Question

Statistics Question:

Answer 1

The Correlation coefficient is r = -0.992324879

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 =
`(\sum x )/(N)`

X mean =
`(1+2+3+4+5+...+16)/(16)`

X mean = 8.5

Similarly, we get

Y mean =
`(42.2+42.14+39.38+...+15.42+15.46+13.4)/(16)`

Y mean = 28.50625

Step2: Find Standard deviation

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

Sx =
`\sqrt {( (-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=(1)/(N-1) \sum((Xi-X mean )/(Sx) ) ((Yi- Y mean )/(Sy) )`

`r=(1)/(16-1) \sum((Xi-8.5 )/(4.760952286) ) ((Yi- 28.50625 )/(9.765590527) )`

`r= -0.992324879`

Thus, The Correlation coefficient is r = -0.992324879