Question

Statistics Question:

Answer 1

The Correlation coefficient is r = -0.992324879

Step-by-step explanation:

The figure shown is the calculation of all data

Given data :

X y

1 42.2

2 42.14

3 39.38

4 38.22

5 37.46

6 35.2

7 30.24

8 29.38

9 25.92

10 24.86

11 24.8

12 21.04

13 20.98

14 15.42

15 15.46

16 13.4

Step1: Find X mean, Y mean

Mean  = $\frac{\sum x }{N}$

X mean = $\frac{1+2+3+4+5+...+16}{16}$

X mean = 8.5

Similarly, we get

Y mean = $\frac{42.2+42.14+39.38+...+15.42+15.46+13.4}{16}$

Y mean = 28.50625

Step2: Find Standard deviation

Standard deviation = $\sqrt {\frac{ \sum (Xi-X mean)^{2} }{N-1}}$

Sx = $\sqrt {\frac{ (-7.5)^{2} + (-6.5)^{2} +(-5.5)^{2} ....+ (7.5)^{2} }{16-1}}$

Sx= 4.760952286

Similarly, we get

Sy= 9.765590527

Step3: Find Correlation coefficient

The formula for the Correlation coefficient is given as  

$r=\frac{1}{N-1} \sum(\frac{Xi-X mean }{Sx} ) (\frac{Yi- Y mean }{Sy} )$

$r=\frac{1}{16-1} \sum(\frac{Xi-8.5 }{4.760952286} ) (\frac{Yi- 28.50625 }{9.765590527} )$

$r= -0.992324879$

Thus, The Correlation coefficient is r = -0.992324879