Question

In: Statistics and Probability

Consider the following bivariate data. Point A B C D E F G H I J...

Consider the following bivariate data.

Point	A	B	C	D	E	F	G	H	I	J
x	0	1	1	2	3	4	5	6	6	7
y	5	5	6	5	4	3	2	0	1	1

(a) Construct a scatter diagram of the given bivariate data. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Calculate the covariance. (Give your answer correct to two decimal places.)

(c) Calculate s_x and s_y. (Give your answers correct to three decimal places.)

s_x	=
s_y	=

(d) Calculate r using formula 13.2. (Give your answer correct to two decimal places.)

(e) Calculate r using formula 13.3. (Give your answer correct to two decimal places.)

Expert Solution

a)

b)

S.No	X	Y	(x-x̅)²	(y-y̅)²	(x-x̅)(y-y̅)
1	0	5	12.2500	3.24	-6.3000
2	1	5	6.2500	3.24	-4.5000
3	1	6	6.2500	7.84	-7.0000
4	2	5	2.2500	3.24	-2.7000
5	3	4	0.2500	0.64	-0.4000
6	4	3	0.2500	0.04	-0.1000
7	5	2	2.2500	1.44	-1.8000
8	6	0	6.2500	10.24	-8.0000
9	6	1	6.2500	4.84	-5.5000
10	7	1	12.2500	4.84	-7.7000
Total	35	32	54.5000	39.60	-44.0000
Mean	3.500	3.20	SSX	SSY	SXY

Cov(x,y)=Ssxy/(n-1)=

-4.90

c)

sx =2.461

sy = 2.098

d)

correlation coefficient r=

S_xy/(√S_xx*S_yy) =

-0.95

e_)

r =Cov(x,y)/(sx*sy) = -0.95

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