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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.

Verified Answer :

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,

\(r = \frac{n(\sum xy)- (\sum x)(\sum y)}{\sqrt{n\sum x^2 - (\sum x)^2} \sqrt{n\sum y^2-(\sum y)^2} }\)

Where n is the number of the term.

here n = 9

thus, correlation coefficient

r = \(\frac{9\times 78617- 570\times 1236}{\sqrt{9\times 36234-(570)^2}\sqrt{9\times 170694-(1236)^2}}\)

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.

Answer:

A 0.90

A. Generally Increases

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