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Old Faithful


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Geyser in the Yellowstone National Park which erupts in a fashion that has challenged analysts of time series. The data in the table refer to the period 1–8 August in 1978. For each day, the table shows x, the duration (in minutes, to the nearest 0.1 minute) of the current eruption, and y, the time (in minutes, to the nearest minute) until the next eruption. Observations refer to daylight hours only.

day

duration (x) and time interval (y) for successive eruptions

1

X

4.4

3.9

4.0

4.0

3.5

4.1

2.3

4.7

1.7

4.9

1.7

4.6

3.4

Y

78

74

68

76

80

84

50

93

55

76

58

74

75

2

X

4.3

1.7

3.9

3.7

3.1

4.0

1.8

4.1

1.8

3.2

1.9

4.6

2.0

Y

80

56

80

69

57

90

42

91

51

79

53

82

51

3

X

4.5

3.9

4.3

2.3

3.8

1.9

4.6

1.8

4.7

1.8

4.6

1.9

3.5

Y

76

82

84

53

86

51

85

45

88

51

80

49

82

4

X

4.0

3.7

3.7

4.3

3.6

3.8

3.8

3.8

2.5

4.5

4.1

3.7

3.8

3.4

Y

75

73

67

68

86

72

75

75

66

84

70

79

60

86

5

X

4.0

2.3

4.4

4.1

4.3

3.3

2.0

4.3

2.9

4.6

1.9

3.6

3.7

3.7

Y

71

67

81

76

83

76

55

73

56

83

57

71

72

77

6

X

1.8

4.6

3.5

4.0

3.7

1.7

4.6

1.7

4.0

1.8

4.4

1.9

4.6

2.9

Y

55

75

73

70

83

50

95

51

82

54

83

51

80

78

7

X

3.5

2.0

4.3

1.8

4.1

1.8

4.7

4.2

3.9

4.3

1.8

4.5

2.0

Y

81

53

89

44

78

61

73

75

73

76

55

86

48

8

X

4.2

4.4

4.1

4.1

4.0

4.1

2.7

4.6

1.9

4.5

4.5

4.8

4.1

Y

77

73

70

88

75

83

61

78

61

81

81

80

79

Old Faithful. Long time intervals between eruptions are generally followed by long eruptions, but predicting the future eruption pattern is a considerable challenge to time series experts.

Subjects: Probability and Statistics.


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