Sesame Street
Chase Rosendale, Lei Wang, Ryan Williams
September 8, 2017
Project Description
The Children’s Television Workshop is interested in finding whether Sesame Street is effective at improving children between 3-5 years old in their knowledge of letters, numbers, and forms. The data of interest that was collected includes information on the test children’s age, sex, and population site. Each child took a pretest and a post-test for their knowledge of letters, numbers, and forms.
The children were chosen from five different populations of interest: - Three to five year old disadvantaged children from inner city areas in various parts of the country - Four year old advantaged suburban children - Advantaged rural children - Disadvantaged rural children - Disadvantaged Spanish-speaking children
Variables of Interest
There were 14 variables of interest that were collected in the study. These variables included the explanatory variables: site, age, sex, view category, setting, and viewing encouraged. The pretest and post-test scores for letters, numbers, and forms were used to create the three response variables; numbers improvement, letters improvement, and form improvement. These variables were calculated using the difference of the post-test and the pretest divided by the maximum score.
| 1 |
Site |
Populations of Interest, listed in Appendix |
Nominal |
5 Levels, each level is a different population of interest |
| 2 |
Sex |
Male 1, Female 2 |
Dichotomous |
2 Levels |
| 3 |
Age |
Age in months |
Numerical Discrete |
Ranges from 34-69 |
| 4 |
Viewing Category |
Viewing categories from rarely watched to watched more than 5 times a week |
Ordinal |
Ranges from 1 to 4 |
| 5 |
Setting |
Setting in which Sesame Street was viewed |
Dichotomous |
2 levels: Home 1, School 2 |
| 6 |
Viewing Encouraged |
Whether children were encouraged to watch |
Dichotomous |
2 Levels: Encouraged 1, Not 2 |
| 7 |
Pretest Letters |
Pretest on knowledge of letters |
Numerical Discrete |
Ranges from 0-58 |
| 8 |
Pretest Numbers |
Pretest on knowledge of numbers |
Numerical Discrete |
Ranges from 0-54 |
| 9 |
Pretest Forms |
Pretest on knowledge of forms |
Numerical Discrete |
Ranges from 0-20 |
| 10 |
Posttest Letters |
Posttest knowledge of letters |
Numerical Discrete |
Ranges from 0-58 |
| 11 |
Posttest Numbers |
Posttest knowledge of numbers |
Numerical Discrete |
Ranges from 0-54 |
| 12 |
Posttest Forms |
Posttest knowledge of forms |
Numerical Discrete |
Ranges from 0-20 |
| 13 |
Numbers Improvement |
Improvement in numbers as a proportion of the maximum score |
Numerical Continuous |
Ranges from -1 to 1 |
| 14 |
Letters Improvement |
Improvement in letters as a proportion of the maximum score |
Numerical Continuous |
Ranges from -1 to 1 |
| 15 |
Forms Improvement |
Improvement in forms as a proportion of the maximum score |
Numerical Continuous |
Ranges from -1 to 1 |
Preface
This report was created using RMarkdown with a Slidy Presentation Output
Requirements to reproduce this report independantly
require(car)
require(ISwR)
require(dplyr)
require(leaps)
require(ggplot2)
require(gdata)
data1 <- read.csv("E:/OneDrive/STAT 470/Sesame_Street_Case_Study_files/sesame.csv", header = TRUE)
attach(data1)
Graphs of Post Scores to Viewing Categories
Graph of POSTLET to VIEWCAT
let <- ggplot(data2, aes(x=factor(viewcat), y=postlet))
let + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of POSTFORM to VIEWCAT
form <- ggplot(data2, aes(x=factor(viewcat), y=postform))
form + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of POSTNUMB to VIEWCAT
numb <- ggplot(data2, aes(x=factor(viewcat), y=postnumb))
numb + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graphs of Improvements from Pre to Post Scores
Graph of DIFFLET to VIEWCAT
difflet <- postlet - prelet #Creating new variable for difference between post and pre scores
dlet <- ggplot(data2, aes(x=factor(viewcat), y=difflet))
dlet + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
diffform <- postform - preform #Creating new variable for difference between post and pre scores
dform <- ggplot(data2, aes(x=factor(viewcat), y=diffform))
dform + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Graph of DIFFNUMB to VIEWCAT
diffnumb <- postnumb - prenumb #Creating new variable for difference between post and pre scores
dnumb <- ggplot(data2, aes(x=factor(viewcat), y=diffnumb))
dnumb + geom_boxplot() + geom_count(color="blue") + ggtitle("Boxplot with overlayed Density Plot") + guides(size = guide_legend("Density"))
Assumptions for this Data
Linearity:
- Cannot see a need to transform the data (see alternate plots in Appendix)
Independance
- We will assume that the children in the study were independent of one another
Normality:
Equal Variance
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 1.602861 Df = 1 p = 0.2054982
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 1.127897 Df = 1 p = 0.2882244
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.03792127 Df = 1 p = 0.8456013
## GVIF Df GVIF^(1/(2*Df))
## prenumb 3.190851 1 1.786295
## preform 2.177062 1 1.475487
## prelet 2.192919 1 1.480851
## factor(site) 1.823159 4 1.077961
## age 1.451306 1 1.204702
## sex 1.031028 1 1.015396
## viewenc 1.389976 1 1.178972
## regular 1.527805 1 1.236044
## setting 1.366760 1 1.169085
## GVIF Df GVIF^(1/(2*Df))
## prenumb 3.190851 1 1.786295
## preform 2.177062 1 1.475487
## prelet 2.192919 1 1.480851
## factor(site) 1.823159 4 1.077961
## age 1.451306 1 1.204702
## sex 1.031028 1 1.015396
## viewenc 1.389976 1 1.178972
## regular 1.527805 1 1.236044
## setting 1.366760 1 1.169085
## GVIF Df GVIF^(1/(2*Df))
## prenumb 3.190851 1 1.786295
## preform 2.177062 1 1.475487
## prelet 2.192919 1 1.480851
## factor(site) 1.823159 4 1.077961
## age 1.451306 1 1.204702
## sex 1.031028 1 1.015396
## viewenc 1.389976 1 1.178972
## regular 1.527805 1 1.236044
## setting 1.366760 1 1.169085
- All values are within an acceptable range
Questions 1 and 2:
Testing A Model for Improvement In Factors
testmodel <- lm(diffform ~ factor(site) + sex + age + factor(viewcat) + setting + viewenc +
agecat + encour, data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
diffformmodel <- lm(diffform ~ factor(viewcat), data = data2)
testmodel <- lm(difflet ~ factor(site) + sex + age + factor(viewcat) + setting + viewenc +
agecat + encour, data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
diffletmodel <- lm(difflet ~ factor(site) + factor(viewcat) + viewenc +
agecat, data = data2)
testmodel <- lm(diffnumb ~ factor(site) + sex + age + factor(viewcat) + setting + viewenc +
agecat + encour, data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
diffnumbmodel <- lm(diffnumb ~ factor(viewcat), data = data2)
Question 4:
- In order to find the best final model, the regression equations with predictors that produced the lowest AIC (Akaike information criterion, lower = better) were selected.
Testing A Model for Post Factors
testmodel <- lm(postnumb ~ ., data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
testmodel <- lm(postform ~ ., data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
testmodel <- lm(postlet ~ ., data = data2)#Form model
#regsubsets generates the best model for the given variables
MSE <- (summary(testmodel)$sigma)^2 #We'll need the MSE
step(testmodel, scale = MSE, direction = "both")
#Step eliminates the insignificant factors from the model
Alternate Models
These are some of the other models we tried
modelform10 <- lm(diffform ~ factor(site), data = data2)
modellet10 <- lm(difflet ~ factor(site), data = data2)
modelnumb11 <- lm(postnumb ~ log(prenumb) + factor(viewcat), data = data2)
modelform11 <- lm(postform ~ log(preform) + factor(viewcat), data = data2)
modellet11 <- lm(postlet ~ log(prelet) + factor(viewcat), data = data2)
Decision on Models
- The final models for each improvement score were determined by the models chosen by the lowest AIC score, while also ensuring that the test variables such as watching regularly, setting, and population of interest are in the final model. The following regression formulas for each improvement score is listed below.
modelnumb <- lm(diffnumb ~ factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform, data = data2)
modelform <- lm(diffform ~ factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform, data = data2)
modellet <- lm(difflet ~ factor(site,levels=c(2,3,1,4,5))+age+sex+viewenc+regular+setting+prenumb+prelet+preform, data = data2)
Checking for Influential Data Points in Our Models
We will use Cook’s Distance to find any influential points in our models
Cook’s Distance for Postnumb Model
cookdis <- cooks.distance(modelnumb) #Create variable for cook's distance
plot(cookdis, pch="*", cex=2, main="Influential Obs for Postnumb Model")
#Plot cook's distance
abline(h = 4*mean(cookdis, na.rm=T), col="red") #Add cutoff line
text(x=1:length(cookdis)+1, y=cookdis, labels=ifelse(cookdis>4*mean(cookdis, na.rm=T),names(cookdis),""), col="red") #Label any points above the cutoff line
Cook’s Distance for Postform Model
cookdis <- cooks.distance(modelform) #Create variable for cook's distance
plot(cookdis, pch="*", cex=2, main="Influential Obs for Postform Model")
#Plot cook's distance
abline(h = 4*mean(cookdis, na.rm=T), col="red") #Add cutoff line
text(x=1:length(cookdis)+1, y=cookdis, labels=ifelse(cookdis>4*mean(cookdis, na.rm=T),names(cookdis),""), col="red") #Label any points above the cutoff line
Cook’s Distance for Postlet Model
cookdis <- cooks.distance(modellet) #Create variable for cook's distance
plot(cookdis, pch="*", cex=2, main="Influential Obs for Postnumb Model")
#Plot cook's distance
abline(h = 4*mean(cookdis, na.rm=T), col="red") #Add cutoff line
text(x=1:length(cookdis)+1, y=cookdis, labels=ifelse(cookdis>4*mean(cookdis, na.rm=T),names(cookdis),""), col="red") #Label any points above the cutoff line
Check to see if removing Influential Points improves model
Original R-Squared Values (Model Correlation to Data, Higher is Better)
## [1] 0.2392241
## [1] 0.3572446
## [1] 0.4020194
New R-Squared Values with influentials removed
## [1] 0.2502526
## [1] 0.4154165
## [1] 0.4563963
As you can see, with the influentials removed, the models have a better correlation to the data, this being true, we will continue to report the models with both the influenctials removed and not removed.
Raw Data
## id site sex age viewcat setting viewenc prebody prelet preform
## 1 1 1 1 66 1 2 1 16 23 12
## 2 2 1 2 67 3 2 1 30 26 9
## 3 3 1 1 56 3 2 2 22 14 9
## 4 4 1 1 49 1 2 2 23 11 10
## 5 5 1 1 69 4 2 2 32 47 15
## 6 6 1 2 54 3 2 2 29 26 10
## 7 7 1 2 47 3 2 2 23 12 11
## 8 8 1 1 51 2 2 1 32 48 19
## 9 9 1 1 69 4 2 1 27 44 18
## 10 10 1 2 53 3 2 1 30 38 17
## 11 11 1 2 58 2 2 2 25 48 14
## 12 12 1 2 58 4 2 2 21 25 13
## 13 13 1 2 49 1 2 2 28 8 9
## 14 14 1 1 64 2 2 1 26 11 15
## 15 15 1 2 58 2 2 1 23 15 9
## 16 16 1 1 49 3 2 1 25 12 17
## 17 17 1 1 57 2 2 1 25 15 13
## 18 18 1 1 45 4 2 1 16 12 8
## 19 19 1 1 45 3 2 1 25 16 12
## 20 20 1 1 60 3 2 2 19 19 8
## 21 21 1 2 65 4 2 1 29 24 14
## 22 22 1 1 44 4 1 1 25 15 17
## 23 23 1 2 38 3 1 1 20 9 2
## 24 24 1 1 35 4 1 1 11 6 8
## 25 25 1 2 42 2 1 1 15 7 8
## 26 26 1 2 50 2 1 1 26 14 10
## 27 27 1 1 61 4 2 2 28 42 16
## 28 28 1 2 34 4 1 1 17 13 7
## 29 29 1 1 60 3 1 2 23 13 9
## 30 30 1 2 39 2 1 1 11 5 5
## 31 31 1 1 39 3 1 1 24 4 11
## 32 32 1 2 41 2 1 1 24 8 3
## 33 33 1 2 55 3 1 1 31 15 17
## 34 34 1 2 42 3 1 1 23 11 7
## 35 35 1 1 50 4 1 1 18 17 12
## 36 36 1 1 58 2 1 1 13 12 6
## 37 37 1 2 59 3 1 2 27 7 13
## 38 38 1 2 36 1 1 2 11 12 9
## 39 39 1 1 51 2 1 1 32 16 16
## 40 40 1 1 51 2 1 1 31 18 13
## 41 41 1 1 48 3 1 1 13 14 8
## 42 42 1 1 43 2 1 1 17 13 14
## 43 43 1 2 35 3 1 2 23 12 8
## 44 44 1 2 36 1 1 2 11 2 6
## 45 45 1 2 39 2 1 2 20 18 6
## 46 46 1 1 45 4 1 2 14 13 9
## 47 47 1 1 58 3 1 2 30 38 15
## 48 48 1 2 38 3 1 1 13 10 7
## 49 49 1 2 57 4 1 1 26 15 11
## 50 50 1 1 49 3 1 2 26 35 10
## 51 51 1 1 55 1 2 2 24 11 10
## 52 52 1 2 44 4 2 2 25 39 18
## 53 53 1 1 56 1 2 2 13 11 6
## 54 54 1 2 48 2 2 2 17 11 9
## 55 55 1 1 50 2 2 2 16 10 8
## 56 56 1 1 52 1 2 2 16 15 6
## 57 57 1 2 51 2 2 1 24 14 10
## 58 58 1 2 58 1 2 2 25 17 17
## 59 59 1 2 48 3 2 2 13 10 10
## 60 60 1 1 54 4 2 2 16 13 10
## 61 61 2 1 52 4 2 2 20 35 15
## 62 62 2 2 48 1 2 2 20 12 11
## 63 63 2 1 55 4 2 2 28 13 10
## 64 64 2 1 55 2 2 2 23 16 5
## 65 65 2 2 55 2 1 2 30 27 11
## 66 66 2 2 56 1 1 1 26 18 10
## 67 67 2 2 50 3 2 1 31 15 10
## 68 68 2 1 51 3 2 1 28 19 14
## 69 69 2 1 58 3 2 2 30 14 17
## 70 70 2 2 55 4 2 2 27 10 10
## 71 71 2 2 41 4 1 2 24 22 14
## 72 72 2 2 51 4 1 2 20 13 11
## 73 73 2 1 52 4 2 1 29 13 9
## 74 74 2 2 54 3 2 1 30 26 13
## 75 75 2 1 47 4 1 1 19 12 11
## 76 76 2 1 50 4 1 1 31 30 15
## 77 77 2 2 55 4 1 1 31 13 18
## 78 78 2 1 50 3 2 1 32 27 13
## 79 79 2 2 57 2 2 1 31 19 14
## 80 80 2 2 55 4 1 2 20 12 9
## 81 81 2 2 55 4 1 2 26 14 8
## 82 82 2 1 50 3 2 1 30 44 15
## 83 83 2 1 52 3 2 1 26 13 11
## 84 84 2 2 45 2 2 1 28 12 9
## 85 85 2 2 52 3 2 1 24 14 8
## 86 86 2 1 53 4 1 1 26 17 15
## 87 87 2 2 53 4 2 2 29 10 17
## 88 88 2 2 53 2 2 2 23 12 12
## 89 89 2 2 56 3 1 2 28 29 11
## 90 90 2 2 54 4 2 2 32 46 15
## 91 91 2 1 50 2 2 1 22 17 8
## 92 92 2 1 50 3 1 1 29 25 14
## 93 93 2 2 53 4 1 1 25 17 12
## 94 94 2 1 45 4 1 1 21 16 12
## 95 95 2 2 56 4 1 1 32 22 15
## 96 96 2 1 53 3 1 1 31 14 16
## 97 97 2 2 46 4 1 1 22 28 14
## 98 98 2 2 46 2 1 2 30 18 14
## 99 99 2 1 50 3 1 2 18 13 8
## 100 0 2 2 47 1 1 2 17 10 5
## 101 101 2 1 56 2 2 1 27 11 15
## 102 102 2 2 46 3 1 1 27 13 13
## 103 103 2 2 45 4 1 1 21 23 14
## 104 104 2 2 46 4 1 1 19 17 4
## 105 105 2 2 47 3 1 1 31 9 14
## 106 106 2 1 52 2 2 1 26 16 12
## 107 107 2 2 52 4 2 1 24 15 12
## 108 108 2 1 56 2 1 1 21 22 12
## 109 109 2 1 48 4 1 1 28 22 13
## 110 110 2 1 49 3 1 1 25 16 13
## 111 111 2 2 55 4 2 1 32 8 13
## 112 112 2 2 45 3 1 1 22 15 12
## 113 113 2 1 45 3 1 1 32 16 14
## 114 114 2 2 48 4 1 1 31 6 8
## 115 115 2 1 58 1 1 2 19 14 12
## 116 116 3 1 55 2 1 1 20 16 7
## 117 117 3 2 48 1 1 2 20 15 5
## 118 118 3 2 52 3 1 1 14 6 3
## 119 119 3 2 58 1 1 1 20 11 5
## 120 120 3 1 50 3 2 2 13 12 5
## 121 121 3 1 58 3 2 2 22 19 11
## 122 122 3 2 49 4 2 2 14 13 7
## 123 123 3 1 56 4 2 2 24 17 9
## 124 124 3 1 50 1 1 2 7 14 4
## 125 125 3 2 49 1 1 1 20 18 3
## 126 126 3 1 46 2 1 1 15 14 8
## 127 127 3 1 57 2 1 1 26 14 9
## 128 128 3 1 44 1 2 2 12 9 7
## 129 129 3 2 41 2 2 2 16 14 9
## 130 130 3 2 58 4 2 1 17 9 11
## 131 131 3 2 60 4 2 1 31 19 11
## 132 132 3 2 40 2 1 1 12 14 3
## 133 133 3 2 37 2 1 1 7 4 6
## 134 134 3 1 45 1 1 1 12 5 5
## 135 135 3 1 60 3 1 1 17 18 9
## 136 136 3 1 52 2 1 2 18 13 9
## 137 137 3 2 46 4 1 1 20 12 4
## 138 138 3 2 60 4 1 1 23 16 9
## 139 139 3 1 60 3 1 1 17 11 10
## 140 140 3 1 59 3 1 1 7 16 11
## 141 141 3 2 52 3 1 1 29 20 8
## 142 142 3 1 60 3 1 1 29 13 12
## 143 143 3 2 56 2 1 1 21 12 12
## 144 144 3 2 54 2 2 2 18 28 9
## 145 145 3 2 61 3 1 1 13 12 8
## 146 146 3 2 61 3 1 1 29 18 12
## 147 147 3 2 51 3 1 1 17 15 5
## 148 148 3 1 49 4 2 1 19 17 7
## 149 149 3 1 52 2 1 1 22 13 10
## 150 150 3 2 55 3 2 1 25 13 12
## 151 151 3 2 60 4 2 1 28 10 10
## 152 152 3 2 43 1 2 2 14 9 5
## 153 153 3 1 55 3 2 1 14 7 9
## 154 154 3 2 52 4 2 1 18 11 9
## 155 155 3 2 56 1 2 1 26 24 13
## 156 156 3 1 56 4 1 1 24 11 11
## 157 157 3 2 47 2 1 1 20 19 9
## 158 158 3 2 56 2 1 1 17 18 8
## 159 159 3 2 52 3 1 1 28 15 13
## 160 160 3 2 51 4 1 1 23 14 11
## 161 161 3 1 51 1 1 1 7 13 6
## 162 162 3 2 53 3 1 1 15 15 8
## 163 163 3 1 50 4 1 1 26 11 14
## 164 164 3 2 59 4 1 1 16 10 8
## 165 165 3 1 53 3 1 1 14 12 7
## 166 166 3 1 55 3 1 1 15 10 7
## 167 167 3 1 57 1 1 1 6 13 2
## 168 168 3 1 58 2 1 1 16 5 5
## 169 169 3 1 44 3 1 1 10 12 4
## 170 170 3 1 39 1 1 2 14 12 4
## 171 171 3 1 53 4 2 1 21 17 12
## 172 172 3 2 52 4 1 1 23 10 9
## 173 173 3 1 57 3 1 2 25 11 10
## 174 174 3 2 40 3 1 1 11 10 7
## 175 175 3 2 47 2 1 1 16 13 7
## 176 176 3 1 51 2 1 1 25 19 11
## 177 177 3 1 48 2 1 1 11 7 4
## 178 178 3 2 49 1 1 2 15 16 6
## 179 179 3 1 50 2 1 1 12 8 5
## 180 180 4 2 53 1 2 2 10 13 4
## 181 181 4 2 52 1 2 2 13 15 8
## 182 182 4 1 51 1 2 2 19 12 9
## 183 183 4 1 52 1 2 2 20 16 12
## 184 184 4 1 46 1 2 2 13 3 3
## 185 185 4 2 51 1 2 2 21 19 12
## 186 186 4 2 47 1 2 2 19 12 13
## 187 187 4 2 51 3 2 1 25 13 12
## 188 188 4 2 54 1 2 1 8 20 5
## 189 189 4 2 54 2 2 1 12 4 9
## 190 190 4 1 57 2 2 1 24 11 10
## 191 191 4 1 53 2 2 1 17 12 8
## 192 192 4 2 50 2 2 1 20 16 8
## 193 193 4 2 57 1 2 2 28 23 16
## 194 194 4 2 58 1 2 2 31 30 12
## 195 195 4 2 58 1 2 2 28 29 9
## 196 196 4 2 53 1 2 2 19 19 14
## 197 197 4 2 49 1 2 2 20 17 7
## 198 198 4 2 51 1 2 2 10 1 2
## 199 199 4 1 58 1 2 2 22 13 9
## 200 200 4 2 51 1 2 2 18 12 4
## 201 201 4 2 53 1 2 2 21 17 9
## 202 202 4 2 56 3 2 1 29 17 17
## 203 203 4 2 51 3 1 1 19 11 10
## 204 204 4 1 47 1 1 1 23 12 11
## 205 205 4 2 54 4 1 1 23 14 12
## 206 206 4 1 54 4 1 1 17 15 6
## 207 207 4 2 46 1 1 1 22 14 7
## 208 208 4 2 52 2 1 1 20 15 14
## 209 209 4 2 48 1 1 1 24 18 5
## 210 210 4 1 49 2 1 2 17 21 7
## 211 211 4 1 58 1 1 2 14 7 3
## 212 212 4 1 46 3 1 2 18 13 10
## 213 213 4 1 57 1 1 2 27 19 11
## 214 214 4 1 48 4 1 2 27 12 15
## 215 215 4 2 52 2 1 2 23 8 9
## 216 216 4 1 57 2 1 1 29 17 12
## 217 217 4 1 46 3 1 1 18 9 10
## 218 218 4 1 55 2 1 1 14 12 8
## 219 219 4 1 44 3 1 1 8 11 6
## 220 220 4 1 56 1 2 2 26 15 12
## 221 221 4 2 44 2 1 1 14 14 12
## 222 222 4 1 59 4 1 1 28 17 12
## 223 223 5 1 48 2 1 1 16 8 8
## 224 224 5 1 56 2 1 1 22 17 11
## 225 225 5 2 58 2 1 1 20 18 8
## 226 226 5 2 53 1 1 1 15 11 2
## 227 227 5 2 53 1 1 1 26 16 8
## 228 228 5 2 65 1 1 2 15 16 5
## 229 229 5 1 46 1 1 2 15 5 5
## 230 230 5 1 49 1 1 2 19 12 12
## 231 231 5 1 55 1 1 2 21 40 8
## 232 232 5 2 46 2 1 1 20 9 6
## 233 233 5 2 58 4 1 1 30 55 19
## 234 234 5 1 47 4 1 1 18 13 9
## 235 235 5 1 53 4 1 1 26 25 14
## 236 236 5 2 51 2 1 1 30 15 8
## 237 237 5 1 49 4 1 1 17 16 12
## 238 238 5 1 43 2 1 1 16 13 6
## 239 239 5 2 60 3 1 1 23 16 9
## 240 240 5 1 51 4 1 1 21 11 10
## prenumb prerelat preclasf postbody postlet postform postnumb postrelat
## 1 40 14 20 18 30 14 44 14
## 2 39 16 22 30 37 17 39 14
## 3 9 9 8 21 46 15 40 9
## 4 14 9 13 21 14 13 19 8
## 5 51 17 22 32 63 18 54 14
## 6 33 14 14 27 36 14 39 16
## 7 13 11 12 22 45 12 44 12
## 8 52 15 23 31 47 18 51 17
## 9 42 15 20 32 50 17 48 14
## 10 31 10 17 32 52 19 52 17
## 11 38 16 18 26 52 15 42 10
## 12 29 16 21 17 29 15 40 10
## 13 13 8 12 20 16 9 18 10
## 14 21 10 15 26 28 15 35 16
## 15 16 9 11 28 21 10 22 10
## 16 24 12 18 28 45 14 45 13
## 17 16 10 18 25 24 16 28 8
## 18 11 6 3 25 16 11 17 9
## 19 23 10 13 32 46 18 35 14
## 20 23 14 10 28 50 12 38 12
## 21 41 10 23 29 48 20 51 15
## 22 22 11 16 32 42 19 45 15
## 23 7 8 9 22 23 17 19 15
## 24 16 8 9 22 27 16 20 14
## 25 11 12 7 14 13 7 21 12
## 26 36 13 17 25 18 14 42 13
## 27 40 16 11 24 27 15 20 14
## 28 10 5 11 21 17 13 13 10
## 29 23 11 14 28 20 18 45 14
## 30 5 5 1 27 15 13 9 8
## 31 25 11 17 21 11 12 13 9
## 32 14 8 8 21 17 10 18 9
## 33 45 16 24 32 43 18 46 13
## 34 15 6 7 29 27 14 33 9
## 35 28 12 17 29 41 15 48 12
## 36 10 6 11 29 23 11 27 8
## 37 23 12 10 32 39 18 49 16
## 38 5 5 3 12 12 6 13 9
## 39 34 15 17 21 17 6 21 8
## 40 33 15 14 21 16 11 7 9
## 41 8 10 11 21 22 10 28 8
## 42 13 11 14 24 19 12 22 11
## 43 9 5 5 29 11 8 9 11
## 44 5 2 4 21 6 11 6 6
## 45 4 4 6 19 8 11 22 10
## 46 16 9 12 29 48 17 48 14
## 47 45 14 18 32 48 19 46 14
## 48 8 5 7 26 36 14 20 10
## 49 22 10 15 24 20 18 28 12
## 50 47 13 17 26 13 7 12 11
## 51 18 8 10 20 10 14 23 10
## 52 41 9 21 30 47 20 50 11
## 53 15 10 11 15 13 9 13 10
## 54 14 8 9 26 32 15 27 11
## 55 9 7 6 21 15 17 17 12
## 56 13 11 13 19 14 14 18 7
## 57 20 10 17 28 21 17 36 19
## 58 23 14 15 25 16 19 28 4
## 59 13 9 7 27 15 14 23 11
## 60 10 9 7 19 20 14 19 12
## 61 21 8 20 27 48 19 47 15
## 62 13 7 11 28 19 17 17 11
## 63 29 11 12 30 31 19 45 15
## 64 32 10 13 28 28 15 46 13
## 65 39 12 17 32 40 19 52 17
## 66 30 12 9 29 46 13 44 13
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