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	102	263
2	82	271
3	105	272
4	61	276
5	109	275
6	80	284
7	118	276
8	61	278

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:

Here, we have to use the regression model for the prediction of the dependent variable or response variable Batting average based on the independent variable or explanatory variable games won. Regression equation by using excel is given as below:

Regression Statistics
Multiple R	0.361260393
R Square	0.130509071
Adjusted R Square	-0.014406083
Standard Error	6.113100321
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	33.65502679	33.65502679	0.900589532	0.379264008
Residual	6	224.2199732	37.36999554
Total	7	257.875
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	283.3580146	9.709437124	29.18377358	1.07263E-07	259.5998779	307.1161513
Games Won	-0.100089299	0.105468847	-0.948993958	0.379264008	-0.358162271	0.157983673

Part a

The correlation coefficient between the dependent variable or response variable Batting average based on the independent variable or explanatory variable games won is given as -0.3613, which mean there is considerable negative linear relationship exists between the given two variable games won and batting average.

The value of R square or coefficient of determination is given as 0.1305, which means only 13.05% of the total variation in the dependent variable batting average is explained by the independent variable games won. So, this relationship is not strong in nature.

Part b

The equation of the least squares line is given as below:

Y = 283.3580146 – 0.100089299*X

Y = 283.36 – 0.10*X

Batting Average = 283.36 – 0.10*Games Won