107.64	25.00	51.88

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	741	2192	1465.875	584.0	-514.00
mean	92.63	274.00	SSxx	SSyy	SSxy

                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    403.769          
                  
std error ,Se =    √(SSE/(n-2)) =    8.203          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.5555  

b)

sample size ,   n =   8          
here, x̅ = Σx / n=   92.63   ,     ȳ = Σy/n =   274.00  
                  
SSxx =    Σ(x-x̅)² =    1465.8750          
SSxy=   Σ(x-x̅)(y-ȳ) =   -514.0          
                  
estimated slope , ß1 = SSxy/SSxx =   -514.0   /   1465.875   =   -0.3506
                  
intercept,   ß0 = y̅-ß1* x̄ =   306.4784          
                  
so, regression line is   Ŷ =   306.4784   +   -0.3506   *x
                  

THANKS

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