Call:
lm(formula = ReproductiveEffort ~ Foodavailability, data = foodav)
Residuals:
Min 1Q Median 3Q Max
-0.37653 -0.25549 -0.04903 0.23662 0.45750
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.89490 0.07262 12.32 <2e-16 ***
Foodavailability 1.19387 0.01590 75.08 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.2652 on 61 degrees of freedom
Multiple R-squared: 0.9893, Adjusted R-squared: 0.9891
F-statistic: 5636 on 1 and 61 DF, p-value: < 2.2e-16Reviewing Linear Models
This lecture
You can access it from: https://rpubs.com/amolina/review571
Review of linear models
Review of glm’s
Linear models assumptions
Linearity
Homoscedasticity
Normality
Independence
No collinearity
Lack of linearity
Lack of normality
Lack of homoscedasticity
How to interpret GLM’s outputs?
- Let’s remember that linear models, and glm’s have a “linear” deterministic component
How to interpret GLM’s outputs?
Let’s remember that linear models, and glm’s have a “linear” deterministic component
In linear models: \(\mu_i = \beta_0 + \beta_1x_{1,i} ...\) (which means, the expected value of y )
In generalized linear models: \(f(\mu_i) = \beta_0 + \beta_1x_{1,i} ...\) (which means, a function of the expected value of y)
The deterministic component is linear
Which is a good thing! Each linear (not polynomial… let’s forget about that for a little while) has two components!
A slope
An intercept
The deterministic component is linear
Which is a good thing! Each linear (not polynomial… let’s forget about that for a little while) has two components!
A slope
An intercept
\[ y = mx + b \]
The deterministic component is linear
Which is a good thing! Each linear (not polynomial… let’s forget about that for a little while) has two components!
A slope
An intercept
\[ y = mx + b = b + mx \]
is not any different than:
\[ \begin{align} \mu_i & = \beta_0 + \beta_1x_{1,i} \\ y_i & ~ N(mean = \mu_i, var=\sigma^2) \end{align} \]
Let’s remember what a slope and an intercept is
Let’s remember what a slope and an intercept is
Let’s remember what a slope and an intercept is
Let’s remember what a slope and an intercept is
Slope: For very change in x of 1, y changes 1.5. Intercept: 2
So, if x = 5, then y = 2 + 1.5(5) = 9.5
So, what about linear models?
Each line in a linear model simply has: 1 slope and 1 intercept.
So, what about linear models?
What is the slope? what is the intercept?
So, what about linear models?
\[ \begin{split} y_i & \sim \beta_0 + \beta_1x_i + \epsilon_i \\ \text{where } \epsilon & \sim normal(0,\sigma) \end{split} \] Or, in this specific case:
\[ Reproductive \ effort_i \sim \beta_0 + \beta_1Food \ availability_i + \epsilon_i \\ \]
So, what about linear models?
Intercept: 0.895
Slope: 1.194
\[ \begin{split} y_i & \sim \beta_0 + \beta_1x_i + \epsilon_i \\ \text{where } \epsilon & \sim normal(0,\sigma) \end{split} \]
Results
| Coefficient1 | Estimate | Col3 | Col4 | Col5 |
|---|---|---|---|---|
| Intercept \(\beta_0\) | 0.895 | |||
| Slope \(\beta_1\) | 1.194 |
\[ \begin{split} y_i & \sim \beta_0 + \beta_1x_i + \epsilon_i \\ \text{where } \epsilon & \sim normal(0,\sigma) \end{split} \]
Results
| Coefficient1 | Estimate | Std. Error | t-value (test) | Col5 |
|---|---|---|---|---|
| Intercept \(\beta_0\) | 0.895 | 0.072 | 12.32 | <0.0001 |
| Slope \(\beta_1\) | 1.194 | 0.0159 | 75.08 | <0.0001 |
\[ \begin{split} y_i & \sim \beta_0 + \beta_1x_i + \epsilon_i \\ \text{where } \epsilon & \sim normal(0,\sigma) \end{split} \]
Test:
Ho: Coefficient == 0
Ha Coefficient != 0
How about this one:
How about this one:
Call:
lm(formula = FC ~ IC + Dose, data = drugz)
Residuals:
Min 1Q Median 3Q Max
-2.2610 -0.6360 0.0000 0.6514 2.2876
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.51804 0.38892 1.332 0.1849
IC 0.93384 0.05647 16.537 <2e-16 ***
Dosedose1 -0.44007 0.20011 -2.199 0.0294 *
Dosedose2 -2.09915 0.20162 -10.412 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9893 on 146 degrees of freedom
Multiple R-squared: 0.7636, Adjusted R-squared: 0.7588
F-statistic: 157.2 on 3 and 146 DF, p-value: < 2.2e-16- Additive model means only one slope is estimated!
Back to the plot
Parallel lines
1 slope, 3 intercepts
Each line: \(y = mx + b\)
Finding values
Call:
lm(formula = FC ~ IC + Dose, data = drugz)
Residuals:
Min 1Q Median 3Q Max
-2.2610 -0.6360 0.0000 0.6514 2.2876
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.51804 0.38892 1.332 0.1849
IC 0.93384 0.05647 16.537 <2e-16 ***
Dosedose1 -0.44007 0.20011 -2.199 0.0294 *
Dosedose2 -2.09915 0.20162 -10.412 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9893 on 146 degrees of freedom
Multiple R-squared: 0.7636, Adjusted R-squared: 0.7588
F-statistic: 157.2 on 3 and 146 DF, p-value: < 2.2e-16\[ \begin{align} \beta_0 & = 0.51 \ \text{intercept for control} \\ \beta_1 & = 0.93 \ \text{slope} \\ \beta_2 & = -0.44 \ \text{Difference in intercept between control and dose 1} \\ \beta_2 & = -2.099 \ \text{Difference in intercept between control and dose 2} \\ \end{align} \]
\[ y_i \sim \beta_0 + \beta_1x_{1,i} + \beta_2x_{2,i} + \beta_3x_{3,i} + \epsilon_i \\ \]
| Site | Value of \(x_2\) | Value of \(x_3\) |
|---|---|---|
| Control | 0 | 0 |
| Dose 1 | 1 | 0 |
| Dose 2 | 0 | 1 |
Finding values
Call:
lm(formula = FC ~ IC + Dose, data = drugz)
Residuals:
Min 1Q Median 3Q Max
-2.2610 -0.6360 0.0000 0.6514 2.2876
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.51804 0.38892 1.332 0.1849
IC 0.93384 0.05647 16.537 <2e-16 ***
Dosedose1 -0.44007 0.20011 -2.199 0.0294 *
Dosedose2 -2.09915 0.20162 -10.412 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9893 on 146 degrees of freedom
Multiple R-squared: 0.7636, Adjusted R-squared: 0.7588
F-statistic: 157.2 on 3 and 146 DF, p-value: < 2.2e-16| Measurement | Intercept | Slope |
|---|---|---|
| Control | 0.51 | 0.93 |
| Dose 1 | 0.51 - 0.44 | 0.93 |
| Dose 2 | 0.51 -2.099 | 0.93 |
Statistical inference
anova
emmeans
contrast
Analysis of Variance Table
Response: FC
Df Sum Sq Mean Sq F value Pr(>F)
IC 1 342.36 342.36 349.825 < 2.2e-16 ***
Dose 2 119.30 59.65 60.949 < 2.2e-16 ***
Residuals 146 142.89 0.98
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 contrast estimate SE df t.ratio p.value
control - dose1 0.44 0.200 146 2.199 0.0747
control - dose2 2.10 0.202 146 10.412 <.0001
dose1 - dose2 1.66 0.198 146 8.377 <.0001
P value adjustment: tukey method for comparing a family of 3 estimates statistical inference
anova compares variance. Is the variance between groups higher than within groups?
Interactive
- Each line has its own slope and its own intercept
Interactive
Call:
lm(formula = FC ~ IC * Dose, data = drugz)
Residuals:
Min 1Q Median 3Q Max
-2.3167 -0.6262 -0.0031 0.6443 2.1836
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.38733 0.59401 0.652 0.5154
IC 0.95418 0.08981 10.624 <2e-16 ***
Dosedose1 0.07353 0.85237 0.086 0.9314
Dosedose2 -2.21858 0.86308 -2.571 0.0112 *
IC:Dosedose1 -0.08529 0.13509 -0.631 0.5288
IC:Dosedose2 0.02324 0.13917 0.167 0.8676
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9939 on 144 degrees of freedom
Multiple R-squared: 0.7647, Adjusted R-squared: 0.7565
F-statistic: 93.59 on 5 and 144 DF, p-value: < 2.2e-16\[ \begin{align} \beta_0 & = 0.38 \ \text{intercept for control} \\ \beta_1 & = 0.954 \ \text{slope for control} \\ \beta_2 & = -0.073 \ \text{Difference in intercept between control and dose 1} \\ \beta_3 & = -2.24 \ \text{Difference in intercept between control and dose 2} \\ \beta_4 & = -0.085 \ \text{Difference in slope between control and dose 1} \\ \beta_5 & = 0.023 \ \text{Difference in slope between control and dose 2} \\ \end{align} \]
| Site | Value of \(x_2\) | Value of \(x_3\) | Value of \(x_4\) | Value of \(x_5\) |
|---|---|---|---|---|
| Control | 0 | 0 | 0 | 0 |
| Dose 1 | 1 | 0 | 1 | 0 |
| Dose 2 | 0 | 1 | 0 | 1 |
Doing inference of interactions
Analysis of Variance Table
Response: FC
Df Sum Sq Mean Sq F value Pr(>F)
IC 1 342.36 342.36 346.5514 <2e-16 ***
Dose 2 119.30 59.65 60.3790 <2e-16 ***
IC:Dose 2 0.63 0.31 0.3168 0.729
Residuals 144 142.26 0.99
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 contrast estimate SE df t.ratio p.value
control - dose1 0.44 0.202 144 2.173 0.0794
control - dose2 2.08 0.204 144 10.175 <.0001
dose1 - dose2 1.64 0.201 144 8.136 <.0001
P value adjustment: tukey method for comparing a family of 3 estimates Interactions
Finding values (predictions)
Assignment question 1 📝
Look at the summary. And before continuing make sure you understand it. If you don’t, now is the time to raise your hand.
You need to calculate the expected probability (we’ll call this \(\pi\)) of an individual being infected for each of the following two cases:
- An individual of length 50 from Area 1, in 1999
- An individual of length 50 from Area 3, in 2001
GLM
Model
'data.frame': 1254 obs. of 12 variables:
$ Sample : int 1 2 3 4 5 6 7 8 9 10 ...
$ Intensity : int 0 0 0 0 0 0 0 0 0 0 ...
$ Prevalence: int 0 0 0 0 0 0 0 0 0 0 ...
$ Year : Factor w/ 3 levels "1999","2000",..: 1 1 1 1 1 1 1 1 1 1 ...
$ Depth : int 220 220 220 220 220 220 220 194 194 194 ...
$ Weight : int 148 144 146 138 40 68 52 3848 2576 1972 ...
$ Length : int 26 26 27 26 17 20 19 77 67 60 ...
$ Sex : Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 1 1 1 1 ...
$ Stage : Factor w/ 5 levels "0","1","2","3",..: 1 1 1 1 1 1 1 1 1 1 ...
$ Age : int 0 0 0 0 0 0 0 0 0 0 ...
$ Area : Factor w/ 4 levels "1","2","3","4": 2 2 2 2 2 2 2 3 3 3 ...
$ WL2 : num 19.2 18.7 19.7 17.9 3.4 ... Sample Intensity Prevalence Year Depth Weight Length Sex Stage Age Area
1 1 0 0 1999 220 148 26 0 0 0 2
2 2 0 0 1999 220 144 26 0 0 0 2
3 3 0 0 1999 220 146 27 0 0 0 2
4 4 0 0 1999 220 138 26 0 0 0 2
5 5 0 0 1999 220 40 17 0 0 0 2
6 6 0 0 1999 220 68 20 0 0 0 2
7 7 0 0 1999 220 52 19 0 0 0 2
8 8 0 0 1999 194 3848 77 0 0 0 3
9 9 0 0 1999 194 2576 67 0 0 0 3
10 10 0 0 1999 194 1972 60 0 0 0 3
11 11 0 0 1999 194 2272 62 0 0 0 3
12 12 0 0 1999 194 1046 49 0 0 0 3
13 13 0 0 1999 194 1186 52 0 0 0 3
14 14 0 0 1999 194 776 45 0 0 0 3
15 15 0 0 1999 194 2372 61 0 0 0 3
16 16 0 0 1999 194 1194 54 0 0 0 3
17 17 0 0 1999 194 3574 71 0 0 0 3
18 18 0 0 1999 194 2138 65 0 0 0 3
19 19 0 0 1999 194 2222 59 0 0 0 3
20 20 0 0 1999 194 2482 62 0 0 0 3
21 21 0 0 1999 194 2164 61 0 0 0 3
22 22 0 0 1999 194 1772 57 0 0 0 3
23 23 0 0 1999 194 494 39 0 0 0 3
24 24 0 0 1999 194 3130 67 0 0 0 3
25 25 0 0 1999 194 2708 65 0 0 0 3
26 26 0 0 1999 194 2394 66 0 0 0 3
27 27 0 0 1999 194 2212 64 0 0 0 3
28 28 0 0 1999 194 3110 65 0 0 0 3
29 29 0 0 1999 194 2218 62 0 0 0 3
30 30 0 0 1999 194 2222 60 0 0 0 3
31 31 0 0 1999 194 2398 62 0 0 0 3
32 32 0 0 1999 235 368 35 0 0 0 4
33 33 0 0 1999 235 306 34 0 0 0 4
34 34 0 0 1999 235 318 35 0 0 0 4
35 35 0 0 1999 235 276 32 0 0 0 4
36 36 0 0 1999 278 84 22 0 0 0 4
37 37 0 0 1999 51 1016 47 2 1 3 1
38 38 0 0 1999 51 1584 53 1 1 5 1
39 39 0 0 1999 51 1354 55 1 1 4 1
40 40 0 0 1999 51 1518 52 1 1 4 1
41 41 0 0 1999 51 1382 51 2 1 4 1
42 42 0 0 1999 51 1648 55 1 1 4 1
43 43 0 0 1999 51 1354 51 2 1 5 1
44 44 0 0 1999 51 1870 54 2 1 5 1
45 45 0 0 1999 51 1272 53 2 1 5 1
46 46 0 0 1999 51 1360 50 1 1 4 1
47 47 0 0 1999 51 936 45 2 1 3 1
48 48 0 0 1999 51 1650 55 2 1 5 1
49 49 0 0 1999 51 1504 53 1 1 5 1
50 50 0 0 1999 51 1008 48 2 1 3 1
51 51 0 0 1999 51 896 46 2 1 3 1
52 52 0 0 1999 51 3016 68 1 1 5 1
53 53 0 0 1999 85 470 37 1 1 2 1
54 54 0 0 1999 85 520 38 1 1 2 1
55 55 0 0 1999 85 470 38 1 1 2 1
56 56 0 0 1999 85 558 39 2 1 3 1
57 57 0 0 1999 85 3076 68 2 1 5 1
58 58 0 0 1999 85 1536 57 2 1 4 1
59 59 0 0 1999 85 1916 60 2 1 4 1
60 60 0 0 1999 85 320 32 1 1 2 1
61 61 0 0 1999 85 1152 49 1 1 4 1
62 62 0 0 1999 85 1284 54 1 1 5 1
63 63 0 0 1999 85 4712 80 1 1 7 1
64 64 0 0 1999 85 2182 60 2 1 4 1
65 65 0 0 1999 85 976 49 1 1 3 1
66 66 0 0 1999 85 408 36 1 1 2 1
67 67 0 0 1999 85 242 30 2 1 2 1
68 68 0 0 1999 85 644 41 2 1 3 1
69 69 0 0 1999 85 540 39 2 1 2 1
70 70 0 0 1999 85 326 33 1 1 2 1
71 71 0 0 1999 85 300 33 1 1 2 1
72 72 0 0 1999 85 232 29 2 1 2 1
73 73 0 0 1999 85 822 45 1 1 3 1
74 74 0 0 1999 85 692 43 1 1 3 1
75 75 0 0 1999 85 438 36 2 1 2 1
76 76 0 0 1999 85 406 35 2 1 2 1
77 77 0 0 1999 85 240 30 2 1 2 1
78 78 0 0 1999 85 358 34 1 1 2 1
79 79 0 0 1999 137 476 38 2 1 3 1
80 80 0 0 1999 137 1478 55 1 1 4 1
81 81 0 0 1999 137 1672 57 1 1 5 1
82 82 0 0 1999 137 1582 56 2 1 3 1
83 83 0 0 1999 137 390 35 2 1 2 1
84 84 0 0 1999 150 1816 59 1 1 5 2
85 85 0 0 1999 150 3888 71 1 1 5 2
86 86 0 0 1999 150 1986 58 1 1 4 2
87 87 0 0 1999 150 2524 66 1 1 5 2
88 88 0 0 1999 150 1712 59 2 1 4 2
89 89 0 0 1999 150 1968 58 2 1 4 2
90 90 0 0 1999 150 2764 64 1 1 5 2
91 91 0 0 1999 150 3412 69 1 1 5 2
92 92 0 0 1999 150 2294 63 1 1 5 2
93 93 0 0 1999 150 552 38 1 1 2 2
94 94 0 0 1999 150 1422 54 2 1 4 2
95 95 0 0 1999 150 1028 47 2 1 3 2
96 96 0 0 1999 150 466 38 2 1 2 2
97 97 0 0 1999 150 432 35 1 1 2 2
98 98 0 0 1999 150 300 31 2 1 2 2
99 99 0 0 1999 150 2706 67 1 1 5 2
100 100 0 0 1999 150 1154 52 1 1 3 2
101 101 0 0 1999 150 1146 52 1 1 4 2
102 102 0 0 1999 100 2352 64 1 1 6 2
103 103 0 0 1999 100 2084 60 2 1 4 2
104 104 0 0 1999 100 1008 48 2 1 3 2
105 105 0 0 1999 100 3970 73 2 1 5 2
106 106 0 0 1999 100 1738 55 2 1 5 2
107 107 0 0 1999 100 844 45 2 1 3 2
108 108 0 0 1999 100 3688 74 1 1 6 2
109 109 0 0 1999 100 2848 67 1 1 5 2
110 110 0 0 1999 100 1090 47 2 1 3 2
111 111 0 0 1999 292 826 49 2 1 3 2
112 112 0 0 1999 220 2086 61 1 1 5 2
113 113 0 0 1999 220 1744 58 2 1 5 2
114 114 0 0 1999 220 2118 60 1 1 5 2
115 115 0 0 1999 220 750 45 2 1 3 2
116 116 0 0 1999 220 1570 58 2 1 5 2
117 117 0 0 1999 220 326 33 2 1 2 2
118 118 0 0 1999 220 4292 77 1 1 6 2
119 119 0 0 1999 220 220 30 1 1 2 2
120 120 0 0 1999 220 262 32 2 1 2 2
121 121 0 0 1999 220 184 28 1 1 2 2
122 122 0 0 1999 220 180 28 1 1 2 2
123 123 0 0 1999 220 976 48 1 1 3 2
124 124 0 0 1999 220 1344 52 2 1 4 2
125 125 0 0 1999 220 2926 67 1 1 5 2
126 126 0 0 1999 220 544 41 1 1 3 2
127 127 0 0 1999 220 774 44 2 1 3 2
128 128 0 0 1999 220 452 37 2 1 2 2
129 129 0 0 1999 220 258 32 1 1 2 2
130 130 0 0 1999 220 190 29 2 1 2 2
131 131 0 0 1999 220 266 32 1 1 2 2
132 132 0 0 1999 220 196 29 1 1 0 2
133 133 0 0 1999 99 1846 59 1 1 4 3
134 134 0 0 1999 99 1312 53 2 1 4 3
135 135 0 0 1999 99 3302 73 2 1 5 3
136 136 0 0 1999 99 1258 50 2 1 4 3
137 137 0 0 1999 99 1848 57 1 1 6 3
138 138 0 0 1999 99 1246 51 2 1 4 3
139 139 0 0 1999 99 2038 59 2 1 4 3
140 140 0 0 1999 99 4738 77 1 1 6 3
141 141 0 0 1999 99 1248 51 2 1 4 3
142 142 0 0 1999 99 1072 48 1 1 3 3
143 143 0 0 1999 99 854 46 2 1 3 3
144 144 0 0 1999 99 2168 62 2 1 4 3
145 145 0 0 1999 99 1108 50 2 1 4 3
146 146 0 0 1999 99 1122 50 1 1 4 3
147 147 0 0 1999 99 2050 61 1 1 4 3
148 148 0 0 1999 99 1168 51 2 1 4 3
149 149 0 0 1999 99 1334 53 2 1 4 3
150 150 0 0 1999 99 964 47 2 1 3 3
151 151 0 0 1999 99 678 41 2 1 2 3
152 152 0 0 1999 99 1076 49 2 1 4 3
153 153 0 0 1999 99 1238 52 1 1 4 3
154 154 0 0 1999 99 1824 58 1 1 4 3
155 155 0 0 1999 99 860 44 1 1 3 3
156 156 0 0 1999 99 1260 50 2 1 4 3
157 157 0 0 1999 99 1154 52 1 1 4 3
158 158 0 0 1999 99 936 43 1 1 3 3
159 159 0 0 1999 99 1598 55 2 1 4 3
160 160 0 0 1999 99 2500 65 2 1 5 3
161 161 0 0 1999 99 1942 59 1 1 4 3
162 162 0 0 1999 270 770 47 2 1 4 3
163 163 0 0 1999 270 538 40 2 1 3 3
164 164 0 0 1999 270 3862 78 1 1 6 3
165 165 0 0 1999 270 878 48 2 1 4 3
166 166 0 0 1999 270 1438 55 1 1 4 3
167 167 0 0 1999 270 1592 59 2 1 5 3
168 168 0 0 1999 270 1250 53 2 1 4 3
169 169 0 0 1999 270 1226 51 1 1 4 3
170 170 0 0 1999 270 1326 53 1 1 4 3
171 171 0 0 1999 270 1104 49 2 1 4 3
172 172 0 0 1999 270 1982 63 2 1 5 3
173 173 0 0 1999 270 2480 64 1 1 5 3
174 174 0 0 1999 270 1142 51 2 1 4 3
175 175 0 0 1999 270 488 39 1 1 4 3
176 176 0 0 1999 270 1382 55 1 1 4 3
177 177 0 0 1999 256 1714 59 2 1 4 3
178 178 0 0 1999 256 754 45 1 1 4 3
179 179 0 0 1999 256 1618 61 1 1 5 3
180 180 0 0 1999 256 2122 64 2 1 5 3
181 181 0 0 1999 256 604 38 1 1 3 3
182 182 0 0 1999 256 2780 65 1 1 6 3
183 183 0 0 1999 256 2318 64 1 1 4 3
184 184 0 0 1999 256 1344 53 1 1 4 3
185 185 0 0 1999 256 1674 60 2 1 8 3
186 186 0 0 1999 256 1144 53 1 1 7 3
187 187 0 0 1999 256 1052 51 2 1 3 3
188 188 0 0 1999 172 2034 57 2 1 5 3
189 189 0 0 1999 172 674 42 2 1 3 3
190 190 0 0 1999 172 862 47 1 1 3 3
191 191 0 0 1999 172 612 40 1 1 3 3
192 192 0 0 1999 172 2528 64 2 1 4 3
193 193 0 0 1999 172 1516 55 1 1 4 3
194 194 0 0 1999 172 906 47 1 1 4 3
195 195 0 0 1999 172 434 38 2 1 3 3
196 196 0 0 1999 172 182 29 1 1 2 3
197 197 0 0 1999 172 230 31 1 1 2 3
198 198 0 0 1999 172 200 29 1 1 2 3
199 199 0 0 1999 172 222 29 1 1 2 3
200 200 0 0 1999 172 238 30 2 1 2 3
201 201 0 0 1999 172 176 28 2 1 2 3
202 202 0 0 1999 172 198 30 1 1 2 3
203 203 0 0 1999 172 168 29 1 1 2 3
204 204 0 0 1999 172 170 28 1 1 2 3
205 205 0 0 1999 172 204 30 2 1 2 3
206 206 0 0 1999 235 2496 68 1 1 6 4
207 207 0 0 1999 235 1198 50 2 1 3 4
208 208 0 0 1999 235 3678 75 1 1 5 4
209 209 0 0 1999 235 1036 50 1 1 4 4
210 210 0 0 1999 235 2898 73 1 1 5 4
211 211 0 0 1999 278 582 40 1 1 3 4
212 212 0 0 1999 278 986 48 2 1 4 4
213 213 0 0 1999 278 662 44 2 1 3 4
214 214 0 0 1999 278 270 33 1 1 2 4
215 215 0 0 1999 278 980 49 2 1 3 4
216 216 0 0 1999 278 1330 52 1 1 4 4
217 217 0 0 1999 278 364 36 2 1 2 4
218 218 0 0 1999 110 3190 68 2 1 6 4
219 219 0 0 1999 110 626 42 1 1 3 4
220 220 0 0 1999 110 788 46 1 1 3 4
221 221 0 0 1999 110 968 51 2 1 5 4
222 222 0 0 1999 110 1322 54 1 1 4 4
223 223 0 0 1999 110 1400 54 2 1 4 4
224 224 0 0 1999 110 942 48 2 1 4 4
225 225 0 0 1999 110 1104 53 2 1 4 4
226 226 0 0 1999 110 500 40 1 1 3 4
227 227 0 0 1999 110 296 33 2 1 2 4
228 228 0 0 1999 110 168 29 1 1 2 4
229 229 0 0 1999 110 370 36 1 1 3 4
230 230 0 0 1999 51 1544 53 2 2 4 1
231 231 0 0 1999 51 1520 53 2 2 4 1
232 232 0 0 1999 51 1912 58 1 2 6 1
233 233 0 0 1999 51 1144 49 2 2 4 1
234 234 0 0 1999 51 1472 51 2 2 4 1
235 235 0 0 1999 51 1418 51 2 2 5 1
236 236 0 0 1999 51 1330 49 2 2 3 1
237 237 0 0 1999 85 948 47 2 2 3 1
238 238 0 0 1999 200 2292 65 1 2 6 1
239 239 0 0 1999 200 2562 63 1 2 6 1
240 240 0 0 1999 100 1708 55 2 2 5 2
241 241 0 0 1999 100 1670 55 2 2 5 2
242 242 0 0 1999 100 1740 57 2 2 5 2
243 243 0 0 1999 100 2396 62 2 2 5 2
244 244 0 0 1999 220 3484 68 2 2 6 2
245 245 0 0 1999 99 2896 64 2 2 7 3
246 246 0 0 1999 99 1712 55 2 2 4 3
247 247 0 0 1999 99 1778 57 1 2 5 3
248 248 0 0 1999 99 1800 55 2 2 4 3
249 249 0 0 1999 99 4086 77 1 2 9 3
250 250 0 0 1999 99 1772 57 2 2 5 3
251 251 0 0 1999 99 2140 62 1 2 5 3
252 252 0 0 1999 99 1116 49 2 2 4 3
253 253 0 0 1999 99 1844 56 2 2 7 3
254 254 0 0 1999 99 1344 51 2 2 5 3
255 255 0 0 1999 270 1110 54 1 2 5 3
256 256 0 0 1999 270 2228 63 2 2 6 3
257 257 0 0 1999 270 1864 58 2 2 5 3
258 258 0 0 1999 270 1266 51 2 2 4 3
259 259 0 0 1999 270 1082 49 2 2 4 3
260 260 0 0 1999 256 2958 63 2 2 5 3
261 261 0 0 1999 256 3198 66 1 2 5 3
262 262 0 0 1999 256 2490 61 2 2 5 3
263 263 0 0 1999 256 3618 70 2 2 5 3
264 264 0 0 1999 256 3034 68 2 2 4 3
265 265 0 0 1999 172 2244 62 2 2 7 3
266 266 0 0 1999 172 1754 55 1 2 5 3
267 267 0 0 1999 172 178 28 1 2 2 3
268 268 0 0 1999 235 1578 54 2 2 4 4
269 269 0 0 1999 278 2130 59 2 2 5 4
270 270 0 0 1999 110 1304 50 1 2 4 4
271 271 0 0 1999 110 4098 74 2 2 8 4
272 272 0 0 1999 110 6390 88 1 2 8 4
273 273 0 0 1999 150 7854 90 1 4 7 2
274 274 0 0 1999 150 NA NA 1 4 8 2
275 275 0 0 1999 100 6916 86 1 4 9 2
276 276 0 0 1999 100 2980 65 1 4 7 2
277 277 0 0 1999 220 4018 72 1 4 6 2
278 278 0 0 1999 270 2552 63 1 4 5 3
279 279 0 0 2000 57 1474 51 1 1 6 1
280 280 0 0 2000 57 1608 57 2 1 6 1
281 281 0 0 2000 57 830 47 1 1 3 1
282 282 0 0 2000 50 992 48 2 1 3 1
283 283 0 0 2000 121 552 40 1 1 2 1
284 284 0 0 2000 121 1744 58 1 1 4 1
285 285 0 0 2000 121 668 42 1 1 2 1
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825 825 13 1 1999 137 916 47 2 1 3 1
826 826 13 1 1999 270 432 38 2 1 2 3
827 827 13 1 1999 110 1078 50 1 1 4 4
828 828 14 1 1999 85 2302 62 2 1 7 1
829 829 14 1 1999 99 958 47 1 1 3 3
830 830 14 1 1999 200 1484 53 2 2 5 1
831 831 14 1 1999 110 1264 52 2 2 4 4
832 832 15 1 1999 235 1094 50 2 1 4 4
833 833 15 1 1999 278 412 37 2 1 2 4
834 834 15 1 1999 270 1518 55 2 2 4 3
835 835 16 1 1999 235 946 47 2 1 3 4
836 836 16 1 1999 278 510 39 2 1 3 4
837 837 16 1 1999 200 2202 59 1 2 5 1
838 838 16 1 1999 110 2054 57 2 2 6 4
839 839 17 1 1999 137 624 40 1 1 3 1
840 840 17 1 1999 292 1826 62 1 1 5 2
841 841 17 1 1999 200 1892 59 2 2 5 1
842 842 17 1 1999 278 2072 58 2 2 5 4
843 843 18 1 1999 150 1954 60 2 1 5 2
844 844 18 1 1999 270 492 40 1 1 3 3
845 845 18 1 1999 235 708 43 1 1 3 4
846 846 19 1 1999 172 200 30 1 1 2 3
847 847 19 1 1999 200 1520 53 1 2 5 1
848 848 20 1 1999 200 842 46 1 1 3 1
849 849 20 1 1999 278 562 40 2 1 2 4
850 850 21 1 1999 256 1108 54 2 1 5 3
851 851 21 1 1999 278 198 29 1 1 2 4
852 852 21 1 1999 278 2034 58 2 2 4 4
853 853 22 1 1999 278 198 30 1 1 2 4
854 854 22 1 1999 200 1416 52 2 2 5 1
855 855 23 1 1999 235 1242 53 1 1 5 4
856 856 23 1 1999 235 1682 56 2 1 4 4
857 857 24 1 1999 235 932 49 0 0 0 4
858 858 25 1 1999 235 1126 49 0 0 0 4
859 859 25 1 1999 110 1238 49 2 2 4 4
860 860 26 1 1999 137 1582 56 2 1 5 1
861 861 27 1 1999 137 2566 68 1 1 4 1
862 862 28 1 1999 292 794 46 1 1 3 2
863 863 28 1 1999 235 1396 56 1 1 4 4
864 864 28 1 1999 235 1996 59 2 2 5 4
865 865 32 1 1999 270 1342 53 1 1 4 3
866 866 33 1 1999 278 382 37 1 1 2 4
867 867 35 1 1999 235 174 30 0 0 0 4
868 868 35 1 1999 235 1182 53 2 1 4 4
869 869 36 1 1999 292 680 45 1 1 3 2
870 870 38 1 1999 278 156 28 0 0 0 4
871 871 39 1 1999 235 714 44 0 0 0 4
872 872 41 1 1999 137 456 38 1 1 3 1
873 873 41 1 1999 200 2312 61 1 2 6 1
874 874 45 1 1999 278 154 27 0 0 0 4
875 875 50 1 1999 137 1284 51 2 1 5 1
876 876 51 1 1999 235 386 36 0 0 0 4
877 877 52 1 1999 200 1458 53 2 2 5 1
878 878 56 1 1999 235 664 43 0 0 0 4
879 879 65 1 1999 278 194 30 1 1 2 4
880 880 68 1 1999 235 320 34 0 0 0 4
881 881 73 1 1999 235 206 29 0 0 0 4
882 882 84 1 1999 150 1732 58 2 1 5 2
883 883 86 1 1999 278 178 28 2 1 2 4
884 884 126 1 1999 235 1248 52 1 1 4 4
885 885 160 1 1999 235 658 42 0 0 0 4
886 886 183 1 1999 235 236 30 0 0 0 4
887 887 NA 1 1999 194 3722 77 0 0 0 3
888 888 NA 1 1999 194 3594 70 0 0 0 3
889 889 NA 1 1999 194 1104 52 0 0 0 3
890 890 NA 1 1999 194 1368 54 0 0 0 3
891 891 NA 1 1999 194 1762 61 0 0 0 3
892 892 NA 1 1999 194 1240 52 0 0 0 3
893 893 NA 1 1999 194 668 42 0 0 0 3
894 894 NA 1 1999 194 2914 74 0 0 0 3
895 895 NA 1 1999 194 1756 55 0 0 0 3
896 896 NA 1 1999 194 1828 57 0 0 0 3
897 897 NA 1 1999 194 2720 66 0 0 0 3
898 898 NA 1 1999 194 1368 55 0 0 0 3
899 899 NA 1 1999 194 1834 60 0 0 0 3
900 900 NA 1 1999 194 420 36 0 0 0 3
901 901 NA 1 1999 194 2020 60 0 0 0 3
902 902 NA 1 1999 194 1886 61 0 0 0 3
903 903 NA 1 1999 194 3056 71 0 0 0 3
904 904 NA 1 1999 100 1744 61 2 1 6 2
905 905 NA 1 1999 100 1562 55 2 1 4 2
906 906 NA 1 1999 100 3002 68 1 1 5 2
907 907 NA 1 1999 100 1412 54 2 1 4 2
908 908 NA 1 1999 278 1320 50 1 1 4 4
909 909 NA 1 1999 278 332 36 1 1 2 4
910 910 NA 1 1999 278 1190 54 2 1 4 4
911 911 NA 1 1999 278 854 45 2 1 3 4
912 912 NA 1 1999 278 1140 50 2 1 4 4
913 913 NA 1 1999 278 984 49 2 1 4 4
914 914 NA 1 1999 278 652 42 1 1 4 4
915 915 NA 1 1999 278 580 42 2 1 3 4
916 916 NA 1 1999 278 476 39 1 1 3 4
917 917 NA 1 1999 278 360 35 2 1 2 4
918 918 NA 1 1999 110 1654 60 2 1 5 4
919 919 NA 1 1999 110 1786 61 1 1 5 4
920 920 NA 1 1999 110 912 48 1 1 3 4
921 921 NA 1 1999 110 2430 67 1 1 6 4
922 922 NA 1 1999 110 252 31 2 1 2 4
923 923 NA 1 1999 110 176 29 2 1 2 4
924 924 NA 1 1999 110 2136 62 1 1 5 4
925 925 NA 1 1999 110 916 49 2 1 3 4
926 926 NA 1 1999 110 526 39 2 1 3 4
927 927 NA 1 1999 110 354 36 2 1 3 4
928 928 NA 1 1999 110 418 36 1 1 3 4
929 929 NA 1 1999 110 356 35 1 1 3 4
930 930 NA 1 1999 110 670 42 2 1 3 4
931 931 NA 1 1999 110 816 45 2 1 3 4
932 932 NA 1 1999 110 324 35 1 1 2 4
933 933 NA 1 1999 110 234 32 2 1 2 4
934 934 NA 1 1999 110 206 31 2 1 2 4
935 935 NA 1 1999 278 2556 63 2 2 5 4
936 936 NA 1 1999 278 3172 68 1 2 6 4
937 937 NA 1 1999 278 2426 65 2 2 5 4
938 938 NA 1 1999 110 1380 52 1 2 5 4
939 939 NA 1 1999 110 1692 56 1 2 5 4
940 940 NA 1 1999 110 2160 60 1 2 5 4
941 941 NA 1 1999 110 1236 50 2 2 5 4
942 942 NA 1 1999 110 1608 53 2 2 5 4
943 943 NA 1 1999 110 1972 57 1 2 5 4
944 944 1 1 2000 121 950 49 1 1 3 1
945 945 1 1 2000 121 1672 62 1 1 5 1
946 946 1 1 2000 121 1280 51 1 1 3 1
947 947 1 1 2000 121 1278 52 1 1 4 1
948 948 1 1 2000 121 3836 78 1 1 6 1
949 949 1 1 2000 121 1072 51 1 1 6 1
950 950 1 1 2000 293 1908 62 1 1 5 2
951 951 1 1 2000 293 1034 51 2 1 3 2
952 952 1 1 2000 237 1548 59 2 1 6 2
953 953 1 1 2000 237 420 36 1 1 5 2
954 954 1 1 2000 285 1680 58 2 1 6 3
955 955 1 1 2000 285 1826 59 1 1 6 3
956 956 1 1 2000 285 2020 62 1 1 6 3
957 957 1 1 2000 285 1418 53 2 1 4 3
958 958 1 1 2000 285 1954 60 1 1 5 3
959 959 1 1 2000 285 1344 53 1 1 4 3
960 960 1 1 2000 285 954 49 2 1 3 3
961 961 1 1 2000 270 432 36 1 1 2 4
962 962 1 1 2000 260 1396 56 1 1 5 4
963 963 1 1 2000 121 2094 61 1 2 6 1
964 964 1 1 2000 121 3388 76 2 2 8 1
965 965 1 1 2000 102 2414 63 2 2 8 2
966 966 1 1 2000 293 4240 82 2 2 9 2
967 967 1 1 2000 237 3594 71 2 2 8 2
968 968 1 1 2000 285 2296 60 2 2 5 3
969 969 1 1 2000 285 2390 64 2 2 6 3
970 970 1 1 2000 285 2724 64 1 3 6 3
971 971 2 1 2000 121 1506 56 2 1 4 1
972 972 2 1 2000 121 6020 89 2 1 8 1
973 973 2 1 2000 102 940 45 2 1 3 2
974 974 2 1 2000 102 3892 69 2 1 7 2
975 975 2 1 2000 102 542 40 1 1 4 2
976 976 2 1 2000 285 2150 64 2 1 6 3
977 977 2 1 2000 285 1348 54 1 1 5 3
978 978 2 1 2000 285 1170 52 2 1 4 3
979 979 2 1 2000 270 2908 69 2 1 5 4
980 980 2 1 2000 270 554 40 2 1 3 4
981 981 2 1 2000 146 764 42 1 1 3 3
982 982 2 1 2000 121 2404 61 1 2 6 1
983 983 2 1 2000 121 2576 67 2 2 6 1
984 984 2 1 2000 121 2676 65 1 4 5 1
985 985 2 1 2000 146 2182 60 1 4 6 3
986 986 2 1 2000 146 1984 59 1 4 7 3
987 987 3 1 2000 121 2710 69 1 1 5 1
988 988 3 1 2000 102 1258 53 2 1 4 2
989 989 3 1 2000 285 2148 62 2 1 5 3
990 990 3 1 2000 285 3364 72 2 1 5 3
991 991 3 1 2000 270 3200 69 2 1 5 4
992 992 3 1 2000 260 990 51 1 1 5 4
993 993 3 1 2000 146 3258 73 1 1 7 3
994 994 3 1 2000 121 4310 74 1 2 6 1
995 995 3 1 2000 121 6600 92 1 2 7 1
996 996 3 1 2000 270 2162 60 2 2 7 4
997 997 3 1 2000 121 2582 61 2 3 5 1
998 998 3 1 2000 121 2778 62 1 4 6 1
999 999 3 1 2000 270 3152 69 1 4 6 4
1000 1000 3 1 2000 146 3200 66 2 4 7 3
1001 1001 3 1 2000 146 2236 64 1 4 4 3
1002 1002 4 1 2000 121 2234 63 1 1 5 1
1003 1003 4 1 2000 102 932 48 2 1 4 2
1004 1004 4 1 2000 237 1802 56 2 1 5 2
1005 1005 4 1 2000 237 870 47 2 1 4 2
1006 1006 4 1 2000 237 1660 55 1 1 4 2
1007 1007 4 1 2000 270 1748 58 2 1 4 4
1008 1008 4 1 2000 146 3372 72 2 1 5 3
1009 1009 4 1 2000 121 2160 59 1 2 6 1
1010 1010 4 1 2000 121 2736 62 1 2 5 1
1011 1011 4 1 2000 121 1286 52 2 2 6 1
1012 1012 4 1 2000 121 1652 55 1 4 6 1
1013 1013 4 1 2000 121 2032 59 1 4 6 1
1014 1014 4 1 2000 260 2804 68 1 4 5 4
1015 1015 5 1 2000 121 600 41 1 1 2 1
1016 1016 5 1 2000 285 3708 71 1 1 7 3
1017 1017 5 1 2000 270 472 38 2 1 3 4
1018 1018 5 1 2000 146 3622 78 2 1 8 3
1019 1019 5 1 2000 146 856 45 1 1 4 3
1020 1020 5 1 2000 121 2094 60 2 2 5 1
1021 1021 5 1 2000 121 4824 79 1 4 7 1
1022 1022 5 1 2000 260 3328 71 1 4 5 4
1023 1023 5 1 2000 146 2146 60 1 4 7 3
1024 1024 6 1 2000 102 902 45 2 1 3 2
1025 1025 6 1 2000 285 1052 51 2 1 4 3
1026 1026 6 1 2000 260 492 38 2 1 2 4
1027 1027 7 1 2000 260 828 46 1 1 3 4
1028 1028 7 1 2000 121 3012 66 2 2 6 1
1029 1029 7 1 2000 146 3002 70 1 4 5 3
1030 1030 8 1 2000 121 986 49 2 1 4 1
1031 1031 8 1 2000 121 988 49 1 1 4 1
1032 1032 8 1 2000 285 1952 60 1 1 5 3
1033 1033 8 1 2000 260 1936 58 2 1 4 4
1034 1034 8 1 2000 146 790 46 1 1 3 3
1035 1035 8 1 2000 146 682 43 2 1 3 3
1036 1036 8 1 2000 260 1712 55 2 2 4 4
1037 1037 8 1 2000 121 2762 65 1 4 6 1
1038 1038 9 1 2000 121 3040 70 1 1 6 1
1039 1039 9 1 2000 237 2490 66 1 1 8 2
1040 1040 9 1 2000 270 756 43 2 1 4 4
1041 1041 10 1 2000 121 726 43 1 1 3 1
1042 1042 10 1 2000 270 278 33 1 1 2 4
1043 1043 11 1 2000 260 1262 53 1 1 4 4
1044 1044 11 1 2000 260 442 35 2 1 3 4
1045 1045 12 1 2000 285 506 38 2 1 3 3
1046 1046 12 1 2000 285 686 44 2 1 3 3
1047 1047 12 1 2000 270 190 28 2 1 2 4
1048 1048 12 1 2000 260 444 35 1 1 3 4
1049 1049 13 1 2000 146 186 29 2 1 3 3
1050 1050 14 1 2000 260 2554 60 1 1 5 4
1051 1051 14 1 2000 121 2426 63 1 2 6 1
1052 1052 14 1 2000 121 2570 68 2 2 6 1
1053 1053 15 1 2000 121 1926 58 1 2 6 1
1054 1054 17 1 2000 260 2374 67 2 1 6 4
1055 1055 19 1 2000 121 1946 58 2 2 5 1
1056 1056 20 1 2000 121 1664 58 1 1 4 1
1057 1057 20 1 2000 260 2188 61 2 2 7 4
1058 1058 22 1 2000 270 1344 54 2 1 4 4
1059 1059 26 1 2000 285 1106 53 2 1 6 3
1060 1060 26 1 2000 270 1120 49 1 1 3 4
1061 1061 27 1 2000 270 1672 53 2 2 5 4
1062 1062 28 1 2000 260 2096 63 1 4 5 4
1063 1063 30 1 2000 260 3008 67 1 1 5 4
1064 1064 30 1 2000 260 418 38 2 1 4 4
1065 1065 30 1 2000 146 974 47 1 1 4 3
1066 1066 31 1 2000 146 700 43 2 1 3 3
1067 1067 31 1 2000 260 5658 80 1 2 6 4
1068 1068 35 1 2000 270 1304 51 2 1 4 4
1069 1069 39 1 2000 285 1430 57 2 1 6 3
1070 1070 40 1 2000 270 1432 53 1 1 5 4
1071 1071 43 1 2000 270 292 34 2 1 2 4
1072 1072 43 1 2000 146 6314 93 1 4 9 3
1073 1073 44 1 2000 270 1548 55 1 1 5 4
1074 1074 45 1 2000 285 1768 60 1 1 6 3
1075 1075 45 1 2000 260 1138 51 1 1 4 4
1076 1076 49 1 2000 270 1072 48 2 1 4 4
1077 1077 52 1 2000 270 1096 49 2 1 5 4
1078 1078 56 1 2000 146 198 29 2 1 2 3
1079 1079 56 1 2000 121 1488 54 2 2 5 1
1080 1080 58 1 2000 270 550 41 1 1 3 4
1081 1081 67 1 2000 102 1250 54 2 1 6 2
1082 1082 67 1 2000 260 2088 60 2 1 5 4
1083 1083 71 1 2000 146 234 30 2 1 2 3
1084 1084 81 1 2000 260 380 35 2 1 2 4
1085 1085 186 1 2000 146 92 22 1 1 1 3
1086 1086 210 1 2000 260 444 37 1 1 2 4
1087 1087 223 1 2000 270 434 36 2 1 3 4
1088 1088 1 1 2001 90 3754 72 1 1 5 1
1089 1089 1 1 2001 199 2472 67 2 1 6 2
1090 1090 1 1 2001 199 984 48 2 1 3 2
1091 1091 1 1 2001 199 2410 62 1 1 6 2
1092 1092 1 1 2001 199 3314 77 1 1 6 2
1093 1093 1 1 2001 199 1448 56 2 1 5 2
1094 1094 1 1 2001 199 3578 71 2 1 5 2
1095 1095 1 1 2001 98 1860 57 1 1 3 3
1096 1096 1 1 2001 220 3412 68 1 1 5 4
1097 1097 1 1 2001 125 2348 68 1 1 5 4
1098 1098 1 1 2001 125 3146 72 2 1 6 4
1099 1099 1 1 2001 140 836 46 1 1 3 4
1100 1100 1 1 2001 140 744 44 1 1 3 4
1101 1101 1 1 2001 140 620 43 2 1 3 4
1102 1102 1 1 2001 140 748 45 2 1 3 4
1103 1103 1 1 2001 140 938 51 1 1 3 4
1104 1104 1 1 2001 228 1558 58 1 1 5 4
1105 1105 1 1 2001 228 910 49 2 1 3 4
1106 1106 1 1 2001 228 600 40 1 1 3 4
1107 1107 1 1 2001 228 1104 52 1 1 4 4
1108 1108 1 1 2001 180 1940 59 1 1 5 3
1109 1109 1 1 2001 193 1266 56 2 1 5 3
1110 1110 1 1 2001 193 266 32 2 1 2 3
1111 1111 1 1 2001 193 414 35 2 1 2 3
1112 1112 1 1 2001 193 274 33 1 1 2 3
1113 1113 1 1 2001 122 1238 54 1 1 5 3
1114 1114 1 1 2001 122 1490 59 2 1 5 3
1115 1115 1 1 2001 122 1478 55 1 1 4 3
1116 1116 1 1 2001 122 2222 68 2 1 5 3
1117 1117 1 1 2001 122 2138 65 2 1 6 3
1118 1118 1 1 2001 122 1730 56 1 1 5 3
1119 1119 1 1 2001 256 1772 61 2 1 5 3
1120 1120 1 1 2001 276 1276 53 2 1 4 2
1121 1121 1 1 2001 276 2592 68 1 1 6 2
1122 1122 1 1 2001 256 2284 57 2 2 6 3
1123 1123 1 1 2001 98 1936 58 2 4 5 3
1124 1124 1 1 2001 125 6044 84 2 4 7 4
1125 1125 1 1 2001 125 6172 84 2 4 7 4
1126 1126 1 1 2001 140 5442 85 2 4 8 4
1127 1127 1 1 2001 140 4098 79 1 4 6 4
1128 1128 1 1 2001 140 3990 72 2 4 6 4
1129 1129 1 1 2001 256 1988 59 1 4 5 3
1130 1130 1 1 2001 276 5732 82 1 4 7 2
1131 1131 2 1 2001 112 252 29 2 1 2 1
1132 1132 2 1 2001 112 198 27 2 1 1 1
1133 1133 2 1 2001 199 3660 72 1 1 6 2
1134 1134 2 1 2001 199 1194 52 1 1 4 2
1135 1135 2 1 2001 220 1246 53 1 1 3 4
1136 1136 2 1 2001 125 1760 61 1 1 4 4
1137 1137 2 1 2001 228 570 42 1 1 3 4
1138 1138 2 1 2001 228 970 49 1 1 3 4
1139 1139 2 1 2001 193 1350 54 1 1 4 3
1140 1140 2 1 2001 122 2114 63 1 1 5 3
1141 1141 2 1 2001 122 1520 56 2 1 5 3
1142 1142 2 1 2001 256 1602 56 1 1 4 3
1143 1143 2 1 2001 256 1812 56 1 1 6 3
1144 1144 2 1 2001 260 968 49 1 1 3 2
1145 1145 2 1 2001 110 560 41 1 1 2 2
1146 1146 2 1 2001 110 1074 57 2 1 4 2
1147 1147 2 1 2001 140 2164 59 2 2 5 4
1148 1148 2 1 2001 125 4076 76 2 4 6 4
1149 1149 2 1 2001 140 NA NA 1 4 9 4
1150 1150 2 1 2001 122 2192 60 2 4 7 3
1151 1151 2 1 2001 256 2808 65 1 4 6 3
1152 1152 2 1 2001 276 7888 94 2 4 9 2
1153 1153 3 1 2001 112 398 34 2 1 2 1
1154 1154 3 1 2001 140 748 44 1 1 3 4
1155 1155 3 1 2001 140 302 34 2 1 2 4
1156 1156 3 1 2001 140 366 34 1 1 2 4
1157 1157 3 1 2001 228 768 45 2 1 4 4
1158 1158 3 1 2001 228 1636 58 1 1 5 4
1159 1159 3 1 2001 228 596 41 2 1 3 4
1160 1160 3 1 2001 180 778 44 1 1 3 3
1161 1161 3 1 2001 193 1334 52 2 1 4 3
1162 1162 3 1 2001 283 66 19 2 1 1 2
1163 1163 3 1 2001 110 1738 65 2 1 4 2
1164 1164 3 1 2001 112 4432 80 1 4 7 1
1165 1165 3 1 2001 140 2154 63 1 4 5 4
1166 1166 3 1 2001 140 1994 61 2 4 5 4
1167 1167 3 1 2001 228 4938 81 2 4 7 4
1168 1168 3 1 2001 256 3412 74 1 4 5 3
1169 1169 4 1 2001 220 1094 52 1 1 4 4
1170 1170 4 1 2001 220 1042 50 2 1 5 4
1171 1171 4 1 2001 220 1588 58 1 1 4 4
1172 1172 4 1 2001 140 444 38 1 1 2 4
1173 1173 4 1 2001 140 760 44 1 1 4 4
1174 1174 4 1 2001 228 546 39 2 1 3 4
1175 1175 4 1 2001 180 886 50 2 1 5 3
1176 1176 4 1 2001 122 1060 49 1 1 4 3
1177 1177 4 1 2001 260 1476 55 2 1 4 2
1178 1178 4 1 2001 228 1820 56 2 2 5 4
1179 1179 4 1 2001 110 4494 78 2 2 6 2
1180 1180 4 1 2001 140 6478 92 1 4 9 4
1181 1181 4 1 2001 180 3074 64 2 4 7 3
1182 1182 4 1 2001 122 2286 63 1 4 7 3
1183 1183 5 1 2001 220 2556 60 1 1 5 4
1184 1184 5 1 2001 140 480 39 1 1 3 4
1185 1185 5 1 2001 228 3620 74 1 1 5 4
1186 1186 5 1 2001 228 1718 59 2 1 6 4
1187 1187 5 1 2001 122 636 44 2 1 3 3
1188 1188 5 1 2001 256 1938 64 2 1 6 3
1189 1189 5 1 2001 283 2650 65 1 1 5 2
1190 1190 5 1 2001 140 2306 60 2 2 7 4
1191 1191 5 1 2001 283 3244 71 2 2 6 2
1192 1192 5 1 2001 140 2604 63 1 4 8 4
1193 1193 6 1 2001 125 2056 63 1 1 4 4
1194 1194 6 1 2001 228 556 41 2 1 3 4
1195 1195 6 1 2001 122 1392 53 1 1 4 3
1196 1196 6 1 2001 276 1252 51 1 1 3 2
1197 1197 6 1 2001 276 366 36 2 1 3 2
1198 1198 6 1 2001 260 1594 53 2 2 4 2
1199 1199 6 1 2001 112 4286 78 2 4 6 1
1200 1200 6 1 2001 199 3716 78 2 4 7 2
1201 1201 7 1 2001 140 1014 47 1 1 4 4
1202 1202 7 1 2001 228 388 37 1 1 3 4
1203 1203 7 1 2001 276 2708 65 1 1 6 2
1204 1204 8 1 2001 199 2640 67 1 1 6 2
1205 1205 8 1 2001 228 416 38 1 1 4 4
1206 1206 8 1 2001 122 2754 70 1 1 6 3
1207 1207 8 1 2001 256 1360 54 1 1 4 3
1208 1208 8 1 2001 256 746 42 2 1 3 3
1209 1209 8 1 2001 110 786 45 1 1 3 2
1210 1210 8 1 2001 140 3398 67 1 2 7 4
1211 1211 8 1 2001 140 2952 67 2 2 6 4
1212 1212 9 1 2001 228 1688 62 2 1 5 4
1213 1213 9 1 2001 193 386 37 1 1 3 3
1214 1214 9 1 2001 283 2916 67 2 4 7 2
1215 1215 10 1 2001 140 504 39 2 1 2 4
1216 1216 10 1 2001 228 698 43 2 1 3 4
1217 1217 10 1 2001 228 2310 59 2 1 4 4
1218 1218 10 1 2001 228 798 46 2 1 3 4
1219 1219 10 1 2001 193 446 39 2 1 3 3
1220 1220 11 1 2001 256 902 49 2 1 4 3
1221 1221 13 1 2001 125 1828 64 2 1 6 4
1222 1222 13 1 2001 140 718 43 1 1 3 4
1223 1223 13 1 2001 228 382 37 2 1 3 4
1224 1224 14 1 2001 112 560 39 1 1 2 1
1225 1225 14 1 2001 256 444 36 2 1 3 3
1226 1226 14 1 2001 140 2602 65 1 4 7 4
1227 1227 16 1 2001 260 3566 71 1 4 7 2
1228 1228 17 1 2001 140 1542 55 2 1 4 4
1229 1229 17 1 2001 122 146 26 2 1 2 3
1230 1230 18 1 2001 228 692 42 2 1 3 4
1231 1231 18 1 2001 260 652 43 1 1 3 2
1232 1232 18 1 2001 256 2514 64 1 2 7 3
1233 1233 19 1 2001 260 2246 67 1 1 5 2
1234 1234 20 1 2001 228 244 31 1 1 2 4
1235 1235 20 1 2001 140 5900 84 1 4 9 4
1236 1236 30 1 2001 228 1004 48 2 1 3 4
1237 1237 34 1 2001 140 1408 52 2 2 6 4
1238 1238 36 1 2001 140 2052 60 2 2 6 4
1239 1239 40 1 2001 256 1962 61 2 1 5 3
1240 1240 42 1 2001 228 372 34 1 1 4 4
1241 1241 45 1 2001 256 1472 53 2 4 5 3
1242 1242 46 1 2001 220 660 43 1 1 3 4
1243 1243 46 1 2001 122 256 32 2 1 2 3
1244 1244 49 1 2001 140 1558 55 1 4 5 4
1245 1245 50 1 2001 228 484 38 2 1 3 4
1246 1246 55 1 2001 228 704 45 1 1 4 4
1247 1247 75 1 2001 140 884 46 2 1 3 4
1248 1248 84 1 2001 260 910 48 2 1 4 2
1249 1249 89 1 2001 260 1414 56 1 1 6 2
1250 1250 90 1 2001 228 224 31 1 1 2 4
1251 1251 104 1 2001 140 690 43 2 1 3 4
1252 1252 125 1 2001 140 754 44 2 1 3 4
1253 1253 128 1 2001 140 1270 55 2 4 7 4
1254 1254 257 1 2001 228 370 35 2 1 3 4
WL2
1 19.24
2 18.72
3 19.71
4 17.94
5 3.40
6 6.80
7 4.94
8 1481.48
9 862.96
10 591.60
11 704.32
12 256.27
13 308.36
14 174.60
15 723.46
16 322.38
17 1268.77
18 694.85
19 655.49
20 769.42
21 660.02
22 505.02
23 96.33
24 1048.55
25 880.10
26 790.02
27 707.84
28 1010.75
29 687.58
30 666.60
31 743.38
32 64.40
33 52.02
34 55.65
35 44.16
36 9.24
37 238.76
38 419.76
39 372.35
40 394.68
41 352.41
42 453.20
43 345.27
44 504.90
45 337.08
46 340.00
47 210.60
48 453.75
49 398.56
50 241.92
51 206.08
52 1025.44
53 86.95
54 98.80
55 89.30
56 108.81
57 1045.84
58 437.76
59 574.80
60 51.20
61 282.24
62 346.68
63 1884.80
64 654.60
65 239.12
66 73.44
67 36.30
68 132.02
69 105.30
70 53.79
71 49.50
72 33.64
73 184.95
74 148.78
75 78.84
76 71.05
77 36.00
78 60.86
79 90.44
80 406.45
81 476.52
82 442.96
83 68.25
84 535.72
85 1380.24
86 575.94
87 832.92
88 505.04
89 570.72
90 884.48
91 1177.14
92 722.61
93 104.88
94 383.94
95 241.58
96 88.54
97 75.60
98 46.50
99 906.51
100 300.04
101 297.96
102 752.64
103 625.20
104 241.92
105 1449.05
106 477.95
107 189.90
108 1364.56
109 954.08
110 256.15
111 202.37
112 636.23
113 505.76
114 635.40
115 168.75
116 455.30
117 53.79
118 1652.42
119 33.00
120 41.92
121 25.76
122 25.20
123 234.24
124 349.44
125 980.21
126 111.52
127 170.28
128 83.62
129 41.28
130 27.55
131 42.56
132 28.42
133 544.57
134 347.68
135 1205.23
136 314.50
137 526.68
138 317.73
139 601.21
140 1824.13
141 318.24
142 257.28
143 196.42
144 672.08
145 277.00
146 280.50
147 625.25
148 297.84
149 353.51
150 226.54
151 138.99
152 263.62
153 321.88
154 528.96
155 189.20
156 315.00
157 300.04
158 201.24
159 439.45
160 812.50
161 572.89
162 180.95
163 107.60
164 1506.18
165 210.72
166 395.45
167 469.64
168 331.25
169 312.63
170 351.39
171 270.48
172 624.33
173 793.60
174 291.21
175 95.16
176 380.05
177 505.63
178 169.65
179 493.49
180 679.04
181 114.76
182 903.50
183 741.76
184 356.16
185 502.20
186 303.16
187 268.26
188 579.69
189 141.54
190 202.57
191 122.40
192 808.96
193 416.90
194 212.91
195 82.46
196 26.39
197 35.65
198 29.00
199 32.19
200 35.70
201 24.64
202 29.70
203 24.36
204 23.80
205 30.60
206 848.64
207 299.50
208 1379.25
209 259.00
210 1057.77
211 116.40
212 236.64
213 145.64
214 44.55
215 240.10
216 345.80
217 65.52
218 1084.60
219 131.46
220 181.24
221 246.84
222 356.94
223 378.00
224 226.08
225 292.56
226 100.00
227 48.84
228 24.36
229 66.60
230 409.16
231 402.80
232 554.48
233 280.28
234 375.36
235 361.59
236 325.85
237 222.78
238 744.90
239 807.03
240 469.70
241 459.25
242 495.90
243 742.76
244 1184.56
245 926.72
246 470.80
247 506.73
248 495.00
249 1573.11
250 505.02
251 663.40
252 273.42
253 516.32
254 342.72
255 299.70
256 701.82
257 540.56
258 322.83
259 265.09
260 931.77
261 1055.34
262 759.45
263 1266.30
264 1031.56
265 695.64
266 482.35
267 24.92
268 426.06
269 628.35
270 326.00
271 1516.26
272 2811.60
273 3534.30
274 0.00
275 2973.88
276 968.50
277 1446.48
278 803.88
279 375.87
280 458.28
281 195.05
282 238.08
283 110.40
284 505.76
285 140.28
286 80.64
287 73.80
288 311.61
289 415.26
290 874.20
291 273.42
292 1521.75
293 108.80
294 69.65
295 100.23
296 269.76
297 249.12
298 389.55
299 1630.50
300 79.20
301 585.28
302 599.63
303 268.03
304 226.78
305 1196.35
306 211.60
307 790.02
308 231.71
309 505.04
310 98.67
311 185.68
312 45.26
313 354.64
314 264.00
315 488.88
316 1392.93
317 425.15
318 1185.80
319 365.20
320 60.86
321 370.15
322 1777.50
323 608.17
324 218.55
325 86.26
326 491.26
327 383.35
328 225.89
329 680.76
330 511.53
331 242.32
332 1489.60
333 385.32
334 634.84
335 411.04
336 834.15
337 323.83
338 31.20
339 386.10
340 697.97
341 174.68
342 51.81
343 86.64
344 104.14
345 957.43
346 35.67
347 44.16
348 349.35
349 965.47
350 585.00
351 764.82
352 437.94
353 1892.16
354 1606.64
355 1158.51
356 723.84
357 1776.71
358 1707.09
359 2135.64
360 0.00
361 563.92
362 1733.60
363 537.51
364 2934.75
365 2.89
366 183.61
367 546.36
368 339.66
369 486.75
370 546.06
371 378.95
372 286.50
373 519.84
374 287.63
375 323.40
376 312.63
377 545.40
378 224.66
379 60.39
380 41.70
381 41.85
382 241.11
383 283.71
384 61.95
385 220.34
386 41.54
387 115.20
388 652.20
389 90.00
390 192.60
391 128.00
392 22.36
393 68.60
394 55.42
395 26.32
396 30.80
397 22.10
398 1003.68
399 686.07
400 182.83
401 437.36
402 164.26
403 400.95
404 658.98
405 237.16
406 249.60
407 1038.50
408 64.01
409 97.66
410 1072.36
411 345.27
412 1119.67
413 499.14
414 203.78
415 94.38
416 38.72
417 355.32
418 776.16
419 504.45
420 176.30
421 432.88
422 559.20
423 617.14
424 966.14
425 399.09
426 282.73
427 486.00
428 352.56
429 400.14
430 290.57
431 418.55
432 412.56
433 122.00
434 631.78
435 212.52
436 72.72
437 251.37
438 282.54
439 387.43
440 395.82
441 418.88
442 438.48
443 503.40
444 540.02
445 767.65
446 657.72
447 271.46
448 254.80
449 172.80
450 191.36
451 381.70
452 246.72
453 129.97
454 96.52
455 1099.08
456 817.08
457 195.51
458 139.32
459 111.11
460 88.14
461 60.52
462 29.29
463 28.13
464 13.20
465 10.81
466 16.90
467 4.94
468 3.40
469 4.14
470 372.32
471 706.80
472 319.28
473 103.36
474 144.06
475 91.08
476 162.97
477 339.00
478 233.59
479 434.16
480 238.29
481 111.15
482 156.20
483 1006.07
484 625.58
485 497.61
486 842.16
487 197.40
488 37.20
489 16.50
490 30.74
491 18.50
492 20.52
493 1213.92
494 786.76
495 512.40
496 343.44
497 190.08
498 792.66
499 437.80
500 616.14
501 238.76
502 30.16
503 17.50
504 362.88
505 572.18
506 149.21
507 22.14
508 4.14
509 3.23
510 1000.31
511 216.00
512 322.40
513 196.88
514 249.60
515 91.58
516 905.28
517 174.60
518 179.52
519 796.25
520 421.85
521 726.02
522 434.16
523 769.36
524 70.92
525 95.38
526 847.98
527 339.08
528 342.38
529 230.77
530 1242.46
531 63.00
532 92.04
533 20.02
534 357.76
535 789.88
536 435.78
537 350.37
538 409.32
539 221.76
540 801.99
541 368.16
542 73.50
543 265.68
544 276.85
545 1231.10
546 647.40
547 466.02
548 502.17
549 316.20
550 438.35
551 300.90
552 315.18
553 220.00
554 752.22
555 460.08
556 302.82
557 372.59
558 412.50
559 375.30
560 363.58
561 1206.10
562 885.30
563 512.43
564 454.14
565 4308.02
566 797.27
567 520.98
568 881.76
569 513.30
570 107.16
571 790.02
572 1215.20
573 798.72
574 980.85
575 624.60
576 479.92
577 322.42
578 256.22
579 492.25
580 1138.13
581 627.76
582 694.40
583 627.60
584 1314.72
585 502.70
586 630.71
587 700.56
588 499.52
589 414.40
590 534.24
591 368.00
592 1277.19
593 410.75
594 1526.25
595 549.84
596 1298.59
597 1391.94
598 3271.50
599 3224.31
600 2094.28
601 1421.28
602 1049.49
603 1175.76
604 702.45
605 803.88
606 5044.95
607 1045.80
608 1713.80
609 1018.08
610 990.26
611 890.10
612 885.06
613 0.00
614 1940.54
615 1507.45
616 682.00
617 3016.65
618 1006.34
619 2419.82
620 1671.54
621 1825.60
622 577.02
623 720.44
624 677.66
625 3459.84
626 928.62
627 1564.80
628 899.57
629 910.14
630 368.82
631 883.20
632 3295.11
633 1846.26
634 1551.92
635 2445.24
636 2972.06
637 3414.08
638 3875.96
639 1932.34
640 1129.31
641 2407.20
642 1166.24
643 808.69
644 1164.84
645 1255.28
646 1087.50
647 1258.12
648 1133.87
649 3791.96
650 1239.93
651 805.12
652 1062.60
653 539.85
654 1084.20
655 635.43
656 404.88
657 1887.30
658 268.84
659 590.40
660 399.36
661 67.68
662 256.80
663 11.50
664 1388.98
665 1020.60
666 497.04
667 103.23
668 424.44
669 226.00
670 307.02
671 409.75
672 63.35
673 136.50
674 527.80
675 380.60
676 510.00
677 386.96
678 185.85
679 154.37
680 164.69
681 131.46
682 927.95
683 1548.88
684 636.00
685 570.72
686 559.12
687 3370.64
688 0.00
689 314.00
690 499.89
691 1259.98
692 650.40
693 1239.12
694 663.16
695 846.95
696 148.26
697 722.24
698 236.16
699 431.20
700 37.82
701 466.69
702 690.06
703 393.26
704 189.88
705 213.38
706 222.72
707 66.30
708 259.21
709 357.75
710 36.58
711 342.10
712 363.00
713 581.40
714 611.65
715 305.24
716 346.09
717 541.14
718 548.34
719 669.69
720 534.66
721 393.12
722 834.56
723 528.08
724 381.07
725 487.30
726 593.54
727 22.96
728 90.44
729 422.76
730 74.88
731 44.95
732 66.24
733 47.36
734 148.35
735 143.22
736 596.40
737 342.91
738 2241.00
739 448.80
740 591.00
741 770.56
742 0.00
743 1226.40
744 487.08
745 1647.68
746 1502.27
747 99.06
748 88.92
749 304.98
750 132.30
751 1847.61
752 111.93
753 528.24
754 741.76
755 395.01
756 251.50
757 24.94
758 30.60
759 86.58
760 643.20
761 401.85
762 851.50
763 471.35
764 466.95
765 619.38
766 102.09
767 166.84
768 397.65
769 672.00
770 631.96
771 677.04
772 423.90
773 815.92
774 498.96
775 322.91
776 77.70
777 47.36
778 730.24
779 589.62
780 474.44
781 589.41
782 101.20
783 343.20
784 511.86
785 748.16
786 456.84
787 118.02
788 558.32
789 792.32
790 312.00
791 364.50
792 503.27
793 1130.72
794 186.76
795 368.28
796 3078.80
797 48.84
798 155.70
799 272.64
800 516.42
801 806.68
802 317.73
803 182.88
804 958.12
805 584.40
806 59.76
807 1224.75
808 140.70
809 29.87
810 708.66
811 528.64
812 572.79
813 600.62
814 220.01
815 661.12
816 239.61
817 491.34
818 287.50
819 37.80
820 314.28
821 90.87
822 744.00
823 411.48
824 347.68
825 215.26
826 82.08
827 269.50
828 713.62
829 225.13
830 393.26
831 328.64
832 273.50
833 76.22
834 417.45
835 222.31
836 99.45
837 649.59
838 585.39
839 124.80
840 566.06
841 558.14
842 600.88
843 586.20
844 98.40
845 152.22
846 30.00
847 402.80
848 193.66
849 112.40
850 299.16
851 28.71
852 589.86
853 29.70
854 368.16
855 329.13
856 470.96
857 228.34
858 275.87
859 303.31
860 442.96
861 872.44
862 182.62
863 390.88
864 588.82
865 355.63
866 70.67
867 26.10
868 313.23
869 153.00
870 21.84
871 157.08
872 86.64
873 705.16
874 20.79
875 327.42
876 69.48
877 386.37
878 142.76
879 29.10
880 54.40
881 29.87
882 502.28
883 24.92
884 324.48
885 138.18
886 35.40
887 1432.97
888 1257.90
889 287.04
890 369.36
891 537.41
892 322.40
893 140.28
894 1078.18
895 482.90
896 520.98
897 897.60
898 376.20
899 550.20
900 75.60
901 606.00
902 575.23
903 1084.88
904 531.92
905 429.55
906 1020.68
907 381.24
908 330.00
909 59.76
910 321.30
911 192.15
912 285.00
913 241.08
914 136.92
915 121.80
916 92.82
917 63.00
918 496.20
919 544.73
920 218.88
921 814.05
922 39.06
923 25.52
924 662.16
925 224.42
926 102.57
927 63.72
928 75.24
929 62.30
930 140.70
931 183.60
932 56.70
933 37.44
934 31.93
935 805.14
936 1078.48
937 788.45
938 358.80
939 473.76
940 648.00
941 309.00
942 426.12
943 562.02
944 232.75
945 518.32
946 326.40
947 332.28
948 1496.04
949 273.36
950 591.48
951 263.67
952 456.66
953 75.60
954 487.20
955 538.67
956 626.20
957 375.77
958 586.20
959 356.16
960 233.73
961 77.76
962 390.88
963 638.67
964 1287.44
965 760.41
966 1738.40
967 1275.87
968 688.80
969 764.80
970 871.68
971 421.68
972 2678.90
973 211.50
974 1342.74
975 108.40
976 688.00
977 363.96
978 304.20
979 1003.26
980 110.80
981 160.44
982 733.22
983 862.96
984 869.70
985 654.60
986 585.28
987 934.95
988 333.37
989 665.88
990 1211.04
991 1104.00
992 252.45
993 1189.17
994 1594.70
995 3036.00
996 648.60
997 787.51
998 861.18
999 1087.44
1000 1056.00
1001 715.52
1002 703.71
1003 223.68
1004 504.56
1005 204.45
1006 456.50
1007 506.92
1008 1213.92
1009 637.20
1010 848.16
1011 334.36
1012 454.30
1013 599.44
1014 953.36
1015 123.00
1016 1316.34
1017 89.68
1018 1412.58
1019 192.60
1020 628.20
1021 1905.48
1022 1181.44
1023 643.80
1024 202.95
1025 268.26
1026 93.48
1027 190.44
1028 993.96
1029 1050.70
1030 241.57
1031 242.06
1032 585.60
1033 561.44
1034 181.70
1035 146.63
1036 470.80
1037 897.65
1038 1064.00
1039 821.70
1040 162.54
1041 156.09
1042 45.87
1043 334.43
1044 77.35
1045 96.14
1046 150.92
1047 26.60
1048 77.70
1049 26.97
1050 766.20
1051 764.19
1052 873.80
1053 558.54
1054 795.29
1055 564.34
1056 482.56
1057 667.34
1058 362.88
1059 293.09
1060 274.40
1061 443.08
1062 660.24
1063 1007.68
1064 79.42
1065 228.89
1066 150.50
1067 2263.20
1068 332.52
1069 407.55
1070 379.48
1071 49.64
1072 2936.01
1073 425.70
1074 530.40
1075 290.19
1076 257.28
1077 268.52
1078 28.71
1079 401.76
1080 112.75
1081 337.50
1082 626.40
1083 35.10
1084 66.50
1085 10.12
1086 82.14
1087 78.12
1088 1351.44
1089 828.12
1090 236.16
1091 747.10
1092 1275.89
1093 405.44
1094 1270.19
1095 530.10
1096 1160.08
1097 798.32
1098 1132.56
1099 192.28
1100 163.68
1101 133.30
1102 168.30
1103 239.19
1104 451.82
1105 222.95
1106 120.00
1107 287.04
1108 572.30
1109 354.48
1110 42.56
1111 72.45
1112 45.21
1113 334.26
1114 439.55
1115 406.45
1116 755.48
1117 694.85
1118 484.40
1119 540.46
1120 338.14
1121 881.28
1122 650.94
1123 561.44
1124 2538.48
1125 2592.24
1126 2312.85
1127 1618.71
1128 1436.40
1129 586.46
1130 2350.12
1131 36.54
1132 26.73
1133 1317.60
1134 310.44
1135 330.19
1136 536.80
1137 119.70
1138 237.65
1139 364.50
1140 665.91
1141 425.60
1142 448.56
1143 507.36
1144 237.16
1145 114.80
1146 306.09
1147 638.38
1148 1548.88
1149 0.00
1150 657.60
1151 912.60
1152 3707.36
1153 67.66
1154 164.56
1155 51.34
1156 62.22
1157 172.80
1158 474.44
1159 122.18
1160 171.16
1161 346.84
1162 6.27
1163 564.85
1164 1772.80
1165 678.51
1166 608.17
1167 1999.89
1168 1262.44
1169 284.44
1170 260.50
1171 460.52
1172 84.36
1173 167.20
1174 106.47
1175 221.50
1176 259.70
1177 405.90
1178 509.60
1179 1752.66
1180 2979.88
1181 983.68
1182 720.09
1183 766.80
1184 93.60
1185 1339.40
1186 506.81
1187 139.92
1188 620.16
1189 861.25
1190 691.80
1191 1151.62
1192 820.26
1193 647.64
1194 113.98
1195 368.88
1196 319.26
1197 65.88
1198 422.41
1199 1671.54
1200 1449.24
1201 238.29
1202 71.78
1203 880.10
1204 884.40
1205 79.04
1206 963.90
1207 367.20
1208 156.66
1209 176.85
1210 1138.33
1211 988.92
1212 523.28
1213 71.41
1214 976.86
1215 98.28
1216 150.07
1217 681.45
1218 183.54
1219 86.97
1220 220.99
1221 584.96
1222 154.37
1223 70.67
1224 109.20
1225 79.92
1226 845.65
1227 1265.93
1228 424.05
1229 18.98
1230 145.32
1231 140.18
1232 804.48
1233 752.41
1234 37.82
1235 2478.00
1236 240.96
1237 366.08
1238 615.60
1239 598.41
1240 63.24
1241 390.08
1242 141.90
1243 40.96
1244 428.45
1245 91.96
1246 158.40
1247 203.32
1248 218.40
1249 395.92
1250 34.72
1251 148.35
1252 165.88
1253 349.25
1254 64.75Model
Call:
glm(formula = Prevalence ~ Length + Year + Area, family = binomial(link = "logit"),
data = cod)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.465947 0.269333 -1.730 0.083629 .
Length 0.009654 0.004468 2.161 0.030705 *
Year2000 0.566536 0.169715 3.338 0.000843 ***
Year2001 -0.680315 0.140175 -4.853 1.21e-06 ***
Area2 -0.626192 0.186617 -3.355 0.000792 ***
Area3 -0.510470 0.163396 -3.124 0.001783 **
Area4 1.233878 0.184652 6.682 2.35e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1727.8 on 1247 degrees of freedom
Residual deviance: 1537.6 on 1241 degrees of freedom
(6 observations deleted due to missingness)
AIC: 1551.6
Number of Fisher Scoring iterations: 4These are all from a linear model. Need to transform them to get the real value in probabilistic scale
Additive! One slope
How to estimate the values?
Call:
glm(formula = Prevalence ~ Length + Year + Area, family = binomial(link = "logit"),
data = cod)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.465947 0.269333 -1.730 0.083629 .
Length 0.009654 0.004468 2.161 0.030705 *
Year2000 0.566536 0.169715 3.338 0.000843 ***
Year2001 -0.680315 0.140175 -4.853 1.21e-06 ***
Area2 -0.626192 0.186617 -3.355 0.000792 ***
Area3 -0.510470 0.163396 -3.124 0.001783 **
Area4 1.233878 0.184652 6.682 2.35e-11 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 1727.8 on 1247 degrees of freedom
Residual deviance: 1537.6 on 1241 degrees of freedom
(6 observations deleted due to missingness)
AIC: 1551.6
Number of Fisher Scoring iterations: 4\[ logistic(\pi_i) = \beta_0 + \beta_1 x_{1,i}+ \beta_2 x_{2,i} + \beta_3 x_{3,i}+ \beta_4 x_{4,i} + \beta_5 x_{5,i} + \beta_6 x_{6,i} \]
Site
| Value of \(x_2\) | Value of \(x_3\) | Value of \(x_4\) | Value of \(x_5\) | Value of \(x_6\) | Value of \(x_7\) | |
|---|---|---|---|---|---|---|
| 2000 | 2001 | Area 1 | Area 2 | Area 3 | Area 4 | |
| Area-1 1999 | 0 | 0 | 0 | 0 | 0 | 0 |
| Area-1 2000 | 1 | 0 | 0 | 0 | 0 | 0 |
| Area-1 2001 | 0 | 1 | 0 | 0 | 0 | 0 |
| Area-2 1999 | 0 | 0 | 0 | 1 | 0 | 0 |
| Area-2 2000 | 0 | 1 | 0 | 1 | 0 | 0 |
| Area-2 2001 | 0 | 0 | 1 | 1 | 0 | 0 |
| Area 3- 1999 | 0 | 0 | 0 | 0 | 1 | 0 |
| Area 3 -2000 | 1 | 0 | 0 | 0 | 1 | 0 |
| Area 3 - 2001 | 0 | 1 | 0 | 0 | 1 | 0 |
| Area 4 - 1999 | 0 | 0 | 0 | 0 | 0 | 1 |
| Area 4 - 2000 | 0 | 1 | 0 | 0 | 0 | 1 |
| Area 4 2001 | 0 | 0 | 1 | 0 | 0 | 1 |
Categorical
Logistic regression assumptions
Binomial distribution
Binary data (1, 0)
Poisson assumptions
Count-data
While we usually think Poisson, it has an important assumption: \(Var(y_i) = \lambda\_i\)
GLM’s other assumptions
Data is independently distributed
Error is independent