請讀入「MS.csv」資料。將Y當成反應變數，X1, X2, X3, X4, X5為解釋變數。

    MS <- read.csv('MS.csv')
    head(MS)
##         Time       Y      Y1      X1       X2       X3       X4     X5     X6
## 1 1999/12/31 2477386 2466906 3694036 0.072009 0.072976 0.000157 0.0786 290351
## 2  2000/1/31 2493525 2477386 3733085 0.033724 0.072252 0.000155 0.0786 293420
## 3  2000/2/29 2511507 2493525 3805669 0.066437 0.071374 0.000569 0.0773 294178
## 4  2000/3/31 2502434 2511507 3781284 0.065821 0.072481 0.000538 0.0773 292293
## 5  2000/4/30 2494887 2502434 3792181 0.068475 0.070920 0.000648 0.0773 293136
## 6  2000/5/31 2510839 2494887 3799946 0.074182 0.071335 0.000608 0.0764 290316
##         X7       X8      X9 X10 liquidity equity revenue
## 1 0.005660 0.005736 1.2e-05   1    266005 269575     579
## 2 0.002651 0.005679 1.2e-05   2    125896 269722     579
## 3 0.005136 0.005517 4.4e-05   3    252839 271626    2165
## 4 0.005088 0.005603 4.2e-05   4    248889 274070    2035
## 5 0.005293 0.005482 5.0e-05   5    259670 268940    2456
## 6 0.005667 0.005450 4.6e-05   6    281887 271070    2312
    1. 以「向後消去法」，AIC為篩選準則，選擇出最佳模型M1。寫出所配適之最佳預測模型。
    none=lm(Y~1,data=MS)
full=lm(Y~X1+X2+X3+X4+X5,data = MS)
step(full,
     scope=list(upper=full,lower=none),direction = 'backward')
    ## Start:  AIC=1652.91
## Y ~ X1 + X2 + X3 + X4 + X5
## 
##        Df  Sum of Sq        RSS    AIC
## - X4    1 4.1476e+09 4.2630e+11 1651.6
## <none>               4.2216e+11 1652.9
## - X3    1 2.3181e+10 4.4534e+11 1654.8
## - X5    1 1.0263e+11 5.2478e+11 1666.8
## - X2    1 2.4003e+11 6.6218e+11 1683.8
## - X1    1 2.6017e+11 6.8232e+11 1686.0
## 
## Step:  AIC=1651.62
## Y ~ X1 + X2 + X3 + X5
## 
##        Df  Sum of Sq        RSS    AIC
## <none>               4.2630e+11 1651.6
## - X3    1 2.3863e+10 4.5017e+11 1653.6
## - X5    1 1.0533e+11 5.3163e+11 1665.7
## - X2    1 2.5753e+11 6.8383e+11 1684.1
## - X1    1 2.6535e+11 6.9166e+11 1685.0
    ## 
## Call:
## lm(formula = Y ~ X1 + X2 + X3 + X5, data = MS)
## 
## Coefficients:
## (Intercept)           X1           X2           X3           X5  
##  -1.254e+06    7.222e-01   -2.037e+06    7.654e+06    8.007e+06
  1. 個別迴歸係數的意義為何？
  2. 檢定M1的整體模式是否顯著？
  3. 模型M1的解釋能力為何？
  4. 模型M1的相關係數為何？
    1. 以「向前選取法」，BIC為篩選準則，選擇出最佳模型M2。寫出所配適之最佳預測模型。
    none=lm(Y~1,data = MS)
full=lm(Y~X1+X2+X3+X4+X5,data = MS)
step(none,
     scope=list(upper=full,lower=none),direction = 'forward')
    ## Start:  AIC=1736.99
## Y ~ 1
## 
##        Df  Sum of Sq        RSS    AIC
## + X2    1 8.0223e+11 7.2952e+11 1684.8
## + X1    1 2.3004e+11 1.3017e+12 1727.1
## + X4    1 8.6172e+10 1.4456e+12 1734.8
## <none>               1.5318e+12 1737.0
## + X3    1 3.2355e+10 1.4994e+12 1737.4
## + X5    1 2.1392e+10 1.5104e+12 1738.0
## 
## Step:  AIC=1684.84
## Y ~ X2
## 
##        Df  Sum of Sq        RSS    AIC
## + X3    1 3.7368e+10 6.9215e+11 1683.0
## + X5    1 3.5202e+10 6.9432e+11 1683.2
## <none>               7.2952e+11 1684.8
## + X4    1 1.4101e+10 7.1542e+11 1685.4
## + X1    1 1.8884e+08 7.2933e+11 1686.8
## 
## Step:  AIC=1683
## Y ~ X2 + X3
## 
##        Df  Sum of Sq        RSS    AIC
## + X1    1 1.6052e+11 5.3163e+11 1665.7
## <none>               6.9215e+11 1683.0
## + X4    1 9.4304e+09 6.8272e+11 1684.0
## + X5    1 4.9720e+08 6.9166e+11 1685.0
## 
## Step:  AIC=1665.74
## Y ~ X2 + X3 + X1
## 
##        Df  Sum of Sq        RSS    AIC
## + X5    1 1.0533e+11 4.2630e+11 1651.6
## <none>               5.3163e+11 1665.7
## + X4    1 6.8475e+09 5.2478e+11 1666.8
## 
## Step:  AIC=1651.62
## Y ~ X2 + X3 + X1 + X5
## 
##        Df  Sum of Sq        RSS    AIC
## <none>               4.2630e+11 1651.6
## + X4    1 4147621971 4.2216e+11 1652.9
    ## 
## Call:
## lm(formula = Y ~ X2 + X3 + X1 + X5, data = MS)
## 
## Coefficients:
## (Intercept)           X2           X3           X1           X5  
##  -1.254e+06   -2.037e+06    7.654e+06    7.222e-01    8.007e+06
  1. 檢定M2的整體模式是否顯著？
  2. 模型M2的解釋能力為何？
    1. 以「逐步迴歸選取法」，AIC為篩選準則，選擇出最佳模型M3。寫出所配適之最佳預測模型。
    none=lm(Y~1,data = MS)
full=lm(Y~X1+X2+X3+X4+X5,data = MS)
step(none,
     scope=list(upper=full,lower=none),direction = 'both')
    ## Start:  AIC=1736.99
## Y ~ 1
## 
##        Df  Sum of Sq        RSS    AIC
## + X2    1 8.0223e+11 7.2952e+11 1684.8
## + X1    1 2.3004e+11 1.3017e+12 1727.1
## + X4    1 8.6172e+10 1.4456e+12 1734.8
## <none>               1.5318e+12 1737.0
## + X3    1 3.2355e+10 1.4994e+12 1737.4
## + X5    1 2.1392e+10 1.5104e+12 1738.0
## 
## Step:  AIC=1684.84
## Y ~ X2
## 
##        Df  Sum of Sq        RSS    AIC
## + X3    1 3.7368e+10 6.9215e+11 1683.0
## + X5    1 3.5202e+10 6.9432e+11 1683.2
## <none>               7.2952e+11 1684.8
## + X4    1 1.4101e+10 7.1542e+11 1685.4
## + X1    1 1.8884e+08 7.2933e+11 1686.8
## - X2    1 8.0223e+11 1.5318e+12 1737.0
## 
## Step:  AIC=1683
## Y ~ X2 + X3
## 
##        Df  Sum of Sq        RSS    AIC
## + X1    1 1.6052e+11 5.3163e+11 1665.7
## <none>               6.9215e+11 1683.0
## + X4    1 9.4304e+09 6.8272e+11 1684.0
## - X3    1 3.7368e+10 7.2952e+11 1684.8
## + X5    1 4.9720e+08 6.9166e+11 1685.0
## - X2    1 8.0724e+11 1.4994e+12 1737.4
## 
## Step:  AIC=1665.74
## Y ~ X2 + X3 + X1
## 
##        Df  Sum of Sq        RSS    AIC
## + X5    1 1.0533e+11 4.2630e+11 1651.6
## <none>               5.3163e+11 1665.7
## + X4    1 6.8475e+09 5.2478e+11 1666.8
## - X1    1 1.6052e+11 6.9215e+11 1683.0
## - X3    1 1.9770e+11 7.2933e+11 1686.8
## - X2    1 4.2847e+11 9.6010e+11 1706.9
## 
## Step:  AIC=1651.62
## Y ~ X2 + X3 + X1 + X5
## 
##        Df  Sum of Sq        RSS    AIC
## <none>               4.2630e+11 1651.6
## + X4    1 4.1476e+09 4.2216e+11 1652.9
## - X3    1 2.3863e+10 4.5017e+11 1653.6
## - X5    1 1.0533e+11 5.3163e+11 1665.7
## - X2    1 2.5753e+11 6.8383e+11 1684.1
## - X1    1 2.6535e+11 6.9166e+11 1685.0
    ## 
## Call:
## lm(formula = Y ~ X2 + X3 + X1 + X5, data = MS)
## 
## Coefficients:
## (Intercept)           X2           X3           X1           X5  
##  -1.254e+06   -2.037e+06    7.654e+06    7.222e-01    8.007e+06
  1. 檢定M3的整體模式是否顯著？
    1. 以「所有迴歸模型比較選取法」並以\(R_a^2\)為篩選準則，選擇出最佳模型M4。寫出所配適之最佳預測模型。
    source('criteria.best.R')
library(knitr)
bestsubset(as.matrix(MS[,4:8]),MS$Y)
    ## $model
## $model$R2
## [1] 32
## 
## $model$R2a
## [1] 24
## 
## $model$Cp
## [1] 24
## 
## $model$AIC
## [1] 24
## 
## $model$BIC
## [1] 20
## 
## 
## $stat
##       p X1 X2 X3 X4 X5 SSE          R2           R2a          Cp       AIC     
##  [1,] 1 0  0  0  0  0  1.531751e+12 3.330669e-16 4.440892e-16 172.1026 1736.989
##  [2,] 2 1  0  0  0  0  1.30171e+12  0.1501821    0.1382128    137.593  1727.11 
##  [3,] 2 0  1  0  0  0  729521590534 0.5237337    0.5170257    46.7816  1684.839
##  [4,] 3 1  1  0  0  0  729332746107 0.523857     0.5102529    48.75163 1686.82 
##  [5,] 2 0  0  1  0  0  1.499396e+12 0.02112287   0.007335867  168.9676 1737.431
##  [6,] 3 1  0  1  0  0  9.601e+11    0.3732011    0.3552926    85.37646 1706.889
##  [7,] 3 0  1  1  0  0  692153316384 0.5481295    0.5352189    42.85092 1683.001
##  [8,] 4 1  1  1  0  0  531631647071 0.6529256    0.6378354    19.3747  1665.739
##  [9,] 2 0  0  0  1  0  1.44558e+12  0.05625693   0.04296477   160.4264 1734.762
## [10,] 3 1  0  0  1  0  1.224151e+12 0.2008163    0.1779825    127.2837 1724.625
## [11,] 3 0  1  0  1  0  715420706028 0.5329394    0.5195948    46.54366 1685.414
## [12,] 4 1  1  0  1  0  714844305236 0.5333157    0.5130251    48.45218 1687.356
## [13,] 3 0  0  1  1  0  1.410535e+12 0.07913551   0.0528251    156.8646 1734.971
## [14,] 4 1  0  1  1  0  916863893384 0.4014277    0.3754028    80.5145  1705.525
## [15,] 4 0  1  1  1  0  682722898480 0.5542861    0.5349072    43.35423 1683.999
## [16,] 5 1  1  1  1  0  524784178354 0.657396     0.6372428    20.28794 1666.793
## [17,] 2 0  0  0  0  1  1.51036e+12  0.01396546   7.765025e-05 170.7076 1737.962
## [18,] 3 1  0  0  0  1  699473781829 0.5433503    0.5303032    44.01274 1683.769
## [19,] 3 0  1  0  0  1  694319912330 0.546715     0.533764     43.19478 1683.229
## [20,] 4 1  1  0  0  1  4.50167e+11  0.7061096    0.6933318    6.445521 1653.597
## [21,] 3 0  0  1  0  1  1.495332e+12 0.02377602   -0.004116094 170.3226 1739.232
## [22,] 4 1  0  1  0  1  683834841352 0.5535602    0.5341497    43.5307  1684.118
## [23,] 4 0  1  1  0  1  691656112559 0.5484541    0.5288216    44.77201 1684.948
## [24,] 5 1  1  1  0  1  426304054504 0.7216885    0.7053172    4.658265 1651.621
## [25,] 3 0  0  0  1  1  1.421038e+12 0.07227866   0.04577233   158.5315 1735.512
## [26,] 4 1  0  0  1  1  676972905195 0.55804      0.5388243    42.44165 1683.382
## [27,] 4 0  1  0  1  1  684783054037 0.5529411    0.5335038    43.68119 1684.219
## [28,] 5 1  1  0  1  1  445337353183 0.7092626    0.6921604    7.679019 1654.81 
## [29,] 4 0  0  1  1  1  1.407659e+12 0.08101343   0.04105749   158.4081 1736.822
## [30,] 5 1  0  1  1  1  662183464630 0.5676952    0.5422655    42.09444 1683.769
## [31,] 5 0  1  1  1  1  682324896084 0.5545459    0.5283427    45.29106 1685.957
## [32,] 6 1  1  1  1  1  422156432533 0.7243962    0.7038288    6        1652.907
##       BIC     
##  [1,] 1739.28 
##  [2,] 1731.69 
##  [3,] 1689.42 
##  [4,] 1693.692
##  [5,] 1742.011
##  [6,] 1713.76 
##  [7,] 1689.872
##  [8,] 1674.901
##  [9,] 1739.343
## [10,] 1731.496
## [11,] 1692.286
## [12,] 1696.517
## [13,] 1741.842
## [14,] 1714.687
## [15,] 1693.161
## [16,] 1678.245
## [17,] 1742.543
## [18,] 1690.64 
## [19,] 1690.1  
## [20,] 1662.759
## [21,] 1746.104
## [22,] 1693.28 
## [23,] 1694.11 
## [24,] 1663.073
## [25,] 1742.384
## [26,] 1692.544
## [27,] 1693.381
## [28,] 1666.262
## [29,] 1745.984
## [30,] 1695.222
## [31,] 1697.409
## [32,] 1666.65
  1. 檢定M4的整體模式是否顯著？