Statistic Question

Question

Based on the data shown below, calculate the correlation coefficient (rounded to three decimal places)

xy
2	19.64
3	19.06
4	17.88
5	17.7
6	17.82
7	16.94
8	17.76
9	18.98
10	19.1
11	18.82
12	18.84
13	16.66
14	19.38
15	16.3
16	18.22

Answer 1

since the data set is large enough i think your best approach here is going to be using something a statistical software program like Excel or an online calculator that focuses specifically on computing correlation coefficients.

when i plug those values into this calculator (https://www.socscistatistics.com/tests/pearson/default2.aspx) i end up getting r = -0.233 for this set of data points, meaning that there is a moderately negative correlation between the variables

Answer 2

Hi Kimberly,

Take a TI-80s series calculator. Go to STAT-EDIT-L1–for list 1. Enter in all x data (on the left) into L1. Enter all the y-data (on right) into L2. Then: STAT-Calc-LinReg (ax+b) L1, L2. This will give you the least squares regression line (y = -0.0535x + 18.689, the coefficient of determination (r^2) and the correlation coefficient, which is what you’re looking for:

r = -0.233

This can also be done in Excel, R, and many other statistical software programs. There is also a manual formula, but that is cumbersome for fifteen data points. I hope this helps.