Question

I just need the answers please. Make sure to include four decimals for answers.

IMPORTANT: Make sure you carry all decimals until you reach your answer, then round to four decimals Use the ERA and win% data for the 8 randomly selected MLB pitchers below to answer the following questions. (See exercise 10 on page 695 of your textbook for a similar problem.) RA 0.019 0.029 0.036 0.021 0.023 0.026 0.034 0.035 win% 0.6060426 0.372 0.486 0.482 0.540 0.460 0.564 Question 1A Compute the IQR for ERA. Question 1B Compute the covariance between ERA and Win%. Question 1CCompute the correlation between ERA and Win

Answer 1

1.A

Sample has 8 observations.

Sample Median: 0.0275
Q1=25th Percentile: 0.0225
Q3=75th Percentile: 0.0343
Interquartile Range:

Q3-Q1= 0.0118

1.B Covariance is calculated as

Covariance(X,Y) = SUM(x_i - x_mean)*(y_i - y_mean)/(samplesize -1)

hence,

Sum(X) = 0.019 + 0.029 + 0.036 + 0.021 + 0.023 + 0.026 + 0.034 + 0.035 = 0.223 XMean = 0.028 Sum(Y) = 0.606 + 0.426 + 0.372 + 0.564 + 0.468 + 0.482 + 0.540 + 0.460 = 3.918 YMean = 0.49

now,

Covariance= (0.019-0.028)*(0.606-0.49)+(0.029-0.028)*(0.426-0.49)+(0.036-0.028)*(0.372-0.49)+(0.021-0.028)*(0.564-0.49)+(0.023-0.028)*(0.468-0.49)+(0.026-0.028)*(0.482-0.49)+(0.034-0.028)*(0.54-0.49)+(0.035-0.028)*(0.46-0.49))/7
= 0

1.C Correlation calculated as

r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

X Values
∑ = 0.223
Mean = 0.028
∑(X - M_x)² = SS_x = 0

Y Values
∑ = 3.918
Mean = 0.49
∑(Y - M_y)² = SS_y = 0.041

X and Y Combined
N = 8
∑(X - M_x)(Y - M_y) = -0.002
now

r = -0.002 / √((0)(0.041)) = -0.6624