a   b   i  x          y          x2         xy         y2         x_y_ols_fit x_y_pca_fit xy_y2_ols_fit xy_y2_pca_fit
cat pan 1  0.51173890 0.08295225 0.26187670 0.04244989 0.00688108 0.08295225  0.08295225  0.00688108    0.00688108
cat hat 12 0.63354457 0.15467179 0.40137872 0.09799147 0.02392336 0.15467179  0.15467179  0.02392336    0.02392336
pan wye 2  0.52259404 0.51167874 0.27310454 0.26740026 0.26181513 0.44501562  0.43583532  0.23740195    0.03336393
pan pan 8  0.61650721 0.25924336 0.38008114 0.15982540 0.06720712 0.37216516  0.35647661  0.35312155    0.38551716
pan hat 11 0.02547500 0.78619549 0.00064898 0.02002833 0.61810335 0.83064155  0.85591193  0.50350299    0.84315186
pan pan 16 0.39591778 0.63398585 0.15675089 0.25100627 0.40193806 0.54328112  0.54287957  0.25503717    0.08703071
wye cat 3  0.81504017 0.07989552 0.66429048 0.06511805 0.00638329 0.33782665  -0.22766037 0.13706635    0.11249379
wye cat 6  0.04870918 0.58518790 0.00237258 0.02850402 0.34244488 0.54864044  1.27134677  0.09347962    0.06152080
wye hat 10 0.38346489 0.49997093 0.14704533 0.19172130 0.24997093 0.45655084  0.61653676  0.28777966    0.28874712
wye dog 15 0.46891753 0.09048353 0.21988365 0.04242931 0.00818727 0.43304325  0.44938430  0.11005681    0.08090718
wye wye 18 0.67706137 0.89630723 0.45841209 0.60685499 0.80336664 0.37578393  0.04223765  0.78197058    0.86668412
dog hat 4  0.44887336 0.57305305 0.20148729 0.25722825 0.32838980 0.56304289  0.66875003  0.40199109    0.40662172
dog pan 5  0.29465580 0.68504373 0.08682204 0.20185210 0.46928491 0.61023498  1.50495630  0.29757930    0.25511169
dog hat 7  0.85000031 0.29840987 0.72250054 0.25364849 0.08904845 0.44029409  -1.50626091 0.39524145    0.39682744
dog dog 14 0.54400474 0.93360885 0.29594116 0.50788764 0.87162549 0.53393175  0.15292379  0.87460972    1.09242997
dog hat 17 0.34033845 0.88459347 0.11583026 0.30106117 0.78250561 0.59625564  1.25725351  0.48463813    0.52654933
dog wye 19 0.48653732 0.44117766 0.23671857 0.21464940 0.19463773 0.55151735  0.46452655  0.32170862    0.29012530
dog dog 20 0.32233117 0.08115611 0.10389738 0.02615914 0.00658631 0.60176605  1.35489347  -0.03369000   -0.22558715
hat hat 9  0.33786884 0.60367356 0.11415535 0.20396249 0.36442177 0.60367356  0.60367356  0.36442177    0.36442177
hat wye 13 0.35922068 0.85026781 0.12903950 0.30543379 0.72295535 0.85026781  0.85026781  0.72295535    0.72295535
