For the following paired observations calculate the Pearson

For the following paired observations, calculate the Pearson product-moment correlation coefficient and test for significance at the .01 level.

                        x                      x²                     y                      y²                    xy

                        17                    289                  23                    529                  391

                        17                    289                  19                    361                  323

                        18                    324                  20                    400                  360

                        19                    361                  17                    289                  323

                        21                    441                  15                    225                  315

                        22                    484                  19                    361                  418

                        21                    441                  20                    400                  420

                        23                    529                  19                    361                  437

                        22                    484                  20                    400                  440

                        18                    324                  16                    256                  288

                      198                 3,966                188                 3,582               3,715

Solution

=Result Details & Calculation

X Values
? = 198
Mean = 19.8
?(X - M_x)² = SS_x = 45.6

Y Values
? = 188
Mean = 18.8
?(Y - M_y)² = SS_y = 47.6

X and Y Combined
N = 10
?(X - M_x)(Y - M_y) = -7.4

R Calculation
r = ?((X - M_y)(Y - M_x)) / ?((SS_x)(SS_y))

r = -7.4 / ?((45.6)(47.6)) = -0.1588

Meta Numerics (cross-check)
r = -0.1588