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 0.46496300  0.36690417  0.11853132    -0.04262873
pan wye 2  0.52259404 0.51167874 0.27310454 0.26740026 0.26181513 0.45900483  0.34246572  0.41758057    0.48327025
wye cat 3  0.81504017 0.07989552 0.66429048 0.06511805 0.00638329 0.29848705  -0.31592540 0.14866640    0.01036591
dog hat 4  0.44887336 0.57305305 0.20148729 0.25722825 0.32838980 0.49946863  0.50843491  0.40405789    0.45948966
dog pan 5  0.29465580 0.68504373 0.08682204 0.20185210 0.46928491 0.58411553  0.85562868  0.33044079    0.33002885
wye cat 6  0.04870918 0.58518790 0.00237258 0.02850402 0.34244488 0.71911067  1.40933430  0.09999167    -0.07523200
dog hat 7  0.85000031 0.29840987 0.72250054 0.25364849 0.08904845 0.27929813  -0.39463203 0.39929895    0.45112074
pan pan 8  0.61650721 0.25924336 0.38008114 0.15982540 0.06720712 0.40745779  0.13103671  0.27457044    0.23177696
hat hat 9  0.33786884 0.60367356 0.11415535 0.20396249 0.36442177 0.56039676  0.75834209  0.33324633    0.33496260
wye hat 10 0.38346489 0.49997093 0.14704533 0.19172130 0.24997093 0.53537001  0.65569058  0.31697288    0.30634461
pan hat 11 0.02547500 0.78619549 0.00064898 0.02002833 0.61810335 0.73186344  1.46164199  0.08872407    -0.09504685
cat hat 12 0.63354457 0.15467179 0.40137872 0.09799147 0.02392336 0.39810632  0.09268009  0.19236835    0.08721884
hat wye 13 0.35922068 0.85026781 0.12903950 0.30543379 0.72295535 0.54867717  0.71027216  0.46814238    0.57218671
dog dog 14 0.54400474 0.93360885 0.29594116 0.50788764 0.87162549 0.44725293  0.29426329  0.73728476    1.04549235
wye dog 15 0.46891753 0.09048353 0.21988365 0.04242931 0.00818727 0.48846678  0.46330897  0.11850396    -0.04267684
pan pan 16 0.39591778 0.63398585 0.15675089 0.25100627 0.40193806 0.52853487  0.62765509  0.39578639    0.44494365
dog hat 17 0.34033845 0.88459347 0.11583026 0.30106117 0.78250561 0.55904125  0.75278220  0.46232942    0.56196422
wye wye 18 0.67706137 0.89630723 0.45841209 0.60685499 0.80336664 0.37422083  -0.00529034 0.86885205    1.27686262
dog wye 19 0.48653732 0.44117766 0.23671857 0.21464940 0.19463773 0.47879563  0.42364110  0.34745352    0.35994694
dog dog 20 0.32233117 0.08115611 0.10389738 0.02615914 0.00658631 0.56892508  0.79332242  0.09687438    -0.08071396
