與Matlab的功能問題rsquare

Question

我計算確定我的模型的係數，這樣做：

Rsqrd1 = 1- sum((DataSeries(:)-ModelSeries(:)).^2)/sum((DataSeries(:)-mean(ModelSeries(:))).^2) ; 

然而，當我使用下面的MATLAB函數，我收到一個不同的結果（零，這是） 。我的問題是什麼？ （我不完全理解了Matlab功能的編碼以及如何測試它，這就是爲什麼我只能比較它的一部分...）

[Rsqrd2, ~] = rsquare(DataSeries,ModelSeries); 

僅供參考，下面是我使用的數據的樣本有以下兩個結果：

Rsqrd1 = 0.300314935784522; 
Rsqrd2 = 0; 

DataSeries = [ 8.109999999999999; 7.340000000000000; 8.140000000000001; 8.529999999999999; 8.580000000000000; 10.060000000000000; 34.219999999999999; 37.899999999999999; 41.490000000000002; 41.960000000000001; 43.280000000000001; 42.950000000000003; 40.950000000000003; 41.979999999999997; 43.909999999999997; 43.250000000000000; 41.259999999999998; 49.960000000000001; 59.829999999999998; 56.850000000000001; 49.960000000000001; 39.420000000000002; 43.020000000000003; 36.509999999999998; 37.020000000000003; 35.829999999999998; 32.289999999999999; 30.079999999999998; 30.010000000000002; 28.030000000000001; 27.210000000000001; 30.460000000000001; 36.600000000000001; 38.799999999999997; 40.320000000000000; 40.530000000000001; 38.500000000000000; 36.719999999999999; 33.000000000000000; 32.009999999999998; 32.869999999999997; 40.210000000000001; 47.490000000000002; 44.950000000000003; 36.890000000000001; 34.520000000000003; 36.000000000000000; 32.289999999999999; 33.060000000000002; 29.039999999999999; 25.590000000000000; 23.340000000000000; 23.250000000000000; 24.989999999999998; 15.119999999999999; 26.010000000000002; 34.649999999999999; 36.189999999999998; 37.500000000000000; 38.560000000000002; 36.930000000000000; 33.030000000000001; 29.930000000000000; 28.390000000000001; 26.390000000000001; 33.039999999999999; 38.990000000000002; 33.930000000000000; 27.079999999999998; 18.899999999999999; 25.070000000000000; 12.250000000000000; 13.630000000000001; 15.380000000000001; 22.480000000000000; 26.090000000000000; 28.390000000000001; 31.320000000000000; 48.689999999999998; 59.969999999999999; 54.789999999999999; 44.000000000000000; 42.090000000000003; 38.390000000000001; 37.649999999999999; 32.590000000000003; 29.800000000000001; 28.649999999999999; 29.180000000000000; 34.960000000000001; 37.640000000000001; 36.939999999999998; 29.579999999999998; 26.370000000000001; 19.079999999999998; 8.789999999999999; 11.279999999999999; 10.460000000000001; 8.619999999999999; 8.770000000000000; 7.270000000000000; 20.059999999999999; 31.820000000000000; 39.460000000000001; 38.840000000000003; 38.520000000000003; 38.039999999999999; 33.590000000000003; 32.979999999999997; 32.960000000000001; 36.640000000000001; 38.119999999999997; 39.549999999999997; 46.990000000000002; 58.469999999999999; 54.539999999999999; 39.770000000000003; 37.560000000000002; 39.259999999999998; 32.049999999999997; 34.729999999999997; 34.630000000000003; 31.260000000000002; 30.039999999999999; 30.280000000000001; 31.890000000000001; 41.670000000000002; 59.890000000000001; 59.890000000000001; 59.329999999999998; 58.409999999999997; 59.090000000000003; 55.969999999999999; 53.520000000000003; 49.939999999999998; 47.289999999999999; 47.570000000000000; 55.899999999999999; 59.939999999999998; 59.240000000000002; 52.939999999999998; 38.329999999999998; 36.710000000000001; 35.460000000000001; 35.810000000000002; 34.840000000000003; 33.259999999999998; 32.590000000000003; 33.259999999999998; 34.090000000000003; 44.939999999999998; 59.430000000000000; 58.270000000000003; 58.270000000000003; 58.270000000000003; 58.079999999999998; 56.039999999999999; 55.430000000000000; 53.950000000000003; 53.439999999999998; 51.969999999999999; 58.880000000000003; 82.299999999999997; 70.109999999999999; 62.310000000000002; 51.930000000000000; 45.950000000000003; 37.549999999999997]; 

ModelSeries = [ 8.109999999999998; 8.033959427220921; 8.323743041322626; 8.642708281120481; 8.582517975760446; 11.267851534695547; 19.265627892290375; 24.383823505293059; 24.255451695071979; 23.221588621286294; 23.061055862798810; 22.113019289306415; 21.371289863159902; 20.649139051697372; 20.517347467041816; 20.204389732885463; 20.152889919509455; 23.796341860624523; 28.357685405641778; 26.637620279541537; 22.250623983516938; 18.521786633703048; 17.231002075227554; 13.067216036414376; 19.142739022137061; 17.721978391048754; 15.855447009714094; 14.671720684372842; 14.681919810093815; 14.765381876692128; 11.357099766936273; 15.816337667523761; 20.080445840613475; 21.201625338935443; 22.073981571269272; 22.515202276491678; 21.543798733221458; 19.960000354644297; 18.067072108251327; 17.381842068691483; 17.031516337275718; 21.137586012909246; 25.023728337649139; 22.772401470260085; 18.479087827412922; 14.972363725126110; 17.654172434932196; 11.716255484871617; 19.715961876585990; 18.155212284709371; 16.157517128358631; 14.873595374529506; 14.807724678847782; 14.816736894019828; 11.339910137512746; 15.714998343157673; 19.855463769222808; 20.864416383513849; 21.621229985316365; 21.951821367820752; 20.909538825844994; 19.286028051295396; 17.380523953397315; 16.649325149265788; 16.244747678122277; 20.077382742947545; 23.671685948867548; 21.455816819780182; 17.342414495551786; 13.997360909813795; 16.442356118812683; 10.871782060716438; 9.254066806706989; 9.020435845559256; 9.198343907518664; 9.402433405571619; 9.194123813724323; 11.889052472788039; 20.026481568965160; 24.977165077948360; 24.489207826870764; 23.114540096244365; 22.636235398768406; 21.409588152343272; 20.414075626818608; 19.464490741778725; 19.090081921322344; 18.560137046203984; 18.282057191300733; 21.323265914583974; 25.105779337411779; 23.305664987061846; 19.243112642200309; 15.837518714974767; 14.571028978312411; 10.930566921047774; 8.043061483121409; 7.828278448844956; 7.971443209965454; 8.137571402681322; 7.947505847139930; 10.477597371114410; 17.994873577687876; 22.884932423902036; 22.880903074120706; 22.024300523218443; 21.996973699650383; 21.219211759187829; 20.636217357395591; 20.069520890245851; 20.077349735794858; 19.910967044646512; 20.005696385024002; 23.801346418078619; 28.585076924647108; 27.067028838815997; 22.796087957505328; 19.136718350436571; 17.957761530043999; 13.739457493789578; 10.310824888906227; 10.234357169105408; 10.627415478755154; 11.062492850356721; 11.016017242485642; 14.506641643689173; 24.884595907986515; 31.606278720197437; 31.557624279398006; 30.332367155586006; 30.248647555318538; 29.132457008298452; 28.284532096511711; 27.459546453686421; 27.419960762893837; 27.140870313592835; 27.215931128615544; 32.312946353894560; 38.724658154432746; 36.587267960523683; 30.743914731877290; 25.748050465465422; 24.103274970768545; 18.395418569792440; 13.769537490600122; 13.631459113517636; 14.116779371574737; 14.654058009734536; 14.551159058407341; 19.106427552870549; 32.677949691257076; 41.379150497789212; 41.187871023605659; 39.464033938070862; 39.228799119138912; 37.657741343154058; 36.440049352143852; 35.257483623102601; 35.085564440852409; 34.607106722839973; 34.579707730445875; 40.908025648164319; 48.846243022607112; 45.979419502968788; 38.491201346114494; 32.114034660484577; 29.947100964693604; 22.766547766228452]; 

Answer 1

有一些數據有助於找出問題。 您是否指的是發佈的Matlab函數here？

如果是的話，在發佈的例子中它似乎可以處理行向量。也許這可能是問題（？）我沒有訪問Matlab，但可能這可能會工作：

rsquareColumnTest = @（x，y）rsquare（（x（:)。'），（y（： ）。'））;

然後Rsqrd2 = rsquareColumnTest（DataSeries，ModelSeries）;

如果通過測試，當然可以直接傳遞數據的轉置，而無需定義匿名函數。

另外編輯後接收到該數據

感謝您提供的數據。

第一：R^2通常不是一個好主意，例如，您可能想看看at this site。

也就是說，如果您想比較一個線性模型與恆定模型的關係，則R^2是有意義的。常數模型是線性模型的一個子集，這就是爲什麼R^2永遠不會是負數（如果使用得當，永遠不應該是負數）。

如果你看一下definition定義R^2爲

Rsqrd1 = 1 - sumSqDiff(DataSeries, ModelSeries)/sumSqDiff(DataSeries, mean(ModelSeries)); 

，我已經定義

sumSqDiff = @(x,y) sum((x(:)-y(:)).^2); 

根據R的定義^ 2（我鼓勵你明白爲什麼），你應該使用：

Rsqrd1 = 1-sumSqDiff(DataSeries, ModelSeries)/sumSqDiff(DataSeries, mean(DataSeries); 

如果你這樣做，你有Rsqrd1 = -0.6791; ，這是沒有意義的，因爲R^2介於0和1之間，但這可能是因爲你的模型不是線性模型（不包含常數模型，作爲子集）。你在網絡上找到的rsquare功能考慮到這一在0糟糕的是，特別是它說

r2 = max(0,1 - sum((y(:)-f(:)).^2)/sum((y(:)-mean(y(:))).^2)); 

因爲R2是否定的，你有0的結果。考慮到您的模型中沒有固定術語，可以使用該功能，將其稱爲rsquare（DataSeries，ModelSeries，false）（如果您查看涉及此案例的文檔）。

再一次，我會鼓勵你不要使用R^2，尤其是在這種情況下，但我希望我澄清了爲什麼你有不同的結果。