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Table 2 Ordinary least squares.

From: The impact of measurement errors in the identification of regulatory networks

EM

n

β 1

β 2

β 3

β 4

β 5

β 6

β 7

β 8

β 9

  

0

-0.1

-0.2

-0.3

-0.4

0.5

0.6

0.7

0.8

0

50

4.94

9.06

21.57

41.73

63.19

81.09

92.15

97.24

99.03

 

100

4.90

13.82

42.31

74.11

93.20

98.83

99.87

100.0

100.0

 

200

4.99

25.62

72.24

96.64

99.95

99.99

100.0

100.0

100.0

 

400

5.17

44.31

95.53

99.98

100.0

100.0

100.0

100.0

100.0

0.2

50

4.81 (4.73)

8.24 (8.45)

17.52 (18.12)

34.39 (34.94)

54.86 (55.38)

76.09 (73.71)

88.70 (86.95)

95.40 (94.61)

98.12 (97.69)

 

100

5.30 (5.20)

11.35 (12.27)

34.69 (36.27)

65.53 (67.16)

88.92 (89.57)

98.22 (97.81)

99.76 (99.66)

99.97 (99.96)

100.0 (100.0)

 

200

5.23 (5.25)

19.93 (22.02)

62.73 (65.22)

92.67 (93.53)

99.50 (99.58)

99.99 (99.99)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

 

400

5.05 (5.09)

36.11 (40.14)

90.44 (92.05)

99.86 (99.92)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

0.4

50

-

-

-

-

-

-

-

-

-

 

100

5.87 (5.17)

7.91 (9.77)

21.92 (25.30)

45.15 (48.55)

70.62 (72.95)

93.44 (88.64)

98.29 (96.46)

99.63 (99.13)

99.96 (99.82)

 

200

5.59 (5.13)

11.58 (16.32)

40.43 (47.45)

76.71 (81.23)

95.15 (96.48)

99.88 (99.58)

100.0 (99.99)

100.0 (100.0)

100.0 (100.0)

 

400

5.84 (4.76)

19.00 (28.10)

68.88 (77.88)

98.88 (98.36)

99.93 (99.98)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

0.6

50

-

-

-

-

-

-

-

-

-

 

100

-

-

-

-

-

-

-

-

-

 

200

6.79 (4.71)

6.75 (10.73)

20.87 (28.78)

48.56 (57.07)

77.02 (81.95)

98.53 (93.71)

99.81 (98.52)

99.99 (99.76)

100.0 (99.99)

 

400

8.42 (4.48)

8.88 (18.17)

38.42 (54.88)

78.94 (88.15)

97.28 (98.78)

99.99 (99.91)

100.0 (100.0)

100.0 (100.0)

100.0 (100.0)

0.8

50

-

-

-

-

-

-

-

-

-

 

100

-

-

-

-

-

-

-

-

-

 

200

-

-

-

-

-

-

-

-

-

 

400

10.95 (4.40)

5.22 (10.97)

17.99 (33.05)

48.43 (63.97)

79.65 (87.84)

99.88 (96.46)

99.99 (99.35)

100.0 (99.95)

100.0 (100.0)

  1. Percentage of the number of associations (rejected hypothesis) obtained using standard OLS and corrected OLS (between brackets) in 10,000 simulations. The first line contains the strength of association between predictors and response variables as described in simulation I. The rate of false-positives was controlled in 5%. In bold, are the rate of false-positives, i.e., the number of false-positives divided by the number of simulations. "-" means that it was not possible to calculate due to high measurement error when compared to sample's size. EM: Standard deviation of the Error of Measure. n: Number of samples. Notice that, in fact, the corrected OLS controls the rate of false positives in 5% while the usual OLS does not (values in bold).