Question

Use the ERA and Win% data for the 8 randomly selected MLB pitchers below to answer the following questions. (See exercise 10 on page 624 of your textbook for a similar problem.) 0,04 0.039 0.038 0,047 0.048 0.037 0.043 ERA 0.046 0.490 0.280 0.314 0.229 0.396 Win% 0.355 0.128 0.036 Question 4A Compute the IQR for ERA. 0.0008 Compute the covariance between ERA and Win%. Question 4B Compute the correlation between ERA and Win%. Question 4C

Answer 1

> #X=ERA
> #Y=WIN%
> x=c(0.038,0.047,0.046,0.04,0.048,0.037,0.043,0.039);x
[1] 0.038 0.047 0.046 0.040 0.048 0.037 0.043 0.039
> y=c(0.49,0.355,0.128,0.28,0.036,0.314,0.229,0.396);y
[1] 0.490 0.355 0.128 0.280 0.036 0.314 0.229 0.396
> #Q4A) IQR for ERA is
> IQR=quantile(x,0.75)-quantile(x,0.25);IQR
>0.0075
IQR=0.0075
> # Q4B)covariance between ERA and WIN% IS
> cov(x,y)
[1] -0.0004432857
#covariance=-0.0004432857
> #Q4C) correlation between ERA and WIN% IS
> cor(x,y)
[1] -0.6996989
> correlation=-0.6996989