Question

Day# 1 2 3 4 5 6 7 Run time (min) 8.2 8.1 7.5 7.8 7.4 7.2 7.1 What is the value of the correlation coefficient

Answer 1

The calculated value of the correlation coefficient is -0.9333

How to determine the value of the correlation coefficient

From the question, we have the following parameters that can be used in our computation:

Day# 1 2 3 4 5 6 7

Run time (min) 8.2 8.1 7.5 7.8 7.4 7.2 7.1

Using a graphing tool, we have the following summary:

X Values

Sum = 28

Mean = 4

∑(X - Mx)² = SSx = 28

Y Values

Sum = 53.3

Mean = 7.614

∑(Y - My)² = SSy = 1.109

X and Y Combined

N = 7

∑(X - Mx)(Y - My) = -5.2

The correlation coefficient is calculated using

`r = (\sum(X - M_y) * (Y - Mx))/(√((SS_x)(SS_y)))`

Substitute the known values into the equation

`r = -(5.2)/(√(28 * 1.109))`

Evaluate

r = -0.9333

Hence, the value of the correlation coefficient is -0.9333