Uji Linieritas

Tujuan:                        Uji linieritas dilakukan dengan mencari persamaan garis regresi variabel bebas x terhadap variabel terikat y. Berdasarkan garis regresi yang dibuat, diuji keberartian koefisien garis regresi serta linieritasnya.

Prosedur Uji Linieritas pada SPSS:

Buat File data terlebih dahulu:

  1. Masuk Variable View à set variable lengkap dengan 9 atribut
  2. Masuk Data View à masukkan data (atau copy dari excel) à save (Ctrl+S)
  3. 3.      Pilih menu-1:    Analyze à Compare Mean à Means

Pilih menu-2:     Analyze à Regression à Curve Estimation

  1. Tafsirkan hasil (output)

 

Contoh:       Akan diuji hubungan linieritas antara variabel bebas insentif (X1), iklim kerja (X2), dan hubungan interpersonal (X3) dengan variabel terikat kinerja (Y). Untuk itu diambil data penelitian sebagai berikut.

 

X1

X2

X3

Y

34

47

44

62

41

43

42

66

43

42

43

66

37

38

39

68

38

30

39

60

36

35

39

64

44

48

44

67

38

45

38

58

41

49

44

63

48

43

44

67

35

49

38

58

48

42

32

65

40

38

39

68

42

32

48

65

37

37

41

70

39

48

41

60

38

31

40

58

35

44

39

55

46

46

49

71

37

36

40

57

45

44

35

74

40

35

42

66

36

37

39

68

43

40

43

70

45

44

47

69

38

32

44

58

39

39

42

61

41

40

45

69

46

45

49

71

42

45

48

66

 

Untuk contoh ini kita pakai 2 variabel dahulu sebagai contoh (yakni X1 dan Y), walau sama mudahnya dengan cara sekaligus (X1,X2,X3,Y).

 

Langkah-1       Gunakan 2 variabel à X1= Insentif ; Y = Kinerja

  • ·         Masuk variable view à atur kedua variable dan 9 atribut à didapat sbb:

 

 

 

  • ·         Masuk jendela data view à masukan data (copy dari excel) à terlihat sbb:

 

     à saving data ini

 

Langkah-2       Klik menu:       Analyze à Compare Mean à Means

  • Masukkan X1 ke kotak variabel independent
  • Masukkan Y ke kotak variabel dependent
  • Pilih Option à tandai Test of Linierity à Continue à OK à terlihat sbb:

 

 

 

 

 

Didapat beberapa out-put, tetapi kita pilih 1 saja yang diperlukan dalam uji linieritas, yakni table Anova (Anova Table), sbb:

 

 

 

Langkah-3       Interpretasi hasil output

 

Hipotesis Linieritas:

H0 : Model regresi linier

H1 : Model regresi tidak linier (Non-Linier)

 

Kriteria Pengujian:

 

 

 

 

 

 

Singkatnya:

 

  • Dengan Linierity:               Sig <  a (o,o5)             à Hubungan linier signifikan
  • Dengan Deviation from linierity:   Sig > a (o,o5) à Hubungan linier signifikan

 

Dari  table Anova didapat :

  1. Pada  baris  Linierity:

Sig (0,000) < a (0,05) à Hubungan linier  signifikan

 

  1. Pada baris  Deviation  from linierity:

Sig. (0.046) < a (0,05) à Tolak  Ho à Terima H1 à Model regresi tidak linier

Atau  karena selisihnya kecil à (0,046 » 0,05) à hubungan mendekati linier

           

Catatan:           Dari Deviation from linierity    à tidak signifikan

Sementara dari Linierity           à signifikan

Berarti ada model lain yang lebih baik dari hubungan linier, yakni model non-linier

 

Pada sesi ini (analisis ke-2) masukkan ke-4 variabel sekaligus:

 

Langkah-1:      Klik   Analyze à Regression à Curve Estimation

  1. Masukkan X1, X2 dan X3 (sekaligus) ke kotak Independent variable
  2. Masukkan Kinerja (Y) ke kotak dependent(s)
  3. Tandai 4 model yang tersedia (Lin,Cubic,Quadratic,Exp)  à OK

 

Sampai tampak sepeerti gambar berikut:

 

 

 

Didapat sejumlah output – tapi kita ambil 3 output  yang perlu saja sbb:

  1. 1.      Linieritas X1 dengan Y

Independent:  X1

 

Dependent Mth   Rsq  d.f.       F  Sigf      b0      b1      b2      b3

 

Y        LIN  .367    28   16.26  .000 34.0012   .7590

Y        QUA  .376    27    8.14  .002 -15.846  3.2103  -.0299

9 Y        CUB  .378    27    8.19  .002 -2.2688  2.0989          -.0003

Y        EXP  .368    28   16.33  .000 39.8354   .0119

 

Notes:

9  Tolerance limits reached; some dependent variables were not entered.

 

Langkah-2:      Interpretasi Output-1

Dari kolom R square & kolom Sig, terlihat bahwa model kubik dan kuadratik masih lebih tepat diterapkan pada model hubungan X1 dan Y, dibanding model linier, karena alasan berikut:

 

Model kuadrat             à R square = 37,6% à signifikan (Sig=0,02 < a=0,05) à pengaruhnya lebih besar

Model kubik    à R square = 37,8% à signifikan (Sig=0,002 < a=0,05) à pengaruhnya lebih besar

Model linier     à R square = 36,7% à signifikan (Sig=0,002 < a=0,05)

 

Kesimpulan:    Syarat linieritas untuk hubungan Insentif (X1) dan Kinerja (Y), terpenuhi, walau diketahui juga bahwa hubungan kuadrat dan kubik (Nonlinier) masih lebih baik diterapkan dibanding model linier.

 

 

 

Perhatikan diagram plot hubungan X1 dengan Y:

 

 

  1. 2.      Linieritas variable X2 dengan Y

Independent:  X2

 

Dependent Mth   Rsq  d.f.       F  Sigf      b0      b1      b2      b3

 

Y        LIN  .019    28     .54  .470 59.7174   .1213

Y        QUA  .236    27    4.17  .026 -61.261  6.3078  -.0775

9 Y        CUB  .238    27    4.21  .026 -22.139  3.2705          -.0007

Y        EXP  .018    28     .51  .482 59.7832   .0019

 

Notes:

9  Tolerance limits reached; some dependent variables were not entered.

 

Langkah-2:      Interpretasi Output-1

Terlihat model hubungan Linier tidak signifikan à Sig (0,470) > a(0,05)

Model hubungan Quadratik dan Qubic signifikan à Sig(0,026) < a(0,05)

Kesimpulan:    model linier antara variable X2 dengan Y tidak signifikan, tetapi model yang lebih baik dipakai adalah model kuadrat atau kubik

 

Perhatikan gambar plot berikut ini:

 

 

  1. 3.      Linieritas X3 dengan Y:

 

Independent:  X3

 

Dependent Mth   Rsq  d.f.       F  Sigf      b0      b1      b2      b3

 

Y        LIN  .072    28    2.17  .152 50.8691   .3293

Y        QUA  .189    27    3.15  .059 183.499 -6.0915   .0770

9 Y        CUB  .188    27    3.13  .060 141.479 -2.9608           .0006

Y        EXP  .075    28    2.28  .142 51.6655   .0053

 

Notes:

9  Tolerance limits reached; some dependent variables were not entered.

 

Langkah-2:      Interpretasi Output-2

Model hubungan linier tidak signifikan à Sig (0,152) > a (0,05)

Taksatu modelpun dari 4 model yang dipilih signifikan

Kesimpulan:    Tidak ada model yang signifikan mewakili hubungan interpersonal (X3) dengan kinerja (Y) dari 4 model yang dicobakan

 

Perhatikan gambar plot berikut:

 

LATIHAN:

 

Penelitian sederhana untuk mengetahui hubungan antara kompetensi (X) dan Kinerja Pegawai (Y), diambil sampel acak sebanyak 15 responden. Analisis data tersebut dan berikan kesimpulan

 

No. Subyek

X

Y

1

40

4

2

55

16

3

32

12

4

55

24

5

50

15

6

52

24

7

61

22

8

44

17

9

30

4

10

22

14

11

40

24

12

64

26

13

58

20

14

48

9

15

44

14

 

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