Question

The table shows the heights and weights of a few students in a class. Height (inches) Weight (pounds)

height         weight
58              122
59               128
60              126
62             133
63             145
64             136
66              144
68            150
70             152

Complete the following sentences based on your observations. The data seems to have a correlation coefficient close to _____ . This indicates that the weight of a student ______ as the height of the student increases.

Answer 1

A 0.90

A. Generally Increases

Answer 2

Answer: Correlation coefficient = 0.945 ( approx) and weight of a student increases as the height of the student increases.

Step-by-step explanation:

Here, value of x are 58, 59, 60, 62, 63, 64, 66, 68, 70

Value of y are, 122, 128, 126, 133, 145, 136, 144, 150, 151.

∑x = 570, ∑y= 1236, ∑
`x^2`= 36234, ∑
`y^2`= 170694

∑xy=78617

Thus the correlation coefficient,

`r = (n(\sum xy)- (\sum x)(\sum y))/(√(n\sum x^2 - (\sum x)^2) √(n\sum y^2-(\sum y)^2) )`

Where n is the number of the term.

here n = 9

thus, correlation coefficient

r =
`(9* 78617- 570* 1236)/(√(9* 36234-(570)^2)√(9* 170694-(1236)^2))`

Thus, r= 0.94452987512

Which is closed to 0.95 and greater than 1

Therefore, weight of a student increases as the height of the student increases.