如何定义线性回归的目标变量

Question

我想对一个96x100维度的数据集进行回归分析。这些列表示天数（100），而自变量是时间。如何执行线性回归，因为我的目标变量是多列的。示例数据集如下：

time    day1    day2    day3    day4    day5    day6    day7    day8    day9    day10   day11   day12   day13   day14   day15   day16   day17   day18   day19   day20   day21   day22   day23   day24   day25   day26   day27   day28   day29   day30   day31   day32   day33   day34   day35   day36   day37   day38   day39   day40   day41   day42   day43   day44   day45   day46   day47   day48   day49   day50   day51   day52   day53   day54   day55   day56   day57   day58   day59   day60   day61   day62   day63   day64   day65   day66   day57   day68   day69   day70   day71   day72   day73   day74   day75   day76   day77   day78   day79   day80   day81   day82   day83   day84   day85   day86   day87   day88   day89   day90   day91   day92   day93   day94   day95   day96   day97   day98   day99   day100
500 6.07588E-10 6.13664E-10 5.89361E-10 5.95437E-10 6.31892E-10 6.37968E-10 5.83285E-10 6.01512E-10 5.83285E-10 6.1974E-10  3.03794E-09 -6.07588E-10    -2.43035E-09    1.21518E-09 2.43035E-09 6.07588E-10 6.07588E-10 -1.21518E-09    -1.21518E-09    0   3.03794E-09 1.82276E-09 -1.82276E-09    1.82276E-09 -2.43035E-09    -1.21518E-09    -1.21518E-09    -1.82276E-09    -1.21518E-09    2.43035E-09 1.82276E-09 -2.43035E-09    1.21518E-09 -6.07588E-10    -1.21518E-09    0   -1.21518E-09    1.21518E-09 -2.43035E-09    -2.43035E-09    3.03794E-09 -1.82276E-09    6.07588E-10 -1.82276E-09    3.03794E-09 -2.43035E-09    1.82276E-09 -1.82276E-09    0   0   1.82276E-09 -3.03794E-09    0   3.03794E-09 -1.21518E-09    -1.21518E-09    0   3.03794E-09 1.21518E-09 6.07588E-10 -3.03794E-09    1.21518E-09 3.03794E-09 0   6.07588E-10 -6.07588E-10    -6.07588E-10    1.82276E-09 -3.03794E-09    -1.21518E-09    1.21518E-09 1.82276E-09 1.82276E-09 2.43035E-09 3.03794E-09 1.21518E-09 1.21518E-09 -2.43035E-09    3.03794E-09 0   -1.21518E-09    -1.82276E-09    -1.82276E-09    1.82276E-09 -3.03794E-09    1.82276E-09 0   2.43035E-09 3.03794E-09 -2.43035E-09    -1.21518E-09    6.07588E-10 -1.21518E-09    6.07588E-10 3.03794E-09 0   -2.43035E-09    -1.21518E-09    -1.82276E-09    0
515 6.07588E-10 5.89361E-10 6.07588E-10 6.01512E-10 6.25816E-10 6.07588E-10 6.1974E-10  6.37968E-10 5.77209E-10 5.95437E-10 1.82276E-09 -3.03794E-09    0   2.43035E-09 1.21518E-09 -3.03794E-09    -3.03794E-09    -1.82276E-09    2.43035E-09 0   1.82276E-09 3.03794E-09 2.43035E-09 6.07588E-10 1.21518E-09 -2.43035E-09    -6.07588E-10    -1.82276E-09    -1.21518E-09    -2.43035E-09    1.82276E-09 -1.21518E-09    6.07588E-10 6.07588E-10 0   6.07588E-10 3.03794E-09 -3.03794E-09    -1.21518E-09    -1.82276E-09    0   -3.03794E-09    1.21518E-09 -2.43035E-09    -2.43035E-09    -2.43035E-09    1.82276E-09 -1.82276E-09    6.07588E-10 -3.03794E-09    -6.07588E-10    -1.21518E-09    3.03794E-09 -1.82276E-09    -6.07588E-10    -1.21518E-09    1.82276E-09 3.03794E-09 -1.21518E-09    -6.07588E-10    -1.82276E-09    -2.43035E-09    -1.21518E-09    1.82276E-09 3.03794E-09 1.21518E-09 6.07588E-10 -1.82276E-09    2.43035E-09 -3.03794E-09    0   -2.43035E-09    -1.82276E-09    -3.03794E-09    3.03794E-09 3.03794E-09 3.03794E-09 -6.07588E-10    -6.07588E-10    -6.07588E-10    -2.43035E-09    -2.43035E-09    -1.82276E-09    -3.03794E-09    -1.21518E-09    -6.07588E-10    6.07588E-10 -3.03794E-09    -1.82276E-09    6.07588E-10 2.43035E-09 1.82276E-09 1.21518E-09 0   0   1.21518E-09 3.03794E-09 2.43035E-09 6.07588E-10 3.03794E-09
530 6.07588E-10 6.01512E-10 6.1974E-10  6.13664E-10 5.95437E-10 6.31892E-10 6.01512E-10 5.77209E-10 6.13664E-10 6.25816E-10 1.82276E-09 2.43035E-09 1.82276E-09 -1.21518E-09    1.82276E-09 2.43035E-09 3.03794E-09 3.03794E-09 2.43035E-09 6.07588E-10 6.07588E-10 -6.07588E-10    2.43035E-09 0   1.82276E-09 6.07588E-10 0   3.03794E-09 -1.82276E-09    3.03794E-09 0   1.82276E-09 1.21518E-09 -2.43035E-09    -2.43035E-09    -3.03794E-09    1.21518E-09 -6.07588E-10    -1.82276E-09    2.43035E-09 3.03794E-09 -1.21518E-09    -6.07588E-10    6.07588E-10 2.43035E-09 0   -6.07588E-10    3.03794E-09 3.03794E-09 -1.82276E-09    3.03794E-09 1.82276E-09 6.07588E-10 0   -2.43035E-09    -3.03794E-09    -6.07588E-10    -2.43035E-09    -3.03794E-09    -1.21518E-09    1.82276E-09 6.07588E-10 3.03794E-09 6.07588E-10 0   3.03794E-09 2.43035E-09 0   -3.03794E-09    -3.03794E-09    1.21518E-09 -1.82276E-09    -3.03794E-09    0   -6.07588E-10    3.03794E-09 6.07588E-10 -2.43035E-09    -1.21518E-09    -2.43035E-09    -3.03794E-09    0   1.21518E-09 3.03794E-09 2.43035E-09 -1.82276E-09    -6.07588E-10    1.82276E-09 -2.43035E-09    1.21518E-09 1.21518E-09 -6.07588E-10    1.21518E-09 -3.03794E-09    -6.07588E-10    -2.43035E-09    -1.82276E-09    3.03794E-09 -2.43035E-09    3.03794E-09
545 6.07588E-10 6.25816E-10 6.07588E-10 6.13664E-10 6.07588E-10 6.01512E-10 5.95437E-10 6.07588E-10 5.95437E-10 6.01512E-10 3.03794E-09 1.21518E-09 -1.82276E-09    -3.03794E-09    3.03794E-09 1.82276E-09 1.21518E-09 6.07588E-10 6.07588E-10 -1.82276E-09    -1.21518E-09    3.03794E-09 1.82276E-09 2.43035E-09 1.21518E-09 2.43035E-09 -1.82276E-09    2.43035E-09 -3.03794E-09    1.82276E-09 -2.43035E-09    -6.07588E-10    3.03794E-09 2.43035E-09 1.21518E-09 3.03794E-09 -3.03794E-09    0   -1.82276E-09    2.43035E-09 -1.21518E-09    6.07588E-10 1.82276E-09 1.21518E-09 1.21518E-09 -6.07588E-10    -1.21518E-09    -6.07588E-10    3.03794E-09 1.21518E-09 2.43035E-09 -1.21518E-09    0   1.82276E-09 -1.82276E-09    1.21518E-09 1.21518E-09 3.03794E-09 -6.07588E-10    -1.21518E-09    6.07588E-10 -6.07588E-10    6.07588E-10 1.82276E-09 -6.07588E-10    3.03794E-09 -1.82276E-09    1.21518E-09 -6.07588E-10    1.21518E-09 1.82276E-09 -2.43035E-09    -2.43035E-09    -6.07588E-10    -6.07588E-10    6.07588E-10 6.07588E-10 3.03794E-09 -6.07588E-10    1.21518E-09 -6.07588E-10    2.43035E-09 -2.43035E-09    -2.43035E-09    -2.43035E-09    -1.82276E-09    0   -1.82276E-09    -3.03794E-09    1.21518E-09 3.03794E-09 1.21518E-09 3.03794E-09 -1.21518E-09    -3.03794E-09    -6.07588E-10    -1.21518E-09    1.21518E-09 -2.43035E-09    -6.07588E-10
600 6.07588E-10 6.13664E-10 6.07588E-10 6.01512E-10 6.13664E-10 6.01512E-10 6.1974E-10  6.1974E-10  5.77209E-10 5.89361E-10 1.21518E-09 -1.82276E-09    -2.43035E-09    1.82276E-09 3.03794E-09 -6.07588E-10    2.43035E-09 1.82276E-09 -6.07588E-10    -3.03794E-09    3.03794E-09 -3.03794E-09    -3.03794E-09    -1.21518E-09    -6.07588E-10    -1.82276E-09    1.82276E-09 3.03794E-09 -2.43035E-09    -2.43035E-09    -1.21518E-09    -3.03794E-09    -1.21518E-09    -3.03794E-09    -1.21518E-09    -3.03794E-09    -6.07588E-10    6.07588E-10 2.43035E-09 -6.07588E-10    -3.03794E-09    1.82276E-09 0   3.03794E-09 -1.21518E-09    3.03794E-09 -2.43035E-09    -1.82276E-09    -1.21518E-09    -1.82276E-09    -6.07588E-10    -1.21518E-09    1.82276E-09 0   0   -1.82276E-09    -1.21518E-09    -3.03794E-09    2.43035E-09 6.07588E-10 1.21518E-09 1.82276E-09 2.43035E-09 1.82276E-09 -1.82276E-09    1.82276E-09 0   3.03794E-09 1.82276E-09 1.82276E-09 1.82276E-09 -6.07588E-10    -1.82276E-09    -1.82276E-09    -6.07588E-10    -1.21518E-09    -1.82276E-09    3.03794E-09 -6.07588E-10    3.03794E-09 1.21518E-09 -1.82276E-09    -6.07588E-10    6.07588E-10 0   2.43035E-09 -2.43035E-09    -6.07588E-10    -3.03794E-09    2.43035E-09 -1.21518E-09    -1.82276E-09    1.21518E-09 3.03794E-09 1.82276E-09 3.03794E-09 3.03794E-09 6.07588E-10 1.21518E-09 -1.82276E-09
615 6.07588E-10 6.13664E-10 6.1974E-10  5.77209E-10 6.37968E-10 6.1974E-10  6.13664E-10 6.37968E-10 6.31892E-10 6.1974E-10  3.03794E-09 -6.07588E-10    6.07588E-10 0   1.82276E-09 -3.03794E-09    1.82276E-09 3.03794E-09 -3.03794E-09    6.07588E-10 2.43035E-09 3.03794E-09 -2.43035E-09    1.82276E-09 1.82276E-09 -1.21518E-09    -3.03794E-09    2.43035E-09 -2.43035E-09    -3.03794E-09    0   -2.43035E-09    -3.03794E-09    -6.07588E-10    -6.07588E-10    -2.43035E-09    3.03794E-09 3.03794E-09 -1.82276E-09    -1.21518E-09    6.07588E-10 -1.21518E-09    0   -1.82276E-09    0   6.07588E-10 3.03794E-09 -6.07588E-10    1.82276E-09 2.43035E-09 3.03794E-09 1.82276E-09 1.82276E-09 2.43035E-09 -3.03794E-09    -1.21518E-09    -1.21518E-09    1.82276E-09 6.07588E-10 6.07588E-10 -6.07588E-10    -3.03794E-09    1.82276E-09 3.03794E-09 -3.03794E-09    3.03794E-09 1.21518E-09 1.82276E-09 -1.82276E-09    -1.21518E-09    2.43035E-09 1.82276E-09 1.21518E-09 1.21518E-09 -1.82276E-09    1.82276E-09 1.82276E-09 3.03794E-09 -6.07588E-10    -1.82276E-09    1.21518E-09 1.21518E-09 -1.21518E-09    -2.43035E-09    -1.21518E-09    1.82276E-09 -6.07588E-10    0   2.43035E-09 -1.21518E-09    1.21518E-09 6.07588E-10 -1.21518E-09    1.82276E-09 1.82276E-09 1.21518E-09 6.07588E-10 -6.07588E-10    1.21518E-09 2.43035E-09
630 6.45127E-10 6.19322E-10 6.45127E-10 6.12871E-10 6.77384E-10 6.5803E-10  6.51578E-10 6.32225E-10 6.70932E-10 6.70932E-10 2.58051E-09 2.58051E-09 -1.29025E-09    -1.29025E-09    -3.22564E-09    1.93538E-09 3.22564E-09 -3.22564E-09    1.93538E-09 2.58051E-09 6.45127E-10 3.22564E-09 -1.29025E-09    0   3.22564E-09 6.45127E-10 -6.45127E-10    -6.45127E-10    -2.58051E-09    -1.93538E-09    -3.22564E-09    2.58051E-09 1.29025E-09 2.58051E-09 1.29025E-09 1.29025E-09 2.58051E-09 -1.29025E-09    -3.22564E-09    -3.22564E-09    1.93538E-09 -1.93538E-09    -3.22564E-09    -6.45127E-10    6.45127E-10 -1.29025E-09    -1.93538E-09    -6.45127E-10    6.45127E-10 -6.45127E-10    -3.22564E-09    1.29025E-09 2.58051E-09 -3.22564E-09    3.22564E-09 -1.93538E-09    -2.58051E-09    -2.58051E-09    -2.58051E-09    3.22564E-09 6.45127E-10 0   -3.22564E-09    3.22564E-09 -2.58051E-09    1.93538E-09 -1.93538E-09    6.45127E-10 6.45127E-10 3.22564E-09 -1.29025E-09    1.93538E-09 1.93538E-09 2.58051E-09 -3.22564E-09    0   -3.22564E-09    -2.58051E-09    1.93538E-09 1.93538E-09 -2.58051E-09    1.93538E-09 1.29025E-09 3.22564E-09 1.93538E-09 -1.93538E-09    3.22564E-09 -3.22564E-09    1.29025E-09 -1.29025E-09    3.22564E-09 -1.93538E-09    -3.22564E-09    -6.45127E-10    3.22564E-09 -3.22564E-09    -1.29025E-09    -2.58051E-09    -3.22564E-09    6.45127E-10

plt.scatter(reg.predict(X), reg.predict(X) - y, 
            color = "green", s = 10, label = 'Train data') 

Answer 1

您可以将时间作为因变量（标签）和不同日期的值，作为模型的特征（自变量）。你可以很容易地学会进行多水平回归：

from sklearn.linear_model import LinearRegression
X=np.array(df.drop("time",1))
y=np.array(df["time"])
clf=LinearRegression()
clf.fit(X,y)