Question

For the following data​ (a) display the data in a scatter​ plot, (b) calculate the sample correlation coefficient​ r, and​ (c) make a conclusion about the type of correlation. Use technology.

The maximum weights​ (in kilograms) for which one repetition of a half squat can be performed and the times​ (in seconds) to run a​ 10-meter sprint for 12 international soccer players are shown in the attached data table.

Maximum_Weight,_x   Time,_y
170 1.78
175 1.75
150 2.04
210 1.42
150 2.05
185 1.62
185 1.72
160 1.91
190 1.59
180 1.65
165 1.96
165 1.89

​(b) The correlation coefficient r is

(c) make a conclusion about the type of correlation

Answer 1

X	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
170 175 150 210 150 185 185 160 190 180 165 165	1.78 1.75 2.04 1.42 2.05 1.62 1.72 1.91 1.59 1.65 1.96 1.89	14.062 1.562 564.062 1314.062 564.062 126.562 126.562 189.062 264.062 39.062 76.562 76.562 Sum: 3356.250	0.000 0.001 0.067 0.131 0.072 0.026 0.004 0.016 0.037 0.017 0.032 0.012 Sum: 0.415	0.006 -0.040 -6.135 -13.110 -6.373 -1.819 -0.694 -1.765 -3.115 -0.823 -1.560 -0.948 Sum: -36.375

1) scatter plot

2) correlation coefficient

∑ x= 2085
Mean = 173.75
∑(X - Mx)2 = SSx = 3356.25

Y Values
∑y = 21.38
Mean = 1.782
∑(Y - My)2 = SSy = 0.415

X and Y Combined
N = 12
∑(X - Mx)(Y - My) = -36.375

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -36.375 / √((3356.25)(0.415)) = -0.9752

3) there is strong negative relation between x and y.