Question

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Answer 1

a) The scatter plot is

Scatter Plot 14 12 LO . CO . . . 6 . 4 2 O 0 2 4 6 8 10 12 14 16

Option c is correct.

b. The linear correlation coefficient is given by

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

From the given data, we have the following values

$\sum x = 99 \sum y = 82.5 \sum xy = 797.43 \sum x^2 = 1001 \sum y^2 = 659.949$

So the linear correlation coefficient is

$\bg_white r = \frac{11*797.43 - 99* 82.5}{\sqrt{[11*1001 - 99^2][11*659.949 - (82.5)^2]}}$

$\bg_white r = \frac{604.23}{\sqrt{[1210][453.189]}} = 0.816$

Taking alpha = 0.05 and the n = 11, the critical value of the correlation coefficient is = 0.602

Since the calculated value is greater than the critical value, hence we will conclude that there is a linear relationship between x and y.

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