Question

3.6.46-T Consider the following sample data for two variables. x 7 8 5 3 9 y 7 5 9 7 7 a. Calculate the sample covariance. b. Calculate the sample correlation coefficient. c. Describe the relationship between x and y. a. s Subscript xyequals 0

Answer 1

Answer:

1. Co-variance= -1.2

2. correlation coefficient= -0.4404

3.  There is weak negative relationship between x and y.

Explanation:

1.

Co-variance= Cov(x,y)= sum[(x-xbar)(y-ybar)]/n

xbar=sumx/n=32/5=6.4

ybar=sumy/n=35/5=7

x 7 8 5 3 9

x-xbar 0.6 1.6 -1.4 -3.4 2.6

y 7 5 9 7 7

y-ybar 0 -2 2 0 0

(x-xbar)(y-ybar) 0 -3.2 -2.8 0 0

Cov(x,y)= sum[(x-xbar)(y-ybar)]/n=-6/5=-1.2

Cov(x,y)=-1.2

2.

correlation coefficient=r

$r=\frac{sum(x-xbar)(y-ybar)}{\sqrt{sum(x-xbar)^2sum(y-ybar)^2} }$

x 7 8 5 3 9

x-xbar 0.6 1.6 -1.4 -3.4 2.6

y 7 5 9 7 7

y-ybar 0 -2 2 0 0

(x-xbar)(y-ybar) 0 -3.2 -2.8 0 0

(x-xbar)² 0.36 2.56 1.96 11.56 6.76

(y-ybar)²  0 4 4 0 0

$r=\frac{-6}{\sqrt{23.2(8)} }$

r=-0.4404

3. Since the value of correlation coefficient is negative and less than 0.5 , so, we can say that there is weak negative relationship between x and y.