Question

Below are four bivariate data sets and the scatter plot for each. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population. x y 1.0 7.9 2.0 5.1 3.0 10.1 4.0 6.4 х 11 10+ 9+ 8+ 7+ 6+ 5- X X 1.0 7.3 117 10+ 2.0 9.0 9+ 3.0 7.3 8+ 7 4.0 5.6 6+ 5.0 7.9 5 4 6.0 5.3 2 7.0 4.8 5.0 1.5 6.0 5.0 3 3 2+ 1- 7.0 8.8 х 1 8.0 3.8 0 8.0 1 3 2 6.8 4 0 5 6 7 8 9 10 11 1 3 56 7 8 9 10 11 9.0 9.6 10.0 7.0 Figure 1 9.0 6.2 10.03.7 Figure 2 W t m n 1.0 7.9 1.0 3.0 11 10+ 9+ 2.0 6.9 2.0 117 10+ 9+ 8 + x 7+ 6+ 4.1 7.8 3.0 3.6 8 3.0 4.0 6.3 4.0 5.4 6 5 4 5.0 7.0 5.0 4.6 6.0 4.3 3+ 2 6.0 7.4 X 3 2 1. 7.0 4.7 P2 8.0 3.4 0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 7.0 6.0 8.0 7.8 9.0 7.5 10.0 7.7 9.0 4.4 Figure 3 Figure 4 10.0 2.9

Answer 1

Ans : We have to given four bivariate data set and scatter plot for each

for fist data set

x	y
1	7.9
2	5.1
3	10.1
4	6.4
5	1.5
6	5
7	8.8
8	3.8
9	9.6
10	7

we have to find the sample correlation coefficient for this data to obtain the relation between pair of variable

Σ(x – Mx)(y – My) r = Σ(x – Mx)? * Σy – My)?

r = 0.017541

12 10 00 Y 6 4 N 0 0 2 4 6 8 10 12 х

Figure 1

since there is no correlation between variable x and y

Since correlation coefficient between u and v is r = 0.017541  Then the sample correlation coefficient r closest to 0

For data set 2

u	v
1	7.3
2	9
3	7.3
4	5.6
5	7.9
6	5.3
7	4.8
8	6.8
9	6.2
10	3.7

we have to find the sample correlation coefficient for this data to obtain the relation between pair of variable

Σ(u - Mu)(ν - Μν) r – Σ(u – Mu)? και Σίν – Μυ)?

r = - 0.69006

10 9 00 7 5 5 4 3 2 1 0 0 2 4 6 8 10 12 u

Figure 2

Since correlation coefficient between u and v is r = - 0.69006  Then the sample correlation coefficient r closest to -1

for data set 3

w	t
1	7.9
2	6.9
3	7.8
4	6.3
5	7
6	4.3
7	4.7
8	3.4
9	4.4
10	2.9

we have to find the sample correlation coefficient for this data to obtain the relation between pair of variable

Σ(w - Mw)(t – Mt) r – Σ(w - Mw) και Σ(t – Mt)?

r = -0.91968

9 9 00 7 6 5 4 t 3 2 1 0 0 N 6 8 10 12 W

figure 3

Since correlation coefficient between u and v is r = -0.91968  Then the sample correlation coefficient r closest to -1

for data set 4

m	n
1	3
2	4.1
3	3.6
4	5.4
5	4.6
6	7.4
7	6
8	7.8
9	7.5
10	7.7

we have to find the sample correlation coefficient for this data to obtain the relation between pair of variable

Σ(m – Mm) (η – Mn) r – Σ(m – Mm)' και Σ(n – Mn)?

r = 0.91873

9 00 7 6 5 4 n 3 2 1 0 0 2 4 9 00 10 12 m

Figure 4

Since correlation coefficient between u and v is r = 0.91873   Then the sample correlation coefficient r closest to 1

Ans :

1. For which data set is the sample correlation coefficient r closest to 0	data set (x,y)
2.For which data set is the sample correlation coefficient r closest to -1	data set (u,v) and data set (w,t)
3) For which data set is the sample correlation coefficient r closest to 1	data set (m,n )
4) which data set indicates the strongest positive linear relationship between its two variables	data set (m,n )