ECON-310 Sec 002-Interme > John Spoor Broome Lib × Aplia: Student Question X- S

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ECON-310 Sec 002-Interme > John Spoor Broome Lib × Aplia: Student Question X- S Statistics and Probability que X+ courses aplia com ati se let/quiz/ctedelil martinez 0 03&quiz; actionstake ue&quiz; pro&Guid-QNAPC0A8010100000; 3b d74d0c a youtube 10. Measures of association between two variables AaAa Consider a data set consisting of observations for three variables: x, y, and z. Their sample means, variances, and standard deviations are shown in Table 1. Table 1 Sample Mean Sample Variance Sample Standard Deviation sx = 2 Sy = 1.732 sz = 3 Table 2 shows the observations for x and y and their corresponding deviations from the sample means. Table 2 2 6 -2 The sample covariance between x and y is The sample correlation coefficient between x and y is Table 3 shows the observations for y and z and their corresponding deviations from the sample means. Table 3 Session Timeout 59:22 3 8-2 EEE] ^ .. 12:30 PM 9/12/2017

Explanation / Answer

answer

n = the number of elements in both samples.

i = an index that assigns a number to each sample element, ranging from 1 ton.

Xi = a single element in the sample for X.

Yi = a single element in the sample for Y.

The sample covariance may have any positive or negative value.

for table 2

cov(x,y)=sum[(xi=xbar)(yi-ybar)]/n-1

=(-2+0+2)

cov(x,y)=0

sample correlation between x and y

corr(x,y)=cov(x,y)/s.r(var(x))*s.r(var(y))

=0

for table 3

cov(y,z)=-3-6+0

=-9

corr(y,z)=-9/1.732*3

=-9/5.196

=-1.7321

for table 4

cov(x,z)=-6

corr(x,z)=-6/2*3

=-6/6

=-1

=0

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