Sabtu, 03 Juni 2017

Pertemuan 10 Halaman 154

Lakukan prediksi BB dengan variable independen TB, BTL, dan AK.
  1. Hitung SS for Regression (X3ІX1,X2);
  2. Hitung SS for Residual;
  3. Hitung Means SS for Regression (X3ІX1,X2);
  4. Hitung Means SS for Residual;
  5. Hitung nilai F parsial;
  6. Hitung nilai r2;
  7. Buktikan bahwa penambahan X3 berperan dalam memprediksi Y.
    BB
    TB
    BTL
    AK
    79.2
    149.0
    54.1
    2670
    64.0
    152.0
    44.3
    820
    67.0
    155.7
    47.8
    1210
    78.4
    159.0
    53.9
    2678
    66.0
    163.3
    47.5
    1205
    63.0
    166.0
    43.0
    815
    65.9
    169.0
    47.1
    1200
    63.1
    172.0
    44.0
    1180
    73.2
    174.5
    44.1
    1850
    66.5
    176.1
    48.3
    1260
    61.9
    176.5
    43.5
    1170
    72.5
    179.0
    43.3
    1852
    101.1
    182.0
    66.4
    1790
    66.2
    170.4
    47.5
    1250
    99.9
    184.9
    66.0
    1889
    63.0
    169.0
    44.0
    915
    BB    = Berat Badan
    TB    = Tinggi Badan
    BTL    = Berat Badan Tanpa Lemak
    AK    = Asupan Kalori
    Model 1. BB = β0 + β1 TB

    Variables Entered/Removedb
    Model
    Variables Entered
    Variables Removed
    Method
    1
    Tinggi Badana
    .
    Enter
    a. All requested variables entered.
    b. Dependent Variable: Berat Badan
    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .378a
    .143
    .081
    11.8405
    a. Predictors: (Constant), Tinggi Badan

    ANOVAb
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    326.204
    1
    326.204
    2.327
    .149a
    Residual
    1962.751
    14
    140.196
    Total
    2288.954
    15
    a. Predictors: (Constant), Tinggi Badan
    b. Dependent Variable: Berat Badan

    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    B
    Std. Error
    Beta
    1
    (Constant)
    -2.492
    48.880
    -.051
    .960
    Tinggi Badan
    .441
    .289
    .378
    1.525
    .149
    a. Dependent Variable: Berat Badan
    Estimasi model 1 BB = -2.492 + 0.441 TB

    Model 2. BB = β0 + β1 BTL
    Variables Entered/Removedb
    Model
    Variables Entered
    Variables Removed
    Method
    1
    Berat Badan Tanpa Lemaka
    .
    Enter
    a. All requested variables entered.
    b. Dependent Variable: Berat Badan

    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .945a
    .893
    .886
    4.1735
    a. Predictors: (Constant), Berat Badan Tanpa Lemak

    ANOVAb
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    2045.099
    1
    2045.099
    117.411
    .000a
    Residual
    243.855
    14
    17.418
    Total
    2288.954
    15
    a. Predictors: (Constant), Berat Badan Tanpa Lemak
    b. Dependent Variable: Berat Badan
    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    B
    Std. Error
    Beta
    1
    (Constant)
    -4.303
    7.112
    -.605
    .555
    Berat Badan Tanpa Lemak
    1.554
    .143
    .945
    10.836
    .000
    a. Dependent Variable: Berat Badan
    Estimasi model 2 BB = -4.303 + 1.554 BTL
    Model 3. BB = β0 + β1 AK
    Variables Entered/Removedb
    Model
    Variables Entered
    Variables Removed
    Method
    1
    Asupan Kaloria
    .
    Enter
    a. All requested variables entered.
    b. Dependent Variable: Berat Badan

    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .617a
    .381
    .337
    10.0593
    a. Predictors: (Constant), Asupan Kalori
    ANOVAb
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    872.301
    1
    872.301
    8.620
    .011a
    Residual
    1416.653
    14
    101.190
    Total
    2288.954
    15
    a. Predictors: (Constant), Asupan Kalori
    b. Dependent Variable: Berat Badan

    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    B
    Std. Error
    Beta
    1
    (Constant)
    52.517
    7.074
    7.423
    .000
    Asupan Kalori
    .013
    .004
    .617
    2.936
    .011
    a. Dependent Variable: Berat Badan
    Estimasi model 3 BB = 52.517 + 0.013 AK
    Model 4. BB = β0 + β1 TB + β2 BTL
    Variables Entered/Removedb
    Model
    Variables Entered
    Variables Removed
    Method
    1
    Berat Badan Tanpa Lemak, Tinggi Badana
    .
    Enter
    a. All requested variables entered.
    b. Dependent Variable: Berat Badan

    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .954a
    .910
    .896
    3.9870
    a. Predictors: (Constant), Berat Badan Tanpa Lemak, Tinggi Badan
    ANOVAb
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    2082.309
    2
    1041.154
    65.499
    .000a
    Residual
    206.645
    13
    15.896
    Total
    2288.954
    15
    a. Predictors: (Constant), Berat Badan Tanpa Lemak, Tinggi Badan
    b. Dependent Variable: Berat Badan
     
    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    B
    Std. Error
    Beta
    1
    (Constant)
    -27.527
    16.631
    -1.655
    .122
    Tinggi Badan
    .155
    .101
    .132
    1.530
    .150
    Berat Badan Tanpa Lemak
    1.496
    .142
    .910
    10.511
    .000
    a. Dependent Variable: Berat Badan
    Estimasi model 4 BB = -27.527 + 0.155 TB + 1.496 BTL
    Model 5. BB = β0 + β1 TB + β3 AK
    Variables Entered/Removedb
    Model
    Variables Entered
    Variables Removed
    Method
    1
    Asupan Kalori, Tinggi Badana
    .
    Enter
    a. All requested variables entered.
    b. Dependent Variable: Berat Badan
    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .747a
    .557
    .489
    8.8280
    a. Predictors: (Constant), Asupan Kalori, Tinggi Badan
    ANOVAb
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    1275.821
    2
    637.911
    8.185
    .005a
    Residual
    1013.133
    13
    77.933
    Total
    2288.954
    15
    a. Predictors: (Constant), Asupan Kalori, Tinggi Badan
    b. Dependent Variable: Berat Badan
    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    B
    Std. Error
    Beta
    1
    (Constant)
    -31.333
    37.369
    -.838
    .417
    Tinggi Badan
    .492
    .216
    .421
    2.275
    .040
    Asupan Kalori
    .014
    .004
    .646
    3.491
    .004
    a. Dependent Variable: Berat Badan
     
    Estimasi model 5 BB = -31.333 + 0.492 TB + 0.014 AK
    Model 6. BB = β0 + β1 TB + β2 BTL + β3 AK
    Variables Entered/Removedb
    Model
    Variables Entered
    Variables Removed
    Method
    1
    Asupan Kalori, Tinggi Badan, Berat Badan Tanpa Lemaka
    .
    Enter
    a. All requested variables entered.
    b. Dependent Variable: Berat Badan
     
    Model Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .969a
    .939
    .923
    3.4224
    a. Predictors: (Constant), Asupan Kalori, Tinggi Badan, Berat Badan Tanpa Lemak
    ANOVAb
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    2148.400
    3
    716.133
    61.141
    .000a
    Residual
    140.554
    12
    11.713
    Total
    2288.954
    15
    a. Predictors: (Constant), Asupan Kalori, Tinggi Badan, Berat Badan Tanpa Lemak
    b. Dependent Variable: Berat Badan
     
    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    B
    Std. Error
    Beta
    1
    (Constant)
    -33.412
    14.489
    -2.306
    .040
    Tinggi Badan
    .210
    .090
    .180
    2.339
    .037
    Berat Badan Tanpa Lemak
    1.291
    .150
    .785
    8.631
    .000
    Asupan Kalori
    .004
    .002
    .209
    2.375
    .035
    a. Dependent Variable: Berat Badan
     
     
    Estimasi model 6 BB = -33.412 + 0.210 TB + 1.291 BTL + 0.004 AK
    Kita lakukan uji parsial F seperti berikut (berdasarkan hasil-hasil yang sudah kita lakukan di atas).
    ANOVA Tabel untuk BB dengan TB, BTL, dan AK.
    Sumber
    Df
    SS
    MS
    F
    r2
    X1
    Regresi X2ІX1
    X3ІX1 X2
    1
    1
    1
    326.204
    2082.309- 326.204 = 1756.105
    2148.400 - 2082.309 = 66.091
    326.204
    1756.105
    66.091
    326.204/11.713 = 27.85
    1756.105/15.896= 110.475
    66.091/11.713 = 5.643
    0.000
    Residual
    12
    140.554
    11.713
    Total
    15
    2288.954
    *p<0.05
      
     
    Berikut ringkasan table analisis yang dapat membantu kita dalam pemilihan model estimasi yang terbaik.
    No.
    Model Estimasi
    F
    r2
    1.
    Y = -2.49 + 0.44 TB
    2.33
    0.15
    2.
    Y = -4.30 + 1.55 BTL
    117.41
    0.00
    3.
    Y = 52.52 + 0.01 AK
    8.62
    0.01
    4.
    Y = -27.53 + 0.16 TB + 1.50 BTL
    65.50
    0.00
    5.
    Y = -31.33 + 0.49 TB + 0.01 AK
    8.19
    0.00
    6.
    Y = -33.41 + 0.21 TB + 1.29 BTL + 0.00 AK
    61.14
    0.00
    Angka dalam tanda kurung adalah Standar Error dari parameter
    *bermakna (p<0.05)
     
    Dari ke enam model estimasi terlihat bahwa variable Tinggi Badan secara konsisten sangat berpengaruh terhadap Berat Badan (p<0.05). Pada model estimasi 1 tampak nilai r2 sebesar 0.149 dan bila disbanding dengan model esimasi 4,5, dan 6 penambahan nilai r2 relatif kecil masing-masing 0.000, 0.005, dan 0.000 atau hanya bertambah sekitar -0.149, -0.144, dan -0.149, ini sangat tidak berarti.
    Dengan demikian kita bias berkesimpulan variable Tinggi Badan sangat bermakna pengaruhnya terhadap Berat Badan. Sebaliknya penambahan variable UM dan UMSQ tidak berperan dalam menjelaskan variasi Berat Badan dan kita tidak perlu menambahkan kedua variable tersebut ke dalam model. Model akhir yaitu : Y =  -2.49 + 0.44 TB
     
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