In: Statistics and Probability
A study of bone density on 5 random women at a hospital produced the following results.
Age | 33 | 41 | 57 | 61 | 65 |
---|---|---|---|---|---|
Bone Density | 355 | 345 | 340 | 320 | 315 |
Step 2 of 3:
Estimate the correlation in words: positive, negative, no correlation.
Step 3 of 3:
Calculate the correlation coefficient, r. Round your answer to three decimal places.
Solution :
X | Y | XY | X^2 | Y^2 |
33 | 355 | 11715 | 1089 | 126025 |
41 | 345 | 14145 | 1681 | 119025 |
57 | 340 | 19380 | 3249 | 115600 |
61 | 320 | 19520 | 3721 | 102400 |
65 | 315 | 20475 | 4225 | 99225 |
n | 5 |
sum(XY) | 85235.00 |
sum(X) | 257.00 |
sum(Y) | 1675.00 |
sum(X^2) | 13965.00 |
sum(Y^2) | 562275.00 |
Numerator | -4300.00 |
Denominator | 4659.61 |
r | -0.9228 |
r square | 0.8516 |
Xbar(mean) | 51.4000 |
Ybar(mean) | 335.0000 |
SD(X) | 12.2898 |
SD(Y) | 15.1658 |
b | -1.1388 |
a | 393.5328 |
Step 2 :
negative
Step 3 :
the correlation coefficient, r = -0.923