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 = [tex]\frac{\sum x }{N}[/tex]
X mean = [tex]\frac{1+2+3+4+5+...+16}{16}[/tex]
X mean = 8.5
Similarly, we get
Y mean = [tex]\frac{42.2+42.14+39.38+...+15.42+15.46+13.4}{16}[/tex]
Y mean = 28.50625
Step2: Find Standard deviation
Standard deviation = [tex]\sqrt {\frac{ \sum (Xi-X mean)^{2} }{N-1}}[/tex]
Sx = [tex]\sqrt {\frac{ (-7.5)^{2} + (-6.5)^{2} +(-5.5)^{2} ....+ (7.5)^{2} }{16-1}}[/tex]
Sx= 4.760952286
Similarly, we get
Sy= 9.765590527
Step3: Find Correlation coefficient
The formula for the Correlation coefficient is given as
[tex]r=\frac{1}{N-1} \sum(\frac{Xi-X mean }{Sx} ) (\frac{Yi- Y mean }{Sy} )[/tex]
[tex]r=\frac{1}{16-1} \sum(\frac{Xi-8.5 }{4.760952286} ) (\frac{Yi- 28.50625 }{9.765590527} )[/tex]
[tex]r= -0.992324879[/tex]
Thus, The Correlation coefficient is r = -0.992324879
