Question

Sasha recorded the height and weight of all of the girls in her physical education course.

Weight Height

99 61

104 61

110 62

133 64

130 65

142 68

146 66

153 67

184 69

185 70




What is the correlation coefficient for the data

Answer 1

Correlation coefficient, r = 0.957

Explanation:

Let y represent the weight

Let x represent the height

y x x² y² xy

99 61 3721 9801 6039

104 61 3721 10816 6344

110 62 3844 12100 6820

133 64 4096 17689 8512

130 65 4225 16900 8550

142 68 4629 20169 9656

146 66 4356 21316 9636

153 67 4489 23409 10251

184 69 4761 33856 12696

185 70 4900 34225 12950

`\sum y = 1386`,
`\sum x = 653`,
`\sum x^2 = 42737`,
`\sum y^2 = 200276`,
`\sum xy = 91454`

Correlation coefficient formula,

`r = (n \sum xy - \sum x \sum y)/(√((n \sum x^2 - (\sum x)^2) (n \sum y^2 - (\sum y)^2)) ) \\r = (10* 91454 - 653*1386)/(√((10* 42737 - (653)^2) (10* 200276 - (1386)^2)) )`

Correlation coefficient, r = 0.957

Answer 2

0.9156

Explanation:

In the picture attached, the data is plotted (I made it using MS Excel, you can use similar programmes or a calculator).

The line that best correlates the data has the following equation:

y = 0.1037x + 50.922

and its correlation coefficient is:

R² = 0.9156