Pearson Correlation

Suppose that we are interested in the

strength of the association between age (the independent variable or X) and

systolic blood pressure (SBP) (the dependent variable or Y). We conduct a small

pilot study, reporting age and systolic blood pressure on 15 subjects. We

calculate a mean age of 51.73 and a mean of SBP of 149.80 mmHg. The data are

displayed in the table below:

Subject Age (X) SBP (Y) X-Xbar (X-Xbar)2 Y-Ybar (Y-Ybar)2 (X-Xbar)(Y-Ybar)

1 39 144 -12.7333 162.1378 -5.8 33.6400

73.8533

2 47 220 -4.7333 22.4044 70.2 4928.0400

-332.2800

3 45 138 -6.7333 45.3378 -11.8 139.2400

79.4533

4 47 145 -4.7333 22.4044 -4.8 23.0400 22.7200

5 65 162 13.2667 176.0044 12.2 148.8400

161.8533

6 46 142 -5.7333 32.8711 -7.8 60.8400 44.7200

7 67 170 15.2667 233.0711 20.2 408.0400

308.3867

8 42 124 -9.7333 94.7378 -25.8 665.6400

251.1200

9 67 158 15.2667 233.0711 8.2 67.2400

125.1867

10 56 154 4.2667 18.2044 4.2 17.6400 17.9200

11 64 162 12.2667 150.4711 12.2 148.8400

149.6533

12 56 150 4.2667 18.2044 0.2 0.0400 0.8533

13 59 140 7.2667 52.8044 -09.8 96.0400

-71.2133

14 34 110 -17.7333 314.4711 -39.8 1584.0400

705.7867

15 42 128 -9.7333 94.7378 -21.8 475.2400

212.1867

Sum 1670.9333 8796.4000 1750.2000

we know that the formula for the Pearson product moment correlation coefficient is:

r= summation of (X-Xbar)(Y-Ybar)

square root of summation of (X-Xbar)²summationof (Y-Ybar)²

1)What is the correlation coefficient (r) showing your calculation using the information in the table provided?

2)Interpret the size of r in two ways. First, give your interpretation the index value both in terms of direction (positive or negative) and strength (weak, moderate, or strong). Second, give your interpretation if the squared value of r.