{
  "description": "공통 학습 자료의 자연로그 OLS. 단순 지수변환은 산술평균 예측이 아님.",
  "models": {
    "level": {
      "intercept": 232.5090245256157,
      "slope": -0.6842961185199762,
      "xmean": 125.93333333333334,
      "ymean": 146.33333333333334,
      "Sxx": 173445.86666666667,
      "Sxy": -118688.33333333333,
      "residuals": [
        8.664276807980016,
        -96.50089326621796,
        -23.451257414417114,
        29.72204391917859,
        29.862820215183348,
        -18.021645562419508,
        262.5454900818238,
        63.62277221557693,
        -5.236451488418311,
        -22.393490303218556,
        -4.64980082162046,
        28.813184363382504,
        -24.707567932819018,
        0.5650051043783435,
        -29.343854451417712,
        -19.872738007017006,
        -0.49276200682021454,
        51.97022317818275,
        -46.60829622921736,
        -11.662810836656831,
        6.03612154877905,
        -38.92237385881785,
        -9.864606747619291,
        59.441339622583456,
        23.4079662895781,
        7.821315622780247,
        -49.079412673618094,
        -53.34873320705637,
        -48.5505291180188,
        -69.7653350440176
      ],
      "SSE": 111542.70085306156,
      "R2": 0.421340967626202,
      "predictions": [
        109.33572319201998,
        167.50089326621796,
        191.4512574144171,
        68.27795608082141,
        205.13717978481665,
        123.02164556241951,
        217.45450991817623,
        20.37722778442307,
        157.2364514884183,
        150.39349030321856,
        95.64980082162046,
        181.1868156366175,
        136.70756793281902,
        61.43499489562166,
        174.3438544514177,
        194.872738007017,
        102.49276200682021,
        188.02977682181725,
        184.60829622921736,
        199.66281083665683,
        81.96387845122095,
        170.92237385881785,
        129.8646067476193,
        208.55866037741654,
        54.5920337104219,
        116.17868437721975,
        164.0794126736181,
        213.34873320705637,
        143.5505291180188,
        177.7653350440176
      ],
      "MAE": 38.164837264627174,
      "smearing": null
    },
    "log_y": {
      "intercept": 5.427591597916576,
      "slope": -0.004342308924456775,
      "xmean": 125.93333333333334,
      "ymean": 4.880750160696653,
      "Sxx": 173445.86666666667,
      "Sxy": -753.1555347368065,
      "residuals": [
        0.1247086329513083,
        -0.7523923730518671,
        -0.04308908304591075,
        0.1995300226236214,
        0.20568627320585353,
        -0.07886181984596963,
        0.8417253023234093,
        0.3493409675083372,
        0.07394290461994579,
        -0.05448426306214671,
        -0.048270306508371164,
        0.24518910213515,
        -0.10116947719753355,
        -0.21487998175729128,
        -0.08176159691717633,
        -0.02397863314793902,
        0.02241991101448182,
        0.3352974055151057,
        -0.19637628804739737,
        0.017281193287297825,
        0.0050531799421209556,
        -0.15398187212909598,
        0.011246483533986051,
        0.31537619495026714,
        0.05811754913177669,
        0.1308824848461123,
        -0.24842857710764843,
        -0.2308331327979598,
        -0.3092145461366549,
        -0.3980756568358146
      ],
      "SSE": 2.3016347601410456,
      "R2": 0.5869335323697201,
      "predictions": [
        104.16498032677619,
        150.6670220790644,
        175.3971905549448,
        80.27333158746764,
        191.31078283121994,
        113.61575329036744,
        206.86384052163874,
        59.232823031034414,
        141.16615716918187,
        135.16746984214677,
        95.50034050953727,
        164.33687363860625,
        123.92398438748052,
        76.86221219065966,
        157.3535743760284,
        179.2469756463306,
        99.73861383825412,
        171.63008939837252,
        167.94389632863428,
        184.77904677788237,
        87.55644179863725,
        153.9740058085545,
        118.65798260937744,
        195.5098546477908,
        73.59604424048004,
        108.78778748693706,
        147.43106424339115,
        201.54384444834915,
        129.42368957193827,
        160.8073209428489
      ],
      "MAE": 32.04178981055398,
      "smearing": 1.0406742524450752
    },
    "log_x": {
      "intercept": 570.5624347149791,
      "slope": -91.6827267310353,
      "xmean": 4.6271431545244495,
      "ymean": 146.33333333333334,
      "Sxx": 14.032747238841823,
      "Sxy": -1286.560530384425,
      "residuals": [
        23.542009171245695,
        -82.05058409559024,
        -27.18176107406987,
        29.91748600526023,
        2.6440922202796173,
        -0.25666070039028455,
        192.83276585030035,
        39.38215560763308,
        12.390422166563894,
        -3.6321375344048192,
        6.201748536543164,
        35.27664816286358,
        -5.499182880399019,
        -2.3398422265234444,
        -18.248053604886763,
        -28.159201373101155,
        12.49903944407481,
        52.15677262037508,
        -43.048806420063954,
        -27.64017031100326,
        11.940045706228943,
        -26.007614368419354,
        8.82627170252863,
        23.40157004027094,
        17.256019699705234,
        24.301569934778286,
        -33.34787500312183,
        -105.05683919666251,
        -29.293603839959815,
        -60.806284240055334
      ],
      "SSE": 74805.28913649557,
      "R2": 0.6119265904705893,
      "predictions": [
        94.4579908287543,
        153.05058409559024,
        195.18176107406987,
        68.08251399473977,
        232.35590777972038,
        105.25666070039028,
        287.16723414969965,
        44.61784439236692,
        139.6095778334361,
        131.63213753440482,
        84.79825146345684,
        174.72335183713642,
        117.49918288039902,
        64.33984222652344,
        163.24805360488676,
        203.15920137310115,
        89.50096055592519,
        187.84322737962492,
        181.04880642006395,
        215.64017031100326,
        76.05995429377106,
        158.00761436841935,
        111.17372829747137,
        244.59842995972906,
        60.743980300294766,
        99.69843006522171,
        148.34787500312183,
        265.0568391966625,
        124.29360383995981,
        168.80628424005533
      ],
      "MAE": 32.83790779124344,
      "smearing": null
    },
    "log_log": {
      "intercept": 7.339424795967869,
      "slope": -0.5313591028337017,
      "xmean": 4.6271431545244495,
      "ymean": 4.880750160696653,
      "Sxx": 14.032747238841823,
      "Sxy": -7.456427983123096,
      "residuals": [
        0.19058472184094288,
        -0.6570009793905642,
        -0.03989356329022975,
        0.1577300639651682,
        0.08028039537594722,
        0.011275359377395766,
        0.4768148527714269,
        0.13957191220465504,
        0.1820987549332962,
        0.05648278522017147,
        -0.013256127033833387,
        0.301819345253425,
        0.004860759529865533,
        -0.2784118912761473,
        -0.002047867695582184,
        -0.045305855983508,
        0.07360202084643408,
        0.35931280198629345,
        -0.15469449060206575,
        -0.04598493709298346,
        0.003865112559268802,
        -0.06560804403239295,
        0.11051362131204456,
        0.1407287407575426,
        -0.02799716667802077,
        0.20981001948292288,
        -0.14749356918147516,
        -0.4936537817489315,
        -0.1991391657611148,
        -0.3288638276499505
      ],
      "SSE": 1.6100278766762997,
      "R2": 0.7110538390703639,
      "predictions": [
        97.52413663762258,
        136.95889665995003,
        174.83759993505709,
        83.69986919457708,
        216.8715231024205,
        103.82273677083103,
        297.9635760844722,
        73.05736004443472,
        126.69489137982596,
        120.97059247956939,
        92.2143384903162,
        155.28904479597043,
        111.45691590254228,
        81.90387277091759,
        145.2972450712677,
        183.11087247607364,
        94.76221865580635,
        167.55742383119525,
        161.0875773453378,
        196.84702414915142,
        87.66052656891411,
        140.95066938140505,
        107.4448960723136,
        232.8182810807375,
        80.21463611065764,
        100.53154372085451,
        133.27647067586898,
        262.12660100165596,
        115.9334196004697,
        150.05397380993227
      ],
      "MAE": 27.156255371865786,
      "smearing": 1.025843924654872
    }
  },
  "curves": [
    {
      "x": 22.0,
      "level": 217.45450991817623,
      "log_y": 206.86384052163874,
      "log_log": 297.9635760844722
    },
    {
      "x": 24.88,
      "level": 215.4837370968387,
      "log_y": 204.29294156766383,
      "log_log": 279.1090289193473
    },
    {
      "x": 27.759999999999998,
      "level": 213.51296427550116,
      "log_y": 201.75399368553835,
      "log_log": 263.32835068205196
    },
    {
      "x": 30.64,
      "level": 211.54219145416363,
      "log_y": 199.24659978809134,
      "log_log": 249.87259474326862
    },
    {
      "x": 33.519999999999996,
      "level": 209.5714186328261,
      "log_y": 196.77036772314196,
      "log_log": 238.22510056411053
    },
    {
      "x": 36.4,
      "level": 207.60064581148856,
      "log_y": 194.3249102121674,
      "log_log": 228.01649134510077
    },
    {
      "x": 39.28,
      "level": 205.62987299015103,
      "log_y": 191.9098447897333,
      "log_log": 218.97481208792746
    },
    {
      "x": 42.16,
      "level": 203.6591001688135,
      "log_y": 189.52479374367678,
      "log_log": 210.8948444379617
    },
    {
      "x": 45.04,
      "level": 201.68832734747596,
      "log_y": 187.1693840560327,
      "log_log": 203.61845443366585
    },
    {
      "x": 47.92,
      "level": 199.71755452613843,
      "log_y": 184.84324734469456,
      "log_log": 197.02157435762703
    },
    {
      "x": 50.8,
      "level": 197.74678170480092,
      "log_y": 182.54601980580003,
      "log_log": 191.0053260950262
    },
    {
      "x": 53.68,
      "level": 195.77600888346336,
      "log_y": 180.27734215683256,
      "log_log": 185.48981469508885
    },
    {
      "x": 56.56,
      "level": 193.80523606212586,
      "log_y": 178.03685958043036,
      "log_log": 180.409692518292
    },
    {
      "x": 59.44,
      "level": 191.83446324078832,
      "log_y": 175.82422166889344,
      "log_log": 175.71092673415623
    },
    {
      "x": 62.32,
      "level": 189.8636904194508,
      "log_y": 173.6390823693805,
      "log_log": 171.3484026994534
    },
    {
      "x": 65.2,
      "level": 187.89291759811326,
      "log_y": 171.48109992978684,
      "log_log": 167.28411937279577
    },
    {
      "x": 68.08,
      "level": 185.92214477677572,
      "log_y": 169.34993684529485,
      "log_log": 163.4858114458086
    },
    {
      "x": 70.96000000000001,
      "level": 183.9513719554382,
      "log_y": 167.24525980558892,
      "log_log": 159.92588392365792
    },
    {
      "x": 73.84,
      "level": 181.98059913410066,
      "log_y": 165.16673964272618,
      "log_log": 156.58057878377755
    },
    {
      "x": 76.72,
      "level": 180.00982631276312,
      "log_y": 163.11405127965526,
      "log_log": 153.42931627874637
    },
    {
      "x": 79.6,
      "level": 178.0390534914256,
      "log_y": 161.0868736793747,
      "log_log": 150.45416924156717
    },
    {
      "x": 82.47999999999999,
      "level": 176.0682806700881,
      "log_y": 159.08488979472344,
      "log_log": 147.63943979803815
    },
    {
      "x": 85.36,
      "level": 174.09750784875052,
      "log_y": 157.10778651879502,
      "log_log": 144.97131573074472
    },
    {
      "x": 88.24,
      "level": 172.12673502741302,
      "log_y": 155.1552546359683,
      "log_log": 142.43758937816935
    },
    {
      "x": 91.12,
      "level": 170.15596220607546,
      "log_y": 153.22698877354662,
      "log_log": 140.02742605884316
    },
    {
      "x": 94.0,
      "level": 168.18518938473795,
      "log_y": 151.322687353998,
      "log_log": 137.7311720353076
    },
    {
      "x": 96.88,
      "level": 166.2144165634004,
      "log_y": 149.442052547789,
      "log_log": 135.54019428467916
    },
    {
      "x": 99.76,
      "level": 164.2436437420629,
      "log_y": 147.58479022680456,
      "log_log": 133.44674603599162
    },
    {
      "x": 102.64,
      "level": 162.27287092072532,
      "log_y": 145.75060991834698,
      "log_log": 131.44385331968078
    },
    {
      "x": 105.52,
      "level": 160.30209809938782,
      "log_y": 143.93922475970643,
      "log_log": 129.5252187584936
    },
    {
      "x": 108.4,
      "level": 158.33132527805026,
      "log_y": 142.15035145329608,
      "log_log": 127.6851395885321
    },
    {
      "x": 111.28,
      "level": 156.36055245671275,
      "log_y": 140.3837102223449,
      "log_log": 125.91843748982343
    },
    {
      "x": 114.16,
      "level": 154.38977963537522,
      "log_y": 138.63902476714088,
      "log_log": 124.22039826856444
    },
    {
      "x": 117.04,
      "level": 152.4190068140377,
      "log_y": 136.91602222181854,
      "log_log": 122.58671979821811
    },
    {
      "x": 119.92,
      "level": 150.44823399270015,
      "log_y": 135.21443311168278,
      "log_log": 121.01346691642186
    },
    {
      "x": 122.8,
      "level": 148.47746117136262,
      "log_y": 133.53399131106383,
      "log_log": 119.49703220615326
    },
    {
      "x": 125.68,
      "level": 146.5066883500251,
      "log_y": 131.87443400169542,
      "log_log": 118.03410177555907
    },
    {
      "x": 128.56,
      "level": 144.53591552868755,
      "log_y": 130.23550163161053,
      "log_log": 116.62162530109076
    },
    {
      "x": 131.44,
      "level": 142.56514270735005,
      "log_y": 128.61693787454794,
      "log_log": 115.25678972058003
    },
    {
      "x": 134.32,
      "level": 140.5943698860125,
      "log_y": 127.01848958986311,
      "log_log": 113.9369960624606
    },
    {
      "x": 137.2,
      "level": 138.62359706467498,
      "log_y": 125.43990678293754,
      "log_log": 112.65983897897478
    },
    {
      "x": 140.07999999999998,
      "level": 136.65282424333745,
      "log_y": 123.88094256608,
      "log_log": 111.4230886184654
    },
    {
      "x": 142.95999999999998,
      "level": 134.68205142199992,
      "log_y": 122.34135311991362,
      "log_log": 110.22467452747703
    },
    {
      "x": 145.84,
      "level": 132.71127860066235,
      "log_y": 120.82089765524309,
      "log_log": 109.06267131961826
    },
    {
      "x": 148.72,
      "level": 130.74050577932485,
      "log_y": 119.31933837539552,
      "log_log": 107.9352858866738
    },
    {
      "x": 151.6,
      "level": 128.76973295798732,
      "log_y": 117.83644043902953,
      "log_log": 106.84084595973144
    },
    {
      "x": 154.48,
      "level": 126.79896013664978,
      "log_y": 116.37197192340639,
      "log_log": 105.77778985519704
    },
    {
      "x": 157.36,
      "level": 124.82818731531223,
      "log_y": 114.92570378811773,
      "log_log": 104.74465726343632
    },
    {
      "x": 160.24,
      "level": 122.85741449397472,
      "log_y": 113.497409839264,
      "log_log": 103.74008095712023
    },
    {
      "x": 163.12,
      "level": 120.88664167263718,
      "log_y": 112.08686669407811,
      "log_log": 102.76277931276665
    },
    {
      "x": 166.0,
      "level": 118.91586885129965,
      "log_y": 110.69385374598878,
      "log_log": 101.811549552946
    },
    {
      "x": 168.88,
      "level": 116.94509602996213,
      "log_y": 109.31815313011799,
      "log_log": 100.88526162855248
    },
    {
      "x": 171.76,
      "level": 114.9743232086246,
      "log_y": 107.95954968920736,
      "log_log": 99.98285267076002
    },
    {
      "x": 174.64,
      "level": 113.00355038728706,
      "log_y": 106.6178309399678,
      "log_log": 99.10332195106066
    },
    {
      "x": 177.52,
      "level": 111.03277756594952,
      "log_y": 105.2927870398476,
      "log_log": 98.2457262953381
    },
    {
      "x": 180.4,
      "level": 109.062004744612,
      "log_y": 103.98421075421334,
      "log_log": 97.40917590445126
    },
    {
      "x": 183.28,
      "level": 107.09123192327446,
      "log_y": 102.69189742393874,
      "log_log": 96.59283053945221
    },
    {
      "x": 186.16,
      "level": 105.12045910193693,
      "log_y": 101.41564493339636,
      "log_log": 95.79589603445469
    },
    {
      "x": 189.04,
      "level": 103.14968628059941,
      "log_y": 100.15525367884705,
      "log_log": 95.01762110443323
    },
    {
      "x": 191.92,
      "level": 101.17891345926188,
      "log_y": 98.9105265372222,
      "log_log": 94.25729441894238
    },
    {
      "x": 194.8,
      "level": 99.20814063792434,
      "log_y": 97.68126883529409,
      "log_log": 93.51424191598632
    },
    {
      "x": 197.68,
      "level": 97.23736781658681,
      "log_y": 96.46728831922933,
      "log_log": 92.78782433310711
    },
    {
      "x": 200.56,
      "level": 95.26659499524928,
      "log_y": 95.26839512452061,
      "log_log": 92.07743493525119
    },
    {
      "x": 203.44,
      "level": 93.29582217391174,
      "log_y": 94.0844017462923,
      "log_log": 91.38249742115438
    },
    {
      "x": 206.32,
      "level": 91.32504935257421,
      "log_y": 92.91512300997495,
      "log_log": 90.70246399191906
    },
    {
      "x": 209.2,
      "level": 89.35427653123668,
      "log_y": 91.76037604234429,
      "log_log": 90.03681356714915
    },
    {
      "x": 212.08,
      "level": 87.38350370989914,
      "log_y": 90.61998024292024,
      "log_log": 89.38505013551385
    },
    {
      "x": 214.96,
      "level": 85.41273088856161,
      "log_y": 89.49375725572118,
      "log_log": 88.74670122794014
    },
    {
      "x": 217.84,
      "level": 83.44195806722408,
      "log_y": 88.38153094136949,
      "log_log": 88.12131650280911
    },
    {
      "x": 220.72,
      "level": 81.47118524588655,
      "log_y": 87.28312734954359,
      "log_log": 87.50846643358379
    },
    {
      "x": 223.6,
      "level": 79.50041242454904,
      "log_y": 86.19837469177243,
      "log_log": 86.90774109022279
    },
    {
      "x": 226.48,
      "level": 77.5296396032115,
      "log_y": 85.12710331456799,
      "log_log": 86.31874900656852
    },
    {
      "x": 229.36,
      "level": 75.55886678187395,
      "log_y": 84.06914567289188,
      "log_log": 85.74111612663646
    },
    {
      "x": 232.24,
      "level": 73.58809396053641,
      "log_y": 83.02433630395149,
      "log_log": 85.17448482339616
    },
    {
      "x": 235.12,
      "level": 71.6173211391989,
      "log_y": 81.99251180132188,
      "log_log": 84.61851298422862
    },
    {
      "x": 238.0,
      "level": 69.64654831786137,
      "log_y": 80.97351078938938,
      "log_log": 84.07287315777337
    },
    {
      "x": 240.88,
      "level": 67.67577549652384,
      "log_y": 79.96717389811263,
      "log_log": 83.537251757359
    },
    {
      "x": 243.76,
      "level": 65.70500267518631,
      "log_y": 78.9733437380974,
      "log_log": 83.01134831663771
    },
    {
      "x": 246.64,
      "level": 63.734229853848774,
      "log_y": 77.99186487598115,
      "log_log": 82.49487479343132
    },
    {
      "x": 249.52,
      "level": 61.76345703251124,
      "log_y": 77.02258381012355,
      "log_log": 81.98755491814534
    },
    {
      "x": 252.4,
      "level": 59.79268421117371,
      "log_y": 76.06534894659902,
      "log_log": 81.48912358341877
    },
    {
      "x": 255.28,
      "level": 57.821911389836174,
      "log_y": 75.12001057548775,
      "log_log": 80.9993262719647
    },
    {
      "x": 258.15999999999997,
      "level": 55.85113856849867,
      "log_y": 74.18642084746129,
      "log_log": 80.51791851981069
    },
    {
      "x": 261.03999999999996,
      "level": 53.880365747161136,
      "log_y": 73.2644337506592,
      "log_log": 80.04466541238158
    },
    {
      "x": 263.91999999999996,
      "level": 51.9095929258236,
      "log_y": 72.35390508785294,
      "log_log": 79.5793411110781
    },
    {
      "x": 266.8,
      "level": 49.93882010448604,
      "log_y": 71.45469245389383,
      "log_log": 79.12172840819474
    },
    {
      "x": 269.68,
      "level": 47.96804728314851,
      "log_y": 70.56665521344098,
      "log_log": 78.67161830819715
    },
    {
      "x": 272.56,
      "level": 45.997274461811,
      "log_y": 69.68965447896625,
      "log_log": 78.22880963353289
    },
    {
      "x": 275.44,
      "level": 44.02650164047347,
      "log_y": 68.82355308903239,
      "log_log": 77.7931086532977
    },
    {
      "x": 278.32,
      "level": 42.055728819135936,
      "log_y": 67.96821558684132,
      "log_log": 77.364328733208
    },
    {
      "x": 281.2,
      "level": 40.0849559977984,
      "log_y": 67.12350819904886,
      "log_log": 76.94229000545135
    },
    {
      "x": 284.08,
      "level": 38.11418317646087,
      "log_y": 66.28929881484278,
      "log_log": 76.52681905709537
    },
    {
      "x": 286.96,
      "level": 36.143410355123336,
      "log_y": 65.46545696528096,
      "log_log": 76.11774863583464
    },
    {
      "x": 289.84,
      "level": 34.17263753378583,
      "log_y": 64.65185380288621,
      "log_log": 75.71491737194991
    },
    {
      "x": 292.72,
      "level": 32.20186471244824,
      "log_y": 63.848362081494756,
      "log_log": 75.3181695154334
    },
    {
      "x": 295.6,
      "level": 30.231091891110736,
      "log_y": 63.054856136355184,
      "log_log": 74.9273546873134
    },
    {
      "x": 298.48,
      "level": 28.260319069773203,
      "log_y": 62.27121186447464,
      "log_log": 74.54232764428211
    },
    {
      "x": 301.36,
      "level": 26.28954624843567,
      "log_y": 61.497306705209354,
      "log_log": 74.16294805579336
    },
    {
      "x": 304.24,
      "level": 24.318773427098137,
      "log_y": 60.73301962109637,
      "log_log": 73.78908029285772
    },
    {
      "x": 307.12,
      "level": 22.348000605760603,
      "log_y": 59.97823107892348,
      "log_log": 73.42059322781769
    },
    {
      "x": 310.0,
      "level": 20.37722778442307,
      "log_y": 59.232823031034414,
      "log_log": 73.05736004443472
    }
  ],
  "percentages": [
    {
      "change": 1,
      "exact": -0.5273246240015128,
      "approx": -0.5313591028337017
    },
    {
      "change": 10,
      "exact": -4.938290504442843,
      "approx": -5.313591028337017
    },
    {
      "change": 50,
      "exact": -19.381946770167925,
      "approx": -26.567955141685083
    }
  ],
  "retransform": {
    "values": [
      50,
      200
    ],
    "geometric": 100,
    "arithmetic": 125
  }
}