Heart curve regression

At the end of this file, there is a set of data with two columns. The columns are named “x” and “y”.

While the scatter plot looks very innocent and highly linear, if a standard OLS regression was performed between x and y, then plotting x against residues will yield a heart curve.

 

 

 

 


“x” “y”
0 5.01874617094183
1.59992000173331e-05 4.81811723985609
0.000127974402218556 3.63942570530945
0.00043180563790373 4.42790203415732
0.00102318108393247 5.34775704824241
0.00199750135374306 5.48086815280614
0.00344978405003848 3.93445798503133
0.00547456866599489 4.84578111031942
0.0081658219215339 3.66701815399701
0.0116168436208081 5.14058692709777
0.0159201731165795 6.62317025257275
0.0211674964666243 6.42423711386712
0.0274495543666724 5.60179135301969
0.0348560509436926 7.02528315051465
0.043475563492557 7.00499916580736
0.0533954532382698 6.6083680791867
0.06470177720502 5.85078367797611
0.0774792012723222 6.93020054891933
0.0918109144974377 8.4050003480302
0.10777854478213 8.35264333805573
0.125462075960593 7.70111348524685
0.144939766384117 6.57894783689958
0.166288069076697 8.59666836166356
0.189581553534389 7.70165833958218
0.214892829239722 9.14794617808926
0.242292470960939 10.6764564932348
0.27184894590422 11.0453499717996
0.303628542785404 11.5905650448506
0.337695302885928 13.1389820965073
0.374110953156006 13.8143030412205
0.412934841426141 13.0920749671102
0.454223873786213 15.7970112858371
0.49803245418942 17.8250418881863
0.544412426336338 18.0762086222837
0.593413017892321 17.600293269228
0.645080787089349 18.6886264713364
0.69945957176129 21.6858282888554
0.756590440859353 20.8206401047101
0.816511648492259 23.5681856762127
0.879258590533395 24.6117594245322
0.944863763834901 27.7785700647881
1.01335672808629 27.4167273362773
1.08476407035278 28.8968139023912
1.15910937232624 32.1654377047247
1.23641318031893 32.0283534560735
1.31669297802813 34.6919954348252
1.3999631620968 36.7380522921392
1.48623502049342 38.0490308976981
1.57551671373105 39.5773559909147
1.66781325894357 42.8749075412215
1.76312651683422 43.8436269980985
1.86145518150899 45.9940020479006
1.96279477320498 49.8402873351549
2.067137633921 52.8130644504175
2.17447292595526 53.4429156105742
2.28478663335224 56.0436561257984
2.3980615662583 56.7332587092706
2.514277368183 60.6039232437383
2.63341052616027 61.9174838479275
2.75543438380122 65.4028500565023
2.88031915722764 66.4781608020455
3.00803195387259 69.9180953212777
3.138536794132 72.256244608054
3.27179463584871 76.1918545826327
3.40776340160741 79.7352013115995
3.546398008817 82.7529316685061
3.68765040255397 85.1902960978904
3.83146959113791 86.9398828328872
3.97780168440811 90.997821150999
4.1265899346673 92.2489988184569
4.2777747802568 96.9814450878272
4.43129389172416 98.3189149116302
4.58708222054294 101.89193244602
4.74507205034119 105.953678161564
4.90519305059339 107.953319771445
5.06737233272833 113.924761964848
5.23153450860293 114.617162089865
5.3976017512904 119.046031662545
5.56549385812842 121.837027470032
5.73512831597154 127.854592187464
5.90642036858967 130.397502466276
6.07928308615265 133.08220639375
6.25362743673918 137.543638500205
6.42936235980629 141.097025446462
6.60639484155398 144.392237042472
6.78462999211784 147.702339094707
6.96397112452084 151.812749237287
7.14431983531385 156.998934996307
7.32557608683304 157.233815717774
7.50763829100066 161.99500027572
7.69040339459448 165.313555978355
7.87376696590973 169.207027901697
8.05762328273617 173.142163704702
8.24186542157177 177.905429024927
8.42638534799315 181.023678736989
8.61107400810231 182.686705238058
8.79582142096754 186.17408510592
8.98051677197634 192.342665315759
9.16504850701656 195.25922059094
9.34930442740166 199.989492434544
9.53317178545529 201.639924143014
9.71653738066958 206.445970872764
9.89928765635128 208.594867707584
10.0813087966691 213.935693775467
10.2624868240157 216.159053496277
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