REGRESYON ANALĐZĐ 1. Bu veri ile ilgili olarak bazı dönüşümler daha iyi sonuçlar verebilir. Logx, sqrtx, x-sq ve 1/x gibi.

(1)

REGRESYON ANALĐZĐ

1. Bu veri ile ilgili olarak bazı dönüşümler daha iyi sonuçlar verebilir. Logx, sqrtx, x-sq ve 1/x gibi.

Sales(Y) Expandt.(X)

11 39

17 49

26 76

24 68

23 59

29 91

4 34

32 116

33 141

31 149

32 105

30 99

37 171

33 124

Expandt.(X)

Sales(Y)

175 150

125 100

75 50

40

30

20

10

0

S 4,60830

R-Sq 77,7%

R-Sq(adj) 75,9%

Fitted Line Plot

Sales(Y) = 7,535 + 0,1942 Expandt.(X)

The regression equation is

Sales(Y) = 7,535 + 0,1942 Expandt.(X)

S = 4,60830 R-Sq = 77,7% R-Sq(adj) = 75,9%

Analysis of Variance

Source DF SS MS F P Regression 1 888,88 888,877 41,86 0,000 Error 12 254,84 21,236

Total 13 1143,71

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logX

Sales(Y)

2,3 2,2

2,1 2,0

1,9 1,8

1,7 1,6

1,5 40

30

20

10

0

Scatterplot of Sales(Y) vs logX

sqrtX

Sales(Y)

14 13

12 11

10 9

8 7

6 5

40

30

20

10

0

Scatterplot of Sales(Y) vs sqrtX

(3)

x*x

Sales(Y)

30000 25000

20000 15000

10000 5000

0 40

30

20

10

0

Scatterplot of Sales(Y) vs x*x

1/x

Sales(Y)

0,030 0,025

0,020 0,015

0,010 0,005

40

30

20

10

0

Scatterplot of Sales(Y) vs 1/x

The regression equation is Sales(Y) = 42,9 - 1271 1/x

Predictor Coef SE Coef T P Constant 42,8587 0,7695 55,69 0,000 1/x -1271,32 50,92 -24,97 0,000

S = 1,34159 R-Sq = 98,1% R-Sq(adj) = 98,0%

(4)

Source DF SS MS F P Regression 1 1122,1 1122,1 623,44 0,000 Residual Error 12 21,6 1,8

Total 13 1143,7

Unusual Observations

Obs 1/x Sales(Y) Fit SE Fit Residual St Resid 7 0,0294 4,000 5,467 0,892 -1,467 -1,46 X 10 0,0067 31,000 34,326 0,494 -3,326 -2,67R

Residual

Percent

2 0

-2 -4

99 90

50

10 1

Fitted Value

Residual

30 20

10 1

0 -1 -2 -3

Residual

Frequency

2 1 0 -1 -2 -3 8 6 4 2

0

Observ ation Order

Residual

14 13 12 11 10 9 8 7 6 5 4 3 2 1 1 0 -1 -2 -3

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Sales(Y)

2.

Satış(Y) FiyatX1) Reklam(X2)

10 13 9

6 20 7

5 17 5

12 15 14

10 16 15

15 12 12

5 16 6

12 14 10

17 10 15

20 11 21

Satış(Y) = 16,4 - 0,825 Fiyat(X1) + 0,585 Reklam(X2)

(5)

Predictor Coef SE Coef T P Constant 16,406 4,343 3,78 0,007 Fiyat(X1) -0,8248 0,2196 -3,76 0,007 Reklam(X2) 0,5851 0,1337 4,38 0,003

S = 1,50720 R-Sq = 93,2% R-Sq(adj) = 91,2%

Total 9 233,60

Residual

Percent

4 2

0 -2

-4 99 90

50

10 1

Fitted Value

Residual

20 15

10 5

2 1 0 -1 -2

Residual

Frequency

2 1

0 -1

-2 2,0 1,5 1,0 0,5

0,0

Observ ation Order

Residual

10 9 8 7 6 5 4 3 2 1 2 1 0 -1 -2

Residual Plots for Satýþ(Y)

3.

X1= Score Y=Satış

X2=Age

X3=Anxiety X4=Experience

X5= GPA

Y X1 X2 X3 X4 X5

44 10 22 49 0 24

47 19 23 30 1 26

60 27 23 15 0 28

71 31 24 6 3 27

61 64 23 18 2 20

60 81 22 33 1 25

(6)

58 42 24 32 0 25

56 67 22 21 0 23

66 48 22 60 1 28

61 64 23 18 1 34

51 57 21 38 0 30

47 10 23 45 1 27

53 48 22 45 0 28

74 96 25 1 3 38

65 75 23 9 0 37

33 12 21 48 0 21

54 47 22 23 1 18

39 20 21 30 2 15

52 73 21 3 2 19

30 4 20 27 0 22

58 9 23 44 1 28

59 98 21 39 1 29

52 27 23 14 2 32

56 59 22 27 1 27

49 23 23 27 1 24

63 90 22 22 2 26

61 34 24 7 1 34

39 16 21 31 1 23

62 32 24 6 3 40

78 94 25 46 5 36

Y = - 75,6 + 0,208 X1 + 5,17 X2 + 0,0321 X3 + 0,376 X4 + 0,138 X5

Predictor Coef SE Coef T P Constant -75,56 21,68 -3,48 0,002 X1 0,20779 0,03447 6,03 0,000 X2 5,167 1,081 4,78 0,000 X3 0,03210 0,06157 0,52 0,607 X4 0,3760 0,9453 0,40 0,694 X5 0,1376 0,2010 0,68 0,500

S = 4,80085 R-Sq = 84,7% R-Sq(adj) = 81,5%

Total 29 3616,30

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Residual

Percent

10 5

0 -5 -10 99 90

50

10 1

Fitted Value

Residual

80 60

40 10

5 0 -5

Residual

Frequency

12 8

4 0 -4 10,0

7,5 5,0 2,5 0,0

Observ ation Order

Residual

30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 10

5 0

-5

Residual Plots for Y

BEST SUBSETS

Response is Y

Mallows X X X X X Vars R-Sq R-Sq(adj) C-p S 1 2 3 4 5 1 53,8 52,1 46,5 7,7254 X 1 45,7 43,8 59,2 8,3733 X 2 84,2 83,0 0,8 4,6013 X X 2 64,1 61,5 32,3 6,9310 X X 3 84,4 82,7 2,4 4,6507 X X X 3 84,3 82,5 2,6 4,6661 X X X 4 84,6 82,1 4,2 4,7193 X X X X 4 84,5 82,1 4,3 4,7304 X X X X

Buradan X1 ve X2 nin dahil edileceği bir modelin en iyilerden biri olacağı sonucuna varırız.

The regression equation is Y = - 81,1 + 0,215 X1 + 5,62 X2

Predictor Coef SE Coef T P Constant -81,12 15,44 -5,25 0,000 X1 0,21483 0,02981 7,21 0,000 X2 5,6248 0,6938 8,11 0,000

S = 4,60135 R-Sq = 84,2% R-Sq(adj) = 83,0%

Source DF SS MS F P Regression 2 3044,6 1522,3 71,90 0,000

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Residual Error 27 571,7 21,2 Total 29 3616,3

Source DF Seq SS X1 1 1653,2 X2 1 1391,5

Obs X1 Y Fit SE Fit Residual St Resid 4 31,0 71,000 60,536 1,468 10,464 2,40R 9 48,0 66,000 52,939 0,915 13,061 2,90R R denotes an observation with a large standardized residual.

4.

Y X

295 273,4 400 291,3 390 306,9 425 317,1 547 336,1 555 349,4 620 362,9 720 383,9 880 402,8 1050 437,0 1290 472,3 1528 510,4 1586 544,5 1960 588,1 2118 630,4 2116 685,9 2477 742,8 3119 801,3 3702 903,1 3316 983,6 2702 1076,7

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X

Y

1100 1000

900 800

700 600

500 400

300 200

4000

3000

2000

1000

0

Scatterplot of Y vs X

The regression equation is Y = - 786 + 4,24 X

Predictor Coef SE Coef T P Constant -786,2 183,4 -4,29 0,000 X 4,2374 0,3100 13,67 0,000

S = 334,294 R-Sq = 90,8% R-Sq(adj) = 90,3%

Source DF SS MS F P Regression 1 20885630 20885630 186,89 0,000 Residual Error 19 2123296 111752

Total 20 23008926

Obs X Y Fit SE Fit Residual St Resid 19 903 3702,0 3040,6 133,4 661,4 2,16R 21 1077 2702,0 3776,2 180,8 -1074,2 -3,82RX R denotes an observation with a large standardized residual.

X denotes an observation whose X value gives it large influence.

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X

Y

1100 1000 900 800 700 600 500 400 300 200 4000

3000

2000

1000

0

S 334,294

R-Sq 90,8%

R-Sq(adj) 90,3%

Fitted Line Plot

Y = - 786,2 + 4,237 X

Residual

Percent

1000 500

0 -500 -1000

99 90

50

10 1

Fitted Value

Residual

4000 3000

2000 1000

0 500

0 -500

-1000

Residual

Frequency

400 0

-400 -800

8 6 4 2 0

Observ ation Order

Residual

20 18 16 14 12 10 8 6 4 2 500

0

-500

-1000

Residual Plots for Y

Y = 1389 - 10,47 X + 0,02915 X**2 - 0,000017 X**3

S = 170,653 R-Sq = 97,8% R-Sq(adj) = 97,5%

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Source DF SS MS F P Regression 3 22513845 7504615 257,69 0,000 Error 17 495080 29122

Total 20 23008926

Sequential Analysis of Variance

Source DF SS F P Linear 1 20885630 186,89 0,000 Quadratic 1 963768 14,96 0,001 Cubic 1 664448 22,82 0,000

X

Y

1100 1000 900 800 700 600 500 400 300 200 4000

3000

2000

1000

0

S 170,653

R-Sq 97,8%

R-Sq(adj) 97,5%

Fitted Line Plot

Y = 1389 - 10,47 X + 0,02915 X**2 - 0,000017 X**3

(12)

5.

Sales Inc. Rate Y(t-1)

8,0 336,1 5,5

8,2 349,4 5,5 8,0

8,5 362,9 6,7 8,2

9,2 383,9 5,5 8,5

10,2 402,8 5,7 9,2

11,4 437 5,2 10,2

12,8 472,2 4,5 11,4 13,6 510,4 3,8 12,8 14,6 544,5 3,8 13,6 16,4 588,1 3,6 14,6 17,8 630,4 3,5 16,4 18,6 685,9 4,9 17,8 20,0 742,8 5,9 18,6 21,9 801,3 5,6 20,0 24,9 903,1 4,9 21,9 27,3 983,6 5,6 24,9 29,1 1076,7 8,5 27,3

Index

Sales

16 14

12 10

8 6

4 2

30

25

20

15

10

Time Series Plot of Sales

Sales = - 0,014 + 0,0297 Inc. - 0,350 Rate

Predictor Coef SE Coef T P Constant -0,0140 0,2498 -0,06 0,956 Inc. 0,0297492 0,0002480 119,96 0,000 Rate -0,34987 0,04656 -7,51 0,000

S = 0,219930 R-Sq = 99,9% R-Sq(adj) = 99,9%

(13)

Total 16 739,56

Residual

Percent

0,50 0,25

0,00 -0,25

-0,50 99 90

50

10 1

Fitted Value

Residual

30 25

20 15

10 0,4

0,2

0,0

-0,2

Residual

Frequency

0,3 0,2 0,1 0,0 -0,1 -0,2 -0,3 3

2

1

0

Observ ation Order

Residual

16 14 12 10 8 6 4 2 0,4

0,2

0,0

-0,2

Residual Plots for Sales

Bir başka Model denesek:

Sales = 0,049 + 0,0264 Inc. - 0,326 Rate + 0,123 Y(t-1)

16 cases used, 1 cases contain missing values

Predictor Coef SE Coef T P Constant 0,0489 0,2720 0,18 0,860 Inc. 0,026412 0,004110 6,43 0,000 Rate -0,32615 0,05615 -5,81 0,000 Y(t-1) 0,1234 0,1528 0,81 0,435

S = 0,230604 R-Sq = 99,9% R-Sq(adj) = 99,9%

Total 15 671,05

REGRESYON ANALĐZĐ 1. Bu veri ile ilgili olarak bazı dönüşümler daha iyi sonuçlar verebilir. Logx, sqrtx, x-sq ve 1/x gibi.