直線回帰の結果は表 1，表 2 のようになる。$X$ の残差と $Y$ の残差の相関係数は -0.06512 になり，これは $Z$ を制御したときの 変数 $X$ と変数 $Y$ の間の偏相関係数に等しくなっている。
| $X$ | $Z$ | $X$ の予測値 | $X$ の残差 |
|---|---|---|---|
| 61.0 | 58.0 | 54.02012 | 6.97988 |
| 57.3 | 45.7 | 47.91066 | 9.38934 |
| 55.5 | 62.6 | 56.30496 | $-$0.80496 |
| 40.8 | 28.0 | 39.11900 | 1.68100 |
| 27.9 | 52.5 | 51.28825 | $-$23.38825 |
| 57.0 | 67.1 | 58.54013 | $-$1.54013 |
| 57.5 | 49.1 | 49.59946 | 7.90054 |
| 47.7 | 51.6 | 50.84122 | $-$3.14122 |
| 57.1 | 54.4 | 52.23199 | 4.86801 |
| 56.6 | 44.9 | 47.51330 | 9.08670 |
| 43.7 | 39.0 | 44.58274 | $-$0.88274 |
| 61.7 | 62.1 | 56.05661 | 5.64339 |
| 32.0 | 45.0 | 47.56297 | $-$15.56297 |
| 44.4 | 38.3 | 44.23505 | 0.16495 |
| 50.1 | 50.9 | 50.49352 | $-$0.39352 |
| $Y$ | $Z$ | $Y$ の予測値 | $Y$ の残差 |
|---|---|---|---|
| 52.0 | 58.0 | 54.95840 | $-$2.95840 |
| 44.2 | 45.7 | 47.73154 | $-$3.53154 |
| 63.3 | 62.6 | 57.66113 | 5.63887 |
| 29.5 | 28.0 | 37.33191 | $-$7.83191 |
| 46.8 | 52.5 | 51.72688 | $-$4.92688 |
| 50.6 | 67.1 | 60.30510 | $-$9.70510 |
| 41.6 | 49.1 | 49.72921 | $-$8.12921 |
| 67.8 | 51.6 | 51.19808 | 16.60192 |
| 43.1 | 54.4 | 52.84322 | $-$9.74322 |
| 47.8 | 44.9 | 47.26150 | 0.53850 |
| 46.4 | 39.0 | 43.79495 | 2.60505 |
| 60.0 | 62.1 | 57.36736 | 2.63264 |
| 45.7 | 45.0 | 47.32025 | $-$1.62025 |
| 49.3 | 38.3 | 43.38367 | 5.91633 |
| 65.3 | 50.9 | 50.78680 | 14.51320 |
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