Final Extra Credit
2023-05-08
Extra-Credit Work
Math 264, Spring 2023
#1 Thoroughly describe and display a quantitative data set. Be sure to mention center, spread, shape, and possibly outliers; include boxplot and histogram.
We may make some observations: 1. Verbal and Math scores seem to be correlated and normally distributed. 2. Height and Shoe seem to be correlated and right-skewed 3. TV time and Computer time seem to be correlated and right-skewed 4. Dad Height and Mom Height seem to be correlated and normal 5. Dad Age and Mom Age seem to be correlated and normal 6. Exercise is right skewed 7. Siblings is right skewed 8. Age is right skewed 9. Credits is left skewed
newSurvey_Data<-read.csv("~/Downloads/newSurvey_Data.csv")
hist(newSurvey_Data$Math, main="Math Histogram")
hist(newSurvey_Data$Verbal, main="Verbal Histogram")
hist(newSurvey_Data$HT, main="Height Histogram")
hist(newSurvey_Data$Shoe, main="Shoe Histogram")
hist(newSurvey_Data$MomHT, main="Mom Height Histogram")
hist(newSurvey_Data$DadHT, main="Dad Height Histogram")
hist(newSurvey_Data$Credits, main="Credits Histogram")
hist(newSurvey_Data$Exer, main="Exercise Histogram")
hist(newSurvey_Data$Compu, main="Computer time Histogram")
hist(newSurvey_Data$TV, main="TV Time Histogram")
hist(newSurvey_Data$Sleep, main="Sleep Histogram")
hist(newSurvey_Data$Age, main="Age Histogram")
hist(newSurvey_Data$DadAge, main="Dad Age Histogram")
hist(newSurvey_Data$MomAge, main="Mom Age Histogram")
hist(newSurvey_Data$Sibs, main="Sibling Histogram")
hist(newSurvey_Data$Earned, main="Earned Histogram")
Note: In a true analysis, and if we were building a model for the pure goal of predicting rather than understanding the data, we may use PCA to combine those variables defined above that have a dependence relationship. Here is some sample code of using PCA for the Math and Verbal Scores:
#install.packages("factoextra")
library(factoextra)## Loading required package: ggplot2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa# Perform PCA
numerical_data<-data.frame(newSurvey_Data$Math, newSurvey_Data$Verbal)
data_normalized <- scale(numerical_data)
pca <- prcomp(data_normalized, scale = TRUE)
# summarize results
summary(pca)## Importance of components:
## PC1 PC2
## Standard deviation 1.1711 0.7929
## Proportion of Variance 0.6857 0.3143
## Cumulative Proportion 0.6857 1.0000# Create a biplot of the PCA results
fviz_pca_var(pca, col.var = "black")
fviz_eig(pca, addlabels = TRUE, ylim = c(0, 50))
from our summary, we see that the first principle component accounts for 68% of the total variance. this implies almost two-thirds of the data between verbal and math scores may be represented by just the first principal component.
# Perform PCA
numerical_data_2<-data.frame(newSurvey_Data$DadHT, newSurvey_Data$MomHT, newSurvey_Data$MomAge, newSurvey_Data$DadAge)
data_normalized_2 <- scale(numerical_data_2)
pca_2 <- prcomp(data_normalized_2, scale = TRUE)
# summarize results
summary(pca_2)## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.3143 1.1298 0.8511 0.52133
## Proportion of Variance 0.4319 0.3191 0.1811 0.06795
## Cumulative Proportion 0.4319 0.7510 0.9321 1.00000# Create a biplot of the PCA results
fviz_pca_var(pca_2, col.var = "black")
fviz_eig(pca_2, addlabels = TRUE, ylim = c(0, 50))
Given our PCA analysis, we would only need to use three dimensions for these variables, since we would capture 93.2% of the information by the first three components.
#2 Compare values of a quantitative variable for 2 or more groups. Be sure to compare centers, spreads, and shapes; include side-by-side boxplots or side-by-side histograms. Here we will compare values for Verbal and Math scores:
hist(newSurvey_Data$Math, main="Math Histogram")
hist(newSurvey_Data$Verbal, main="Verbal Histogram")
sd(newSurvey_Data$Math)## [1] 71.8319sd(newSurvey_Data$Verbal)## [1] 73.3779mean(newSurvey_Data$Math)## [1] 611.6343mean(newSurvey_Data$Verbal)## [1] 592.8809Our results above indicate the mean and spread for both scores is extremely close. Thus we decide to test whether or not they are equal using Hypothesis testing: Null Hypothesis: Means are equal. Alternative Hypothesis: Means are not equal.
We do not have any concrete reasoning to assume their standard deviations are equal, so I find it will be best to compare them using unpooled standard deviation:
math_sd = sd(newSurvey_Data$Math)
verbal_sd = sd(newSurvey_Data$Verbal)
math_m = mean(newSurvey_Data$Math)
verbal_m = mean(newSurvey_Data$Verbal)
t.test(newSurvey_Data$Math, newSurvey_Data$Verbal, var.equal = FALSE)##
## Welch Two Sample t-test
##
## data: newSurvey_Data$Math and newSurvey_Data$Verbal
## t = 3.47, df = 719.67, p-value = 0.0005515
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 8.14308 29.36384
## sample estimates:
## mean of x mean of y
## 611.6343 592.8809According to our hypothesis test, we reject the null
Now, we may also compare two categorical variables:
sex_fact <- ifelse(newSurvey_Data$Sex == "male", 1, 0)
smoke_fact <- ifelse(newSurvey_Data$Smoke == "yes", 1, 0)
mytable <- table(sex_fact, smoke_fact)
mytable## smoke_fact
## sex_fact 0 1
## 0 191 38
## 1 101 31an interesting analysis would be for the relationship between smoking and gender: Null hypothesis: Proportions are equal Alt hypothesis: Proportions are not equal
successes <- c(sum((sex_fact)), sum(smoke_fact))
trials <- c(361, 361)
# Conduct proportion test
prop.test(successes, trials)##
## 2-sample test for equality of proportions with continuity correction
##
## data: successes out of trials
## X-squared = 26.502, df = 1, p-value = 2.632e-07
## alternative hypothesis: two.sided
## 95 percent confidence interval:
## 0.1076096 0.2414209
## sample estimates:
## prop 1 prop 2
## 0.3656510 0.1911357Given our results, we fail to reject the null
We may continue this comparison using a Fisher Exact Test, testing for independence now: Null Hypothesis: Data is independent Alternative Hypothesis: Data is dependent
result <- fisher.test(mytable)
result##
## Fisher's Exact Test for Count Data
##
## data: mytable
## p-value = 0.1265
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 0.871056 2.712840
## sample estimates:
## odds ratio
## 1.540883Thus we fail to reject the null.
We may now extend our comparisons to multiple quantitative variables using ANOVA: We will use six means: Mom Height, Dad Height, and Height:
result <- aov(newSurvey_Data$HT ~ newSurvey_Data$MomHT + newSurvey_Data$DadHT, data=newSurvey_Data)
result## Call:
## aov(formula = newSurvey_Data$HT ~ newSurvey_Data$MomHT + newSurvey_Data$DadHT,
## data = newSurvey_Data)
##
## Terms:
## newSurvey_Data$MomHT newSurvey_Data$DadHT Residuals
## Sum of Squares 714.442 249.661 4510.568
## Deg. of Freedom 1 1 358
##
## Residual standard error: 3.549557
## Estimated effects may be unbalanced#3 Examine the relationship between 2 quantitative variables. Include a scatterplot, mention of direction, form, and strength; correlation and the regression line equation if the relationship appears linear; mention of outliers or influential observations if present.
with regards to other variables that may not be necessarily related but correlated, such as Exercise and Verbal scores, we may plot the two below:
x <- newSurvey_Data$Sleep
y <- newSurvey_Data$Verbal
plot(x, y, main = "Scatterplot of Sleep and Verbal Scores",
xlab = "Sleep", ylab = "Verbal Scores")
correlation <- cor(x, y)
model <- lm(y ~ x)
# Plot the regression line
abline(model, col = "red")
correlation## [1] -0.008266078model##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 595.9637 -0.4327We have found from this analysis there is no correlation between
exercise and verbal score.
Some notable observations: The data appears to be centered and normally
joint distributed about (7 hours, 600 points). There are some outliers
in all directions. The correlation is extremely low, indicating there is
little relationship between the two variables.
for the Analysis below, We will begin by using one-hot encoding to encode some categorical variables:
library(tidyr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionnewSurvey_Data$Sex <- ifelse(newSurvey_Data$Sex == "male", 1, 0)
newSurvey_Data$Smoke <- ifelse(newSurvey_Data$Smoke == "yes", 1, 0)
newSurvey_Data$Pierced <- ifelse(newSurvey_Data$Pierced == "yes", 1, 0)
newSurvey_Data$Handed <- ifelse(newSurvey_Data$Handed == "right", 1, 0)
newSurvey_Data$Bkfst. <- ifelse(newSurvey_Data$Bkfst. == "yes", 1, 0)
newSurvey_Data$Cell <- ifelse(newSurvey_Data$Cell == "yes", 1, 0)
newSurvey_Data$Dec. <- ifelse(newSurvey_Data$Dec. == "yes", 1, 0)
newSurvey_Data$Live <- ifelse(newSurvey_Data$Live == "on", 1, 0)
# Reshape the data for Color
newSurvey_Data_Color <- newSurvey_Data %>%
mutate(value = 1) %>%
pivot_wider(names_from = Color, values_from = value, values_fill = 0)
# Reshape the data for Veg
newSurvey_Data_Eyes <- newSurvey_Data %>%
mutate(value = 1) %>%
pivot_wider(names_from = Eyes, values_from = value, values_fill = 0)
newSurvey_Data$Veg. <- ifelse(newSurvey_Data$Veg. == "no", 1,
ifelse(newSurvey_Data$Veg. == "some", 2, 3))
newSurvey_Data <- cbind(newSurvey_Data, newSurvey_Data_Color$black, newSurvey_Data_Color$blue, newSurvey_Data_Color$green, newSurvey_Data_Color$orange, newSurvey_Data_Color$red, newSurvey_Data_Color$pink, newSurvey_Data_Color$yellow, newSurvey_Data_Color$purple, newSurvey_Data_Eyes$cl, newSurvey_Data_Eyes$n, newSurvey_Data_Eyes$eg)
names(newSurvey_Data)[34:44] <- c("Black", "Blue", "Green", "Orange", "Red", "Pink",
"Yellow", "Purple", "Closed_Eyes", "Normal_Eyes", "Eyeglasses")
# Remove the original "Color" and "Eyes" columns
newSurvey_Data <- subset(newSurvey_Data, select = -c(Color, Eyes))
newSurvey_Data## Course Math Verbal HT Shoe Sex MomHT DadHT WT Dec. Credits Year Live Exer
## 1 200 420 500 76 11.0 1 66 75 165 1 16 3 0 45
## 2 200 650 580 65 7.5 0 69 69 125 1 14 2 1 0
## 3 200 550 590 60 6.0 0 61 69 105 1 18 2 1 120
## 4 200 570 540 66 8.0 0 62 71 117 1 16 1 1 30
## 5 200 650 700 62 7.5 0 63 70 107 0 17 1 1 30
## 6 200 630 590 66 8.5 0 64 72 145 1 17 2 1 0
## 7 200 640 560 68 10.0 0 65 65 175 1 15 2 1 120
## 8 200 510 510 64 8.0 0 64 70 133 1 13 3 1 40
## 9 200 590 520 75 12.0 1 69 71 175 0 14 2 1 45
## 10 200 610 600 66 10.5 1 64 65 160 0 14 2 1 0
## 11 200 520 710 63 7.5 0 61 69 125 1 16 2 0 30
## 12 200 550 600 67 10.0 1 64 73 160 1 13 3 0 10
## 13 200 620 480 65 9.0 0 67 71 143 0 18 2 1 180
## 14 200 550 560 62 7.5 0 63 69 125 0 13 2 1 30
## 15 200 550 480 68 9.0 1 65 73 175 1 17 2 1 25
## 16 200 640 550 71 13.0 1 63 68 214 0 13 3 0 90
## 17 200 490 650 64 8.0 0 61 73 116 1 17 3 0 60
## 18 200 620 560 71 11.5 1 63 70 153 0 14 2 1 120
## 19 200 480 520 65 8.5 0 63 73 135 0 16 2 0 60
## 20 200 640 650 70 9.5 1 66 69 165 1 14 2 0 90
## 21 200 620 620 75 15.0 1 67 73 315 0 14 2 0 120
## 22 200 550 530 66 7.0 1 66 67 120 0 17 2 0 30
## 23 200 580 500 64 8.0 0 61 70 155 0 13 2 1 20
## 24 200 600 760 64 6.0 0 69 70 115 0 14 2 1 15
## 25 200 650 675 62 6.5 0 56 66 105 1 15 4 0 120
## 26 200 600 300 65 7.5 0 69 70 215 1 17 other 0 30
## 27 200 610 640 68 11.5 1 64 70 150 1 16 2 0 0
## 28 200 630 640 66 10.0 0 65 70 137 0 15 2 0 3
## 29 200 670 640 68 11.0 1 61 70 155 0 16 2 1 60
## 30 200 640 670 65 8.5 0 60 69 123 1 15 2 1 120
## 31 1100 730 660 65 8.5 0 63 64 143 1 16 1 1 20
## 32 200 420 440 72 10.0 1 64 68 150 1 16 4 0 60
## 33 200 540 660 75 13.0 1 66 72 200 1 16 4 0 20
## 34 200 530 520 74 12.0 1 68 71 165 1 16 3 1 90
## 35 200 540 550 64 8.0 0 63 70 110 0 17 2 1 0
## 36 200 610 610 61 7.5 0 69 75 124 1 17 2 1 60
## 37 200 500 620 64 7.5 0 62 71 121 0 15 2 1 240
## 38 200 580 590 67 9.0 0 66 70 150 0 16 2 1 15
## 39 200 550 550 61 7.0 0 61 66 110 0 13 3 0 120
## 40 200 540 560 66 9.0 0 69 70 135 0 16 2 1 30
## 41 200 600 680 60 6.0 0 62 66 130 1 15 3 0 0
## 42 200 590 590 66 9.0 0 64 71 118 0 17 2 1 120
## 43 200 400 500 63 8.0 0 66 69 125 1 13 4 0 30
## 44 200 550 540 65 7.5 0 67 73 150 0 16 2 1 45
## 45 200 540 540 64 7.5 0 66 72 165 1 15 4 0 45
## 46 200 520 480 68 9.5 0 60 74 133 1 19 4 0 60
## 47 200 560 640 65 7.5 0 67 71 140 1 16 2 1 40
## 48 200 670 660 67 9.0 0 64 71 134 0 16 1 1 30
## 49 200 510 570 63 6.5 0 66 69 105 0 16 3 1 0
## 50 200 560 560 70 13.0 1 65 68 200 1 17 3 0 30
## 51 200 540 520 68 8.5 0 64 73 130 0 15 1 1 20
## 52 1000 620 540 65 6.0 0 65 73 130 1 17 1 1 0
## 53 200 600 600 70 11.0 1 66 68 180 1 16 2 0 45
## 54 200 550 550 68 9.0 0 63 69 140 0 16 3 0 0
## 55 200 560 560 67 9.5 0 67 75 145 0 14 2 1 60
## 56 200 540 580 68 9.0 1 65 67 135 0 16 2 1 45
## 57 200 550 550 68 10.0 0 71 71 160 1 15 2 1 60
## 58 200 700 780 69 10.5 0 62 75 145 1 18 3 0 50
## 59 1000 670 670 68 10.5 1 64 66 180 0 14 2 1 20
## 60 1000 610 630 66 9.0 0 63 65 114 1 14 2 1 0
## 61 1000 660 570 68 9.0 1 62 67 170 0 15 1 1 40
## 62 1000 620 590 64 9.0 0 62 72 124 0 16 2 1 120
## 63 1000 650 670 69 10.0 1 60 69 160 0 14 2 1 90
## 64 1000 590 610 75 13.0 1 66 74 204 1 13 4 0 25
## 65 1000 600 580 71 10.0 0 66 71 160 1 16 2 1 0
## 66 1000 450 650 68 10.0 1 62 66 225 1 13 3 0 0
## 67 1000 620 600 64 8.0 0 64 71 124 1 16 1 1 90
## 68 1000 510 590 64 7.0 0 63 71 130 0 15 2 1 45
## 69 1000 520 600 68 9.5 1 65 68 150 1 15 2 1 90
## 70 1000 580 660 63 8.5 0 64 69 135 1 17 3 0 30
## 71 1000 690 610 66 8.0 0 65 73 135 1 15 2 0 20
## 72 1000 500 600 65 9.5 0 68 70 152 1 16 3 0 45
## 73 1000 560 570 67 9.5 0 65 70 150 1 18 3 0 60
## 74 1000 580 700 61 6.0 0 65 70 104 1 14 2 1 30
## 75 1000 660 670 68 11.0 1 61 68 130 0 14 2 1 10
## 76 1000 670 620 66 8.5 0 64 74 146 1 16 3 0 0
## 77 1000 600 640 64 7.5 0 64 71 132 0 17 2 1 0
## 78 1100 600 620 70 11.0 1 67 71 145 0 16 2 0 0
## 79 1000 690 610 65 10.0 0 69 71 145 0 14 2 0 30
## 80 1000 640 720 69 10.0 0 71 74 135 1 17 1 1 0
## 81 1000 690 720 68 10.0 1 66 68 172 1 16 3 0 120
## 82 1000 650 600 63 6.5 0 61 69 112 0 14 2 1 180
## 83 1000 600 680 64 7.0 0 67 69 110 0 17 1 0 30
## 84 1000 710 700 62 8.0 0 61 70 105 0 16 2 0 0
## 85 1000 500 600 68 8.5 0 68 70 125 0 14 3 1 0
## 86 1000 670 590 67 8.5 0 63 71 118 1 14 1 1 30
## 87 1000 710 640 65 9.5 1 63 68 160 0 15 1 1 45
## 88 1000 600 600 62 6.0 0 63 68 155 0 16 3 0 30
## 89 1000 580 500 72 11.5 1 65 73 195 0 16 2 1 60
## 90 1000 570 570 67 8.0 0 68 72 140 0 16 2 0 0
## 91 1000 780 670 72 12.0 1 66 70 145 1 15 2 1 0
## 92 1000 620 480 71 11.5 1 65 67 145 0 13 3 0 0
## 93 1000 690 660 67 9.0 0 69 72 130 1 17 3 0 60
## 94 1000 590 620 69 8.5 0 70 70 145 0 15 2 0 0
## 95 1000 600 800 66 9.5 1 65 67 170 0 17 2 1 60
## 96 1000 550 550 72 10.5 1 64 69 250 0 7 other 0 30
## 97 1000 650 600 67 8.0 0 67 71 133 1 16 2 1 180
## 98 1000 560 540 68 10.5 1 66 67 155 1 16 3 0 120
## 99 1000 580 590 69 10.0 1 65 72 158 1 15 2 1 90
## 100 1000 520 500 76 14.0 1 67 68 185 1 13 3 0 0
## 101 1000 450 450 74 12.0 1 68 74 222 1 16 3 0 60
## 102 1000 600 590 66 6.0 0 67 73 105 0 15 2 0 0
## 103 1000 800 660 69 12.0 1 64 77 175 1 15 4 0 30
## 104 1000 620 640 62 7.0 0 64 72 98 0 15 2 1 0
## 105 1000 570 580 71 11.0 1 65 68 190 1 16 4 0 60
## 106 1000 580 590 62 8.0 0 61 70 130 0 17 2 0 75
## 107 1000 590 580 65 7.5 0 67 67 112 0 16 2 0 20
## 108 1000 580 520 71 10.5 1 61 71 175 1 14 2 0 60
## 109 1000 610 690 62 5.5 0 63 69 113 0 14 2 0 45
## 110 1000 700 550 75 16.0 1 69 74 233 1 18 1 1 45
## 111 1000 670 550 64 6.0 0 59 72 117 1 17 3 0 0
## 112 1000 620 500 66 8.5 0 68 68 129 1 14 2 1 30
## 113 1000 620 580 66 10.0 0 64 66 138 1 16 2 1 70
## 114 1000 700 520 76 13.0 1 66 71 180 1 14 2 1 15
## 115 1000 680 480 71 12.0 1 61 73 180 1 14 1 0 30
## 116 1000 640 540 64 7.0 0 63 65 126 0 16 1 0 0
## 117 1000 660 710 74 11.0 1 64 74 167 1 17 4 0 30
## 118 1000 770 590 67 10.0 0 65 73 169 1 15 2 1 120
## 119 1000 600 560 63 8.5 0 63 72 115 0 16 2 1 20
## 120 1000 650 520 60 6.5 0 66 70 130 1 16 3 0 15
## 121 1000 700 790 69 6.0 0 63 66 115 1 17 2 0 45
## 122 200 530 540 66 8.0 0 62 70 140 0 14 2 0 0
## 123 1000 550 610 60 5.0 0 64 71 110 1 16 4 0 0
## 124 1000 630 500 63 9.0 0 62 68 130 0 15 3 0 0
## 125 1000 600 500 70 11.0 1 64 64 190 1 13 3 0 0
## 126 1000 530 550 64 8.5 0 64 70 132 1 16 2 0 30
## 127 1000 540 610 64 6.5 0 68 69 113 0 16 2 0 120
## 128 1000 620 520 70 9.0 0 66 76 165 0 14 2 0 30
## 129 200 610 700 63 6.0 0 68 72 86 1 16 3 1 60
## 130 1000 630 590 68 10.5 1 65 66 155 0 15 3 0 120
## 131 200 680 590 66 8.5 1 63 64 115 1 13 3 0 0
## 132 1000 600 600 63 8.0 0 63 68 130 0 14 2 1 80
## 133 1000 720 690 72 13.0 1 64 70 300 0 13 2 1 20
## 134 1000 750 710 64 7.0 0 63 69 115 1 18 2 1 0
## 135 1000 620 620 66 10.0 0 64 69 150 0 16 2 1 35
## 136 1000 620 600 63 7.0 0 62 65 120 1 16 4 0 0
## 137 1000 660 620 72 12.0 1 64 68 150 1 16 2 0 0
## 138 1000 650 600 63 6.5 0 63 66 145 1 15 2 1 50
## 139 1000 640 620 72 11.5 1 64 72 164 0 16 2 0 0
## 140 1000 660 560 61 7.5 0 63 66 110 0 17 2 1 30
## 141 1000 670 620 65 9.5 0 69 73 120 0 14 2 1 100
## 142 200 500 500 66 8.0 0 63 69 112 0 14 2 0 0
## 143 1000 740 660 70 11.0 1 67 70 143 0 16 3 0 40
## 144 1000 570 500 68 10.5 1 64 71 140 0 16 3 0 20
## 145 200 690 650 74 13.0 1 68 76 170 1 17 3 0 120
## 146 1000 630 630 64 8.0 0 67 70 130 1 15 1 1 0
## 147 1000 640 630 62 8.0 0 68 67 135 1 16 3 0 0
## 148 1000 620 560 69 8.5 0 67 72 160 0 17 2 1 20
## 149 1000 500 600 64 8.5 1 63 72 135 1 16 2 0 20
## 150 1000 700 700 64 6.0 0 62 64 112 1 13 3 0 0
## 151 1000 580 620 66 9.0 0 63 70 129 0 15 2 1 30
## 152 1000 680 650 64 7.0 0 60 68 110 0 14 2 1 0
## 153 1000 680 580 63 7.5 0 65 74 110 1 17 2 1 45
## 154 1000 670 600 67 9.0 1 62 66 140 0 17 2 1 20
## 155 1000 740 660 63 6.0 0 64 71 120 1 17 2 1 90
## 156 1000 550 560 69 8.5 0 69 69 135 1 14 3 0 60
## 157 1000 610 710 65 7.5 0 67 67 130 0 17 2 1 20
## 158 200 710 680 70 11.0 0 68 72 145 0 17 1 1 50
## 159 1000 650 630 69 10.0 0 69 71 174 1 18 2 0 30
## 160 1000 690 740 71 8.5 0 66 77 163 1 17 3 0 60
## 161 1000 650 530 68 8.5 0 63 72 140 0 15 2 0 35
## 162 1000 650 650 64 5.0 0 62 72 105 0 14 2 0 0
## 163 200 540 560 64 6.0 0 66 75 150 0 16 2 1 2
## 164 200 650 620 63 8.0 0 64 65 120 0 14 2 1 30
## 165 200 610 670 66 7.0 0 63 73 136 0 16 3 0 190
## 166 200 660 650 62 8.0 0 64 64 108 1 16 2 1 30
## 167 200 700 720 69 9.0 1 65 68 125 0 13 1 1 30
## 168 200 570 560 64 7.0 0 64 75 125 1 15 2 1 30
## 169 200 580 560 67 9.0 1 63 72 170 1 16 3 0 45
## 170 200 590 630 64 6.5 0 67 71 112 0 16 2 1 0
## 171 200 650 540 61 5.5 0 62 68 115 0 17 2 1 70
## 172 200 530 460 61 7.0 0 59 72 123 1 15 2 0 100
## 173 200 540 500 66 8.5 0 60 70 114 1 12 1 0 30
## 174 200 550 700 68 9.5 1 62 70 165 1 16 3 0 60
## 175 200 600 510 60 6.5 0 64 72 110 1 16 1 1 30
## 176 200 560 560 62 6.0 0 61 65 95 0 16 2 1 20
## 177 200 700 680 73 11.5 1 66 72 152 1 13 1 1 120
## 178 200 580 480 70 10.0 0 68 76 150 1 17 2 1 40
## 179 200 540 520 66 10.0 0 65 72 210 1 14 2 0 0
## 180 200 680 720 66 9.0 0 62 74 175 0 13 2 0 60
## 181 200 730 790 64 7.5 0 65 68 105 1 17 2 1 30
## 182 200 600 650 62 8.0 0 64 74 215 0 16 2 1 0
## 183 200 580 590 68 9.5 0 66 70 160 1 14 2 1 90
## 184 200 520 590 70 11.0 0 64 76 126 1 17 2 1 30
## 185 200 600 700 73 11.5 1 66 69 161 1 16 4 0 0
## 186 200 700 550 70 7.0 0 68 75 155 1 16 4 0 60
## 187 200 580 580 67 8.5 1 60 68 140 1 14 2 0 30
## 188 200 700 610 66 9.0 0 67 67 135 1 15 2 0 120
## 189 200 620 580 73 13.0 1 65 70 180 1 12 2 1 75
## 190 200 540 520 64 6.5 0 62 69 117 0 16 2 1 30
## 191 200 680 670 60 6.5 0 60 72 120 0 17 1 1 60
## 192 200 550 535 63 8.0 0 63 69 130 0 16 2 1 90
## 193 200 650 640 69 12.0 1 62 72 165 0 17 2 1 0
## 194 200 590 600 65 8.5 0 61 70 135 0 17 2 1 0
## 195 200 580 500 62 7.0 0 66 73 175 0 17 2 0 60
## 196 200 650 620 61 6.5 0 61 70 120 0 17 3 0 180
## 197 200 620 580 73 12.0 1 65 71 160 0 14 2 1 0
## 198 200 690 610 75 12.0 1 66 75 190 1 16 2 1 75
## 199 200 580 570 69 11.0 0 66 76 136 0 14 2 1 60
## 200 200 570 570 65 7.5 1 62 66 135 0 17 2 1 60
## 201 200 500 570 62 7.5 0 66 64 118 0 16 2 1 90
## 202 200 610 610 64 6.0 0 65 69 125 1 17 2 1 60
## 203 200 520 600 73 12.0 1 64 68 160 1 13 3 0 20
## 204 200 610 520 73 14.0 1 65 73 162 1 16 2 1 10
## 205 200 590 580 69 8.5 0 69 68 140 0 17 2 1 0
## 206 200 600 620 64 8.0 0 63 72 135 0 16 2 1 40
## 207 200 560 550 64 8.0 0 68 69 134 0 16 2 1 45
## 208 200 550 530 70 9.5 0 66 72 128 1 17 3 0 45
## 209 200 580 660 68 8.0 0 65 74 124 1 16 2 1 0
## 210 200 550 500 67 8.0 0 65 70 150 1 4 other 0 0
## 211 200 620 640 63 8.0 0 59 74 134 1 14 2 0 0
## 212 200 540 510 69 9.0 0 64 74 155 0 16 2 1 0
## 213 200 660 600 71 11.0 1 64 71 173 0 17 2 1 120
## 214 200 500 650 71 13.0 1 66 68 196 1 17 3 1 45
## 215 200 610 600 72 12.0 1 63 73 165 1 14 2 1 180
## 216 200 540 470 64 8.0 0 62 70 105 1 12 2 1 0
## 217 200 450 550 68 9.5 0 66 65 150 1 16 3 0 0
## 218 200 640 610 66 8.0 0 64 74 140 1 15 2 1 45
## 219 200 680 570 68 9.5 0 66 70 138 1 17 2 1 180
## 220 200 490 560 73 13.0 1 68 72 276 1 17 other 0 150
## 221 200 570 590 65 8.0 0 63 70 135 0 15 2 1 0
## 222 200 550 500 71 8.5 0 67 76 135 0 14 2 0 0
## 223 200 600 610 64 7.0 0 65 70 126 0 16 2 0 0
## 224 200 550 550 60 8.0 0 62 64 116 1 16 4 0 0
## 225 200 630 550 68 11.0 1 62 72 150 0 16 2 0 180
## 226 200 560 640 67 10.0 1 61 68 160 1 16 2 1 45
## 227 200 400 400 65 7.0 0 67 71 120 1 16 3 0 30
## 228 200 710 580 61 7.0 0 61 66 103 1 12 2 1 30
## 229 200 500 650 64 7.0 0 65 70 125 1 16 3 0 90
## 230 200 600 500 66 8.5 0 63 73 140 0 16 3 0 0
## 231 1000 550 620 64 9.0 0 64 73 118 0 16 2 1 0
## 232 1000 560 500 64 9.0 0 70 70 128 0 16 3 0 0
## 233 1000 640 590 64 8.0 0 60 65 130 0 14 2 0 30
## 234 1000 630 600 65 9.0 0 66 66 128 1 18 2 1 0
## 235 1000 730 600 70 10.0 1 64 69 135 1 17 2 1 0
## 236 1000 600 600 73 11.5 1 67 73 142 0 17 2 1 30
## 237 1000 550 600 68 11.0 1 63 67 155 0 13 2 1 120
## 238 1000 600 520 63 7.5 0 61 69 132 1 14 2 0 20
## 239 1000 620 630 70 9.0 1 63 69 127 1 13 3 1 0
## 240 1000 620 620 73 11.0 0 68 75 215 1 17 2 0 0
## 241 1000 500 510 70 10.0 0 65 74 175 0 17 2 1 10
## 242 1000 580 560 62 7.0 0 63 70 110 0 15 2 0 20
## 243 1000 660 600 63 6.5 0 62 70 125 1 17 1 1 45
## 244 1000 670 660 66 9.0 0 64 72 160 1 19 3 0 60
## 245 1000 610 460 74 12.0 1 66 70 197 0 15 2 1 15
## 246 1000 600 510 65 6.5 0 64 68 135 1 15 3 0 90
## 247 1000 590 640 68 10.0 0 64 71 141 0 17 2 0 180
## 248 1000 660 700 71 12.0 1 67 68 160 1 16 3 0 45
## 249 200 500 600 67 7.5 0 65 76 138 1 12 4 1 0
## 250 1000 750 760 69 8.5 0 67 74 155 0 16 2 1 20
## 251 1000 680 790 66 8.5 0 66 70 135 0 19 2 1 30
## 252 1000 600 660 61 6.0 0 64 71 111 1 14 1 1 0
## 253 1000 620 540 63 7.5 0 62 72 116 1 14 2 1 0
## 254 1000 500 510 65 8.0 0 64 68 123 1 14 other 0 30
## 255 1000 650 630 62 6.0 0 63 68 98 1 17 3 0 20
## 256 1000 740 750 63 8.0 0 62 67 130 0 16 3 1 0
## 257 1000 650 700 67 10.0 1 63 68 137 1 17 2 1 15
## 258 1000 670 580 71 11.0 1 63 71 158 0 14 2 1 75
## 259 1000 600 600 66 8.5 0 62 75 128 1 11 other 0 60
## 260 1000 680 720 66 9.0 0 65 72 140 1 18 3 1 60
## 261 1000 650 590 79 15.0 1 66 73 200 1 16 2 1 60
## 262 1000 650 540 74 11.5 1 70 72 167 1 14 2 1 120
## 263 1000 570 580 66 8.0 0 67 68 150 1 16 4 0 30
## 264 1000 680 520 67 9.5 1 65 69 135 1 16 3 0 0
## 265 1000 720 680 64 7.5 0 60 65 115 0 16 2 1 75
## 266 1000 650 600 72 11.5 1 67 66 195 0 14 4 0 50
## 267 1000 740 780 66 8.0 0 66 70 135 1 17 other 0 0
## 268 1000 670 540 68 9.5 1 66 67 140 1 15 2 1 0
## 269 1000 720 570 69 10.5 1 64 68 157 1 13 3 1 60
## 270 1000 720 680 72 11.0 1 64 71 161 0 15 3 1 0
## 271 1000 620 620 69 10.0 1 60 63 185 0 14 2 1 60
## 272 1000 680 540 69 11.0 1 66 67 172 1 16 3 0 0
## 273 1000 610 580 67 8.0 0 67 70 120 1 17 1 1 90
## 274 1000 650 650 68 9.5 1 64 71 140 0 13 2 0 0
## 275 1000 580 650 63 6.0 0 62 67 120 0 16 2 1 60
## 276 1000 750 600 72 13.0 1 66 70 190 1 12 3 0 60
## 277 1000 800 750 68 11.0 1 62 67 143 1 16 3 0 60
## 278 1000 630 520 72 10.5 1 67 75 150 1 16 2 1 30
## 279 1000 630 550 64 6.5 0 63 70 125 0 14 2 1 70
## 280 1000 750 720 64 6.5 0 63 70 100 1 15 1 1 0
## 281 1000 590 630 70 10.5 1 68 69 190 1 15 4 0 10
## 282 1000 480 550 64 8.5 0 66 67 141 0 16 2 0 30
## 283 1000 570 540 73 10.0 1 65 70 190 1 16 3 0 70
## 284 1000 690 690 68 10.0 0 68 73 125 1 16 1 1 45
## 285 1000 660 540 70 10.5 1 63 71 145 1 13 3 0 60
## 286 1000 610 590 76 11.5 1 64 73 165 0 14 2 1 0
## 287 1000 700 510 67 9.0 0 67 71 140 0 17 2 1 120
## 288 1000 590 590 64 8.5 0 68 70 125 0 16 2 1 120
## 289 1000 550 530 74 13.0 1 72 74 210 0 17 2 1 90
## 290 1000 650 550 71 11.0 1 68 69 184 1 16 2 0 120
## 291 1000 550 510 63 7.5 0 63 69 110 1 13 4 0 25
## 292 1000 520 680 66 8.5 0 66 69 120 1 14 2 0 10
## 293 1000 590 600 67 10.0 1 59 72 120 1 14 3 0 0
## 294 1000 660 520 66 8.5 0 70 71 125 0 16 2 0 30
## 295 1000 520 600 73 10.5 1 65 75 170 0 17 3 0 0
## 296 1100 650 540 69 9.0 1 60 67 130 0 17 2 0 80
## 297 1100 600 500 66 9.0 0 68 68 140 1 17 2 0 70
## 298 1100 800 620 74 13.0 1 63 71 235 0 17 2 1 65
## 299 200 590 560 73 11.0 1 66 69 175 0 16 2 0 0
## 300 1100 630 550 65 6.5 0 61 68 125 1 16 2 0 60
## 301 1100 670 640 63 8.0 0 62 69 112 0 16 2 1 30
## 302 1100 550 500 67 10.5 1 65 65 150 0 16 3 0 60
## 303 1100 650 530 69 11.0 1 63 71 150 0 14 1 1 120
## 304 1100 550 500 73 12.0 1 66 72 185 0 13 2 0 20
## 305 1100 560 540 64 8.0 0 63 66 130 1 15 2 1 150
## 306 1000 590 590 76 12.0 1 64 71 192 1 14 2 0 120
## 307 1100 690 580 72 11.0 1 67 68 170 0 16 2 1 30
## 308 1100 700 580 69 9.0 0 63 74 135 0 17 2 1 150
## 309 1100 580 590 66 9.0 0 67 75 130 0 16 2 0 0
## 310 1100 720 680 72 12.0 1 66 70 200 1 13 3 0 30
## 311 1100 580 600 72 11.0 1 63 69 190 1 18 other 0 0
## 312 1100 700 680 64 10.0 1 56 64 165 1 16 2 1 60
## 313 200 530 420 67 8.5 0 63 75 135 1 13 1 0 0
## 314 200 630 640 69 10.0 1 67 73 145 1 17 other 0 0
## 315 1100 720 530 72 13.0 1 68 70 250 1 16 2 1 0
## 316 1100 660 600 72 11.0 1 64 67 195 1 16 4 0 0
## 317 1100 680 500 71 13.0 1 71 78 167 0 13 2 0 20
## 318 1100 760 530 71 10.5 1 69 74 160 0 16 2 1 60
## 319 1100 750 450 71 11.5 1 65 72 170 0 17 1 0 30
## 320 1100 640 540 70 11.0 1 64 67 168 1 16 2 1 60
## 321 1100 500 450 72 10.0 1 65 72 260 1 10 1 0 0
## 322 1100 550 700 64 8.0 0 62 72 130 0 16 2 1 30
## 323 200 620 600 67 9.5 0 68 72 140 0 17 2 1 0
## 324 200 560 550 63 8.5 0 59 70 115 0 16 2 1 30
## 325 200 550 730 67 10.0 0 66 68 137 0 18 2 1 75
## 326 200 620 630 63 8.0 0 66 66 115 1 17 2 1 120
## 327 200 630 670 63 9.0 0 63 68 130 1 17 2 1 75
## 328 200 600 580 69 11.0 1 60 73 125 0 15 2 0 0
## 329 200 660 620 64 8.0 0 64 72 114 1 14 2 1 115
## 330 200 660 580 65 8.5 0 68 73 148 0 17 2 1 30
## 331 200 550 530 64 9.0 0 65 66 140 0 16 2 1 65
## 332 200 650 590 71 12.0 1 66 69 175 0 14 2 0 120
## 333 200 770 340 71 9.0 1 62 66 115 1 18 2 1 5
## 334 200 630 640 61 7.0 0 62 68 106 1 14 2 1 60
## 335 200 560 640 63 7.0 0 64 67 140 0 16 2 1 20
## 336 200 610 740 64 7.5 0 63 61 101 0 17 2 1 50
## 337 200 620 580 64 8.5 0 63 71 155 0 17 2 1 0
## 338 200 670 520 79 15.0 1 71 80 192 0 13 3 0 0
## 339 200 740 590 63 8.0 0 60 67 133 1 13 2 0 30
## 340 200 550 560 62 6.5 0 64 67 115 0 17 2 0 30
## 341 200 460 580 61 6.5 0 62 70 105 0 13 3 0 0
## 342 200 650 550 70 10.5 1 62 70 145 0 16 2 1 0
## 343 200 560 650 62 6.5 0 63 67 125 0 13 2 0 0
## 344 200 600 600 63 7.5 0 65 66 120 0 16 1 0 0
## 345 200 570 540 70 10.5 1 67 68 151 0 16 2 1 30
## 346 200 720 600 62 7.5 0 63 70 125 1 16 2 0 20
## 347 200 510 620 63 8.0 0 62 66 120 1 16 3 1 0
## 348 200 600 590 64 9.0 0 67 70 140 0 16 2 0 40
## 349 200 600 620 64 8.0 0 67 71 123 1 16 4 0 20
## 350 200 520 600 63 6.5 0 66 69 120 0 14 3 1 0
## 351 200 540 470 72 10.5 1 67 71 200 1 11 other 1 0
## 352 200 600 580 68 8.0 0 68 71 145 1 17 2 1 60
## 353 200 450 600 62 7.5 0 63 67 140 1 14 3 0 120
## 354 200 610 590 66 8.5 1 60 71 115 0 14 3 0 60
## 355 200 580 560 61 7.0 0 60 70 120 1 16 2 1 60
## 356 200 600 660 65 8.5 0 67 70 138 1 14 3 0 20
## 357 200 620 420 66 10.0 0 66 71 111 0 14 2 1 120
## 358 200 690 630 61 6.5 0 59 71 104 0 16 2 1 20
## 359 200 720 540 63 8.5 0 67 67 130 1 15 3 0 10
## 360 200 700 700 63 7.5 1 66 72 125 0 18 2 1 150
## 361 1100 790 690 72 11.5 1 63 69 175 1 17 3 0 20
## Compu TV Phone Sleep Age MomAge DadAge Sibs Smoke Pierced Earned Cash
## 1 120.0 0 10 6.5 20.08 55 55 1 0 1 6 0
## 2 40.0 0 90 7.5 19.08 45 51 2 0 1 0 3
## 3 60.0 60 60 7.0 19.67 54 58 0 0 1 3 25
## 4 180.0 52 15 7.5 18.50 49 47 1 0 1 2 10
## 5 120.0 30 60 4.0 18.50 40 44 2 0 1 0 0
## 6 20.0 60 30 7.0 19.75 47 47 2 0 1 3 15
## 7 60.0 45 115 8.5 19.17 43 43 1 0 1 0 40
## 8 120.0 30 45 8.5 20.25 50 51 1 0 1 4 0
## 9 90.0 0 15 7.0 19.67 46 47 1 0 0 1 70
## 10 60.0 0 20 9.0 19.42 57 58 3 0 0 2 45
## 11 20.0 0 45 7.0 19.17 45 46 1 0 1 2 0
## 12 20.0 0 10 2.0 22.25 40 45 0 1 0 4 15
## 13 100.0 25 30 7.0 19.42 49 50 1 0 1 2 4
## 14 90.0 30 60 7.0 19.08 44 46 1 0 1 2 20
## 15 10.0 10 0 4.0 18.58 50 54 5 0 0 0 0
## 16 0.0 60 15 5.5 20.17 53 58 2 0 0 9 12
## 17 30.0 60 60 7.0 20.83 53 50 1 1 1 0 9
## 18 80.0 0 100 8.0 19.83 52 53 1 0 0 3 60
## 19 60.0 90 20 8.0 19.42 38 39 1 0 1 1 10
## 20 0.0 25 60 6.5 19.33 46 47 1 1 1 4 65
## 21 40.0 60 10 7.0 19.58 45 47 1 0 0 3 100
## 22 120.0 45 0 7.0 19.67 60 60 1 0 0 1 40
## 23 120.0 0 10 8.0 19.17 53 52 1 0 1 0 20
## 24 60.0 20 10 6.5 19.50 45 50 2 0 1 2 7
## 25 0.0 120 40 7.5 25.50 55 55 1 1 1 15 75
## 26 60.0 30 60 7.0 31.75 51 52 0 0 1 3 130
## 27 120.0 120 45 6.0 19.83 47 47 1 0 1 1 20
## 28 15.0 5 5 7.0 19.33 53 52 1 0 1 0 115
## 29 0.0 10 5 7.0 19.17 34 34 1 0 0 5 10
## 30 120.0 0 60 7.0 19.58 51 53 1 0 1 2 10
## 31 30.0 20 120 7.5 18.33 50 53 1 0 1 3 3
## 32 180.0 45 120 8.0 24.75 54 55 1 0 1 5 120
## 33 30.0 60 10 9.0 21.58 51 53 1 0 0 3 8
## 34 120.0 60 30 9.0 20.33 47 48 1 0 1 2 40
## 35 90.0 30 10 6.0 19.75 50 55 4 0 1 3 0
## 36 200.0 0 90 8.5 19.25 52 59 0 0 1 1 10
## 37 0.0 0 45 9.0 19.92 47 52 3 0 1 0 25
## 38 60.0 15 120 8.0 20.00 55 56 1 0 1 3 15
## 39 0.0 30 10 7.5 21.50 48 50 2 1 1 3 420
## 40 120.0 30 75 7.0 19.08 48 57 1 0 1 5 5
## 41 5.0 120 45 9.0 20.92 49 54 2 0 1 1 10
## 42 60.0 0 15 8.5 19.75 49 50 1 0 1 1 5
## 43 10.0 120 60 7.0 21.58 44 45 2 1 1 2 12
## 44 120.0 60 25 9.0 19.42 45 51 3 0 0 5 25
## 45 60.0 180 100 9.5 21.17 51 55 5 0 1 9 45
## 46 0.0 120 10 2.5 20.08 55 57 3 0 1 1 0
## 47 90.0 20 30 6.5 19.58 44 45 1 1 1 2 20
## 48 60.0 0 30 9.0 18.42 50 51 3 0 1 2 17
## 49 120.0 45 60 6.5 20.50 50 52 1 1 1 1 8
## 50 180.0 30 0 6.0 19.58 45 43 2 0 0 2 25
## 51 120.0 120 90 7.5 19.17 46 45 2 0 1 3 15
## 52 20.0 30 30 8.0 17.92 48 50 1 0 1 1 200
## 53 0.0 90 0 9.5 19.25 53 52 1 0 0 7 40
## 54 60.0 120 30 8.0 20.42 47 50 2 0 1 3 17
## 55 20.0 0 10 5.0 19.17 46 48 0 0 1 3 0
## 56 60.0 90 80 8.0 20.25 47 50 2 0 0 0 2
## 57 20.0 240 60 6.0 18.92 52 53 8 0 1 0 10
## 58 400.0 0 3 5.0 19.83 54 57 1 0 1 6 9
## 59 45.0 0 15 7.5 19.25 47 46 1 0 0 2 3
## 60 0.0 0 60 7.0 19.50 43 51 1 0 1 0 40
## 61 60.0 0 15 8.0 18.17 54 55 6 0 0 1 27
## 62 30.0 45 30 8.0 19.25 52 49 4 0 1 1 10
## 63 180.0 60 25 7.5 19.08 50 55 5 0 0 1 280
## 64 45.0 90 5 8.5 21.83 49 49 5 1 0 6 60
## 65 300.0 60 0 7.0 19.58 49 53 3 0 1 3 60
## 66 90.0 120 60 7.0 24.92 55 60 2 0 0 26 15
## 67 120.0 45 30 7.0 18.75 45 51 2 0 0 0 13
## 68 120.0 0 15 7.5 19.83 56 61 5 0 1 2 20
## 69 120.0 60 60 7.0 19.50 40 42 2 0 0 1 0
## 70 10.0 20 20 6.5 24.42 44 49 2 1 1 11 8
## 71 45.0 0 15 6.5 19.08 53 55 2 0 1 1 21
## 72 70.0 90 5 8.0 20.00 45 46 1 0 1 3 16
## 73 0.0 30 0 8.5 20.67 46 58 1 0 1 4 5
## 74 25.0 80 20 7.0 18.83 51 50 2 0 1 2 45
## 75 30.0 0 30 8.0 19.00 50 49 1 0 0 2 40
## 76 45.0 0 4 8.0 20.67 44 44 2 0 1 20 50
## 77 60.0 0 30 6.0 19.42 52 56 2 0 1 2 15
## 78 15.0 15 5 8.0 20.17 45 50 1 0 0 5 10
## 79 50.0 60 0 7.5 19.58 46 47 1 0 0 1 80
## 80 60.0 0 4 8.0 18.00 52 50 1 1 1 2 15
## 81 90.0 30 30 8.0 20.50 49 53 1 0 0 1 13
## 82 60.0 60 60 6.0 19.33 50 52 1 0 1 4 18
## 83 65.0 40 20 6.5 17.92 50 52 1 0 0 0 40
## 84 30.0 0 30 8.5 19.42 61 63 1 1 1 7 120
## 85 0.0 0 40 7.5 20.67 49 49 6 0 1 1 0
## 86 120.0 60 30 7.0 18.42 49 49 0 1 1 0 40
## 87 60.0 70 25 8.0 18.58 54 52 1 0 0 2 20
## 88 30.0 60 60 7.0 20.25 47 47 2 0 1 3 35
## 89 30.0 60 5 7.5 19.75 48 56 3 0 0 4 0
## 90 0.0 0 60 6.0 19.00 49 56 3 1 1 1 25
## 91 75.0 15 60 9.5 19.83 51 53 1 0 0 2 45
## 92 120.0 60 15 7.0 21.67 44 47 1 0 0 3 120
## 93 45.0 60 10 6.0 20.17 48 46 1 0 1 2 2
## 94 15.0 0 25 7.0 19.67 52 53 4 0 1 2 30
## 95 30.0 10 5 9.0 20.00 53 55 3 0 1 2 0
## 96 360.0 0 60 7.0 28.25 52 51 1 0 0 24 20
## 97 120.0 0 60 5.0 19.75 52 52 2 0 1 1 0
## 98 20.0 30 60 7.0 21.08 54 56 0 1 1 11 0
## 99 45.0 120 25 7.0 20.17 53 55 2 0 0 2 2
## 100 60.0 30 60 5.0 22.08 52 54 4 0 0 1 2
## 101 120.0 0 0 8.0 34.42 68 66 1 1 0 10 0
## 102 45.0 45 60 5.5 19.08 50 51 1 0 1 0 0
## 103 15.0 0 0 7.5 21.58 51 50 1 0 0 4 23
## 104 45.0 0 130 6.5 19.75 47 57 1 1 0 2 40
## 105 60.0 120 15 8.0 23.50 58 78 1 0 1 4 35
## 106 0.0 120 30 8.0 19.33 53 53 2 1 1 2 0
## 107 20.0 120 120 9.0 19.33 44 52 2 0 1 1 10
## 108 240.0 240 30 8.0 19.92 46 49 1 1 1 8 2
## 109 20.0 0 25 7.0 18.42 48 57 1 0 1 1 48
## 110 45.0 0 15 7.5 18.50 47 52 1 0 1 1 33
## 111 20.0 60 45 10.5 20.08 52 51 1 0 1 1 0
## 112 60.0 0 15 7.0 19.25 46 47 1 0 1 2 3
## 113 120.0 45 15 8.5 18.67 42 44 2 0 1 1 9
## 114 10.0 15 30 8.0 19.08 43 43 2 0 0 0 100
## 115 15.0 30 0 7.0 19.67 48 48 2 1 1 1 5
## 116 30.0 60 0 6.0 17.92 42 51 1 0 0 0 1
## 117 60.0 60 30 8.0 21.25 53 57 1 0 0 3 50
## 118 60.0 30 30 11.0 19.33 50 55 1 0 1 3 3
## 119 60.0 60 25 8.5 19.00 48 46 2 1 1 4 10
## 120 180.0 0 45 7.0 19.92 47 52 3 0 1 2 11
## 121 10.0 0 30 6.5 21.17 41 48 5 1 1 25 2
## 122 0.0 15 60 9.0 19.50 43 42 1 0 1 0 20
## 123 20.0 20 0 8.0 20.83 46 46 3 0 1 3 20
## 124 0.0 0 60 6.5 20.50 43 42 1 1 1 0 7
## 125 300.0 30 10 5.0 23.00 58 62 3 1 0 12 5
## 126 120.0 120 100 0.5 19.33 43 48 2 0 1 2 7
## 127 30.0 180 30 9.0 19.33 49 49 2 0 1 1 4
## 128 20.0 90 60 8.0 19.25 46 46 1 1 1 0 15
## 129 60.0 60 30 8.0 20.25 48 48 2 0 1 0 75
## 130 120.0 60 60 8.0 20.00 46 51 1 0 0 1 1
## 131 90.0 45 0 9.0 20.83 50 51 1 0 0 3 150
## 132 120.0 120 30 8.0 19.50 48 62 1 0 1 1 200
## 133 240.0 60 10 8.0 18.67 43 50 3 0 0 2 120
## 134 60.0 90 10 8.0 19.17 50 54 0 0 1 2 0
## 135 45.0 20 5 8.5 19.00 60 58 2 0 1 1 26
## 136 60.0 45 20 7.5 21.92 46 46 3 0 0 3 0
## 137 30.0 120 20 8.0 18.92 40 45 4 1 0 6 45
## 138 20.0 45 15 8.0 19.92 53 53 2 0 1 1 60
## 139 60.0 270 60 7.0 19.00 54 71 6 1 0 1 10
## 140 60.0 0 5 5.5 19.33 46 48 2 0 1 2 0
## 141 25.0 0 20 10.5 19.42 47 47 2 0 1 2 10
## 142 120.0 0 20 8.0 19.25 48 54 2 1 1 1 24
## 143 15.0 120 5 7.5 20.42 44 45 2 0 0 5 20
## 144 0.0 45 45 7.5 20.00 43 44 2 1 0 5 20
## 145 20.0 15 30 8.0 20.58 47 48 2 1 0 1 10
## 146 60.0 0 10 7.5 18.50 44 46 2 0 1 2 0
## 147 60.0 60 5 6.0 20.58 52 55 3 0 1 6 10
## 148 90.0 120 30 8.0 19.33 48 48 3 0 1 3 5
## 149 20.0 20 10 7.0 19.58 50 60 1 1 0 3 4
## 150 30.0 0 60 7.0 20.25 48 60 0 1 1 0 10
## 151 120.0 0 45 8.0 19.08 41 43 2 1 1 2 30
## 152 60.0 120 20 8.0 19.25 36 38 3 0 1 4 0
## 153 30.0 0 20 5.0 19.08 54 54 1 0 0 3 14
## 154 120.0 60 15 8.0 19.00 49 53 1 0 1 1 3
## 155 60.0 60 10 6.5 19.25 53 56 1 0 1 4 0
## 156 120.0 120 45 8.0 19.58 49 50 5 0 1 4 1
## 157 20.0 30 45 7.0 19.42 46 73 5 0 1 2 45
## 158 60.0 0 0 8.5 18.75 47 45 2 0 1 1 20
## 159 20.0 15 5 7.0 19.17 47 51 1 0 1 2 16
## 160 15.0 180 30 7.0 20.17 40 48 1 0 1 2 20
## 161 15.0 45 70 7.5 19.17 50 50 2 0 0 1 46
## 162 10.0 30 5 6.0 19.58 42 47 1 0 1 3 5
## 163 80.0 0 25 7.5 19.42 47 51 2 0 1 2 0
## 164 45.0 0 30 6.5 19.58 51 54 1 0 1 2 11
## 165 20.0 0 15 4.5 20.75 53 55 1 0 1 3 40
## 166 45.0 30 60 9.0 19.92 45 44 1 0 1 4 5
## 167 120.0 10 60 5.0 21.25 50 56 2 0 0 3 34
## 168 120.0 30 30 7.5 19.83 48 49 3 0 1 3 10
## 169 20.0 60 10 9.0 20.83 49 51 9 0 1 3 8
## 170 20.0 120 35 8.0 19.00 50 51 2 0 1 1 7
## 171 300.0 45 20 5.5 19.67 48 48 2 0 1 2 6
## 172 30.0 80 20 8.5 19.83 57 63 2 0 1 3 1
## 173 15.0 0 60 6.5 20.17 43 43 1 0 1 0 40
## 174 0.0 0 0 3.0 20.75 45 46 2 0 0 3 10
## 175 60.0 60 60 6.0 18.58 42 42 3 0 1 0 30
## 176 60.0 10 30 7.0 19.50 56 62 0 0 1 2 20
## 177 240.0 45 20 7.0 18.83 50 50 2 0 0 0 40
## 178 80.0 120 10 6.0 19.17 45 41 1 0 1 1 1
## 179 60.0 120 60 7.5 19.42 51 52 5 0 1 6 0
## 180 10.0 60 15 7.0 19.25 52 51 1 0 1 0 20
## 181 60.0 0 30 6.0 20.17 48 49 1 0 1 1 8
## 182 120.0 180 30 9.0 19.17 53 55 3 0 1 3 2
## 183 90.0 180 30 7.5 19.00 49 54 2 0 1 1 20
## 184 60.0 120 25 7.5 19.50 46 50 1 0 1 0 12
## 185 20.0 10 5 8.0 22.17 47 49 6 1 0 1 31
## 186 10.0 120 60 6.0 22.67 47 52 2 0 1 17 16
## 187 20.0 60 30 5.0 19.83 44 44 1 0 0 5 35
## 188 0.0 60 30 5.0 19.25 49 52 1 1 1 1 23
## 189 0.0 0 120 8.5 19.42 46 47 1 0 0 12 50
## 190 45.0 60 30 6.5 19.33 52 52 2 1 1 1 15
## 191 15.0 60 90 9.5 18.08 42 48 2 1 1 2 15
## 192 30.0 0 60 6.5 19.25 46 45 1 0 1 5 0
## 193 60.0 0 30 8.0 19.00 47 47 2 0 0 0 60
## 194 60.0 120 60 6.0 18.00 45 55 1 0 1 0 10
## 195 30.0 120 120 11.5 19.25 50 50 1 0 1 8 60
## 196 60.0 5 50 5.0 19.92 48 46 4 0 1 1 45
## 197 25.0 60 39 8.0 19.42 50 52 1 0 0 2 7
## 198 90.0 30 15 6.5 19.25 50 50 2 0 0 6 30
## 199 120.0 0 120 9.0 19.00 47 49 1 0 1 1 0
## 200 30.0 75 15 8.5 19.33 48 51 1 0 0 2 0
## 201 180.0 0 30 8.0 19.58 44 44 0 0 1 1 10
## 202 60.0 0 30 6.5 19.58 50 50 1 0 1 1 20
## 203 180.0 60 90 7.5 19.92 61 75 4 0 0 5 16
## 204 60.0 15 45 8.0 20.00 56 56 2 1 1 3 0
## 205 60.0 30 30 5.0 19.00 50 50 0 0 1 2 6
## 206 15.0 90 15 8.5 19.58 54 59 1 1 1 2 20
## 207 60.0 0 35 7.0 19.75 50 50 3 0 1 0 0
## 208 60.0 120 30 7.0 20.83 53 54 0 1 1 5 20
## 209 300.0 120 0 8.0 19.08 35 36 1 0 1 3 50
## 210 3.0 2 1 7.0 23.83 56 58 6 0 1 13 22
## 211 60.0 60 20 7.5 19.33 44 48 2 0 1 2 16
## 212 100.0 120 60 9.0 19.17 52 54 1 0 1 1 0
## 213 50.0 0 0 9.0 19.83 51 53 2 0 0 6 50
## 214 60.0 0 10 8.0 20.25 55 57 2 0 0 2 15
## 215 60.0 15 10 7.5 19.92 45 45 1 0 0 4 10
## 216 360.0 120 60 7.5 19.33 46 45 4 0 1 1 12
## 217 300.0 0 15 7.0 20.00 45 55 2 0 1 1 20
## 218 120.0 60 0 6.0 19.58 51 51 2 0 1 4 1
## 219 30.0 20 20 6.0 19.08 43 44 2 0 0 2 17
## 220 120.0 30 30 8.0 22.17 52 57 3 0 1 6 0
## 221 240.0 90 90 5.5 20.00 53 54 1 0 1 1 0
## 222 15.0 30 5 7.0 19.58 48 50 1 0 1 6 35
## 223 20.0 30 30 7.0 19.33 55 64 3 1 1 2 9
## 224 350.0 60 30 6.0 21.75 42 41 4 0 1 10 11
## 225 15.0 30 0 7.5 19.50 42 58 4 0 0 4 0
## 226 60.0 0 20 8.0 19.50 42 44 2 1 0 7 0
## 227 20.0 60 120 6.0 20.67 45 46 1 0 1 2 3
## 228 1.5 1 1 7.5 19.58 45 47 2 0 1 2 5
## 229 0.0 60 70 8.5 20.08 52 49 1 0 1 2 10
## 230 15.0 0 30 6.0 20.83 45 45 1 0 1 8 13
## 231 180.0 120 10 8.5 19.17 52 53 2 0 1 1 5
## 232 0.0 0 60 5.0 20.33 43 44 1 1 1 9 5
## 233 60.0 180 30 8.5 19.83 47 47 1 1 1 1 50
## 234 60.0 0 30 6.5 20.17 44 45 3 0 1 0 6
## 235 120.0 10 30 8.0 19.58 51 54 3 0 0 0 15
## 236 180.0 120 20 8.5 19.67 49 50 2 1 0 3 0
## 237 240.0 120 30 6.5 19.58 44 48 2 0 0 5 20
## 238 0.0 15 60 8.0 19.33 43 45 1 0 1 2 11
## 239 70.0 0 40 6.5 21.17 47 50 1 0 0 3 7
## 240 0.0 60 15 6.0 19.83 51 53 2 0 1 2 75
## 241 60.0 80 60 8.0 18.92 50 49 5 0 1 1 62
## 242 30.0 30 60 8.0 19.25 42 44 2 0 1 1 15
## 243 200.0 300 15 7.5 18.17 52 52 2 0 1 10 40
## 244 400.0 60 45 8.0 20.33 40 41 7 0 0 3 15
## 245 120.0 120 30 4.5 19.42 42 48 2 0 0 2 25
## 246 15.0 90 20 8.0 20.00 45 45 0 0 1 3 5
## 247 120.0 60 0 6.5 19.17 47 54 2 0 0 2 57
## 248 60.0 120 15 7.5 20.25 43 49 1 0 0 4 25
## 249 10.0 120 30 7.5 21.25 46 48 2 1 1 6 30
## 250 40.0 60 0 7.5 19.25 54 54 2 0 1 1 5
## 251 60.0 0 30 6.0 18.92 43 46 3 0 0 0 1
## 252 120.0 30 30 7.5 18.50 51 48 1 0 1 2 50
## 253 60.0 60 30 7.0 19.42 52 49 1 0 1 2 0
## 254 30.0 60 60 7.0 22.33 48 48 3 0 1 4 10
## 255 40.0 0 30 8.0 20.50 47 47 3 0 1 1 10
## 256 40.0 0 10 6.0 19.75 57 59 1 1 1 1 20
## 257 60.0 120 0 8.0 19.58 55 60 1 0 0 1 10
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## 271 180.0 240 0 6.5 19.42 46 53 2 0 0 4 30
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## 274 30.0 45 30 6.5 19.25 49 51 1 1 1 3 0
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## 301 120.0 30 30 6.0 18.92 39 51 0 1 1 2 50
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## 313 100.0 30 15 7.0 20.17 48 56 0 1 1 20 22
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## 317 180.0 120 0 6.5 19.92 50 50 5 1 0 3 8
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## 322 30.0 60 30 6.0 19.67 40 42 3 0 0 2 20
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## 336 180.0 10 40 7.5 19.42 52 51 1 0 1 1 0
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## 341 20.0 30 60 7.0 20.50 51 52 2 0 1 1 15
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## 343 120.0 30 0 6.5 19.17 45 50 2 0 1 0 25
## 344 0.0 60 60 7.0 20.25 42 45 2 1 1 4 18
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## 360 20.0 5 20 6.0 19.58 40 42 1 0 1 3 10
## 361 5.0 60 20 6.0 20.25 43 56 1 1 1 10 300
## Handed Bkfst. Veg. Cell Random Black Blue Green Orange Red Pink Yellow
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## Purple Closed_Eyes Normal_Eyes Eyeglasses
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## 361 0 1 0 0#5 Examine if you can predict gender from other variables. Use logistic regression to examine which variables among Math, Verbal, WT, HT, Compu, TV, Phone, Shoe, Smoke, and Sibs, which will significantly contribute to predict the gender.
vectorOfDependentVariables <- c("Math", "Verbal", "WT", "HT", "Compu", "TV", "Phone", "Shoe", "Smoke", "Sibs")
# Define the formula
formula <- formula("gender ~ Math + Verbal + WT + HT + Compu + TV + Phone + Shoe + Smoke + Sibs")
# Fit the logistic regression model for each variable
listOfGlms <- lapply(vectorOfDependentVariables, function(x) {
glm(reformulate(x, "Sex"), data = newSurvey_Data, family = binomial)
})
listOfGlms## [[1]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Math
## -3.255745 0.004401
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 466 AIC: 470
##
## [[2]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Verbal
## 0.601235 -0.001948
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 472.4 AIC: 476.4
##
## [[3]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) WT
## -10.23777 0.06622
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 314.3 AIC: 318.3
##
## [[4]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) HT
## -47.5649 0.6961
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 240.5 AIC: 244.5
##
## [[5]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Compu
## -0.824534 0.003262
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 467.9 AIC: 471.9
##
## [[6]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) TV
## -0.688779 0.002419
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 472 AIC: 476
##
## [[7]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Phone
## -0.383381 -0.004853
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 471.8 AIC: 475.8
##
## [[8]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Shoe
## -16.594 1.703
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 206 AIC: 210
##
## [[9]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Smoke
## -0.6372 0.4336
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 471.5 AIC: 475.5
##
## [[10]]
##
## Call: glm(formula = reformulate(x, "Sex"), family = binomial, data = newSurvey_Data)
##
## Coefficients:
## (Intercept) Sibs
## -0.66183 0.05839
##
## Degrees of Freedom: 360 Total (i.e. Null); 359 Residual
## Null Deviance: 474.1
## Residual Deviance: 473.5 AIC: 477.5Given these results,
#6 Try to build a model based on logistic regression and identify which variables among all the available variables which most likely will significantly contribute to predict the gender.
# Fit logistic regression model
mylogit <- glm(sex_fact ~ Math + Verbal + WT + HT + Compu + TV + Phone + Shoe + Smoke + Sibs + MomHT + DadHT + Black + Blue + Green + Orange + Red + Pink + Yellow + Purple + Credits + Year + Live + Exer + Phone + Sleep + Age + MomAge + DadAge + Pierced + Closed_Eyes + Normal_Eyes + Eyeglasses + Earned + Cash + Handed + Bkfst. + Veg. + Cell,
data = newSurvey_Data, family = "binomial")## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred# View model summary
summary(mylogit)##
## Call:
## glm(formula = sex_fact ~ Math + Verbal + WT + HT + Compu + TV +
## Phone + Shoe + Smoke + Sibs + MomHT + DadHT + Black + Blue +
## Green + Orange + Red + Pink + Yellow + Purple + Credits +
## Year + Live + Exer + Phone + Sleep + Age + MomAge + DadAge +
## Pierced + Closed_Eyes + Normal_Eyes + Eyeglasses + Earned +
## Cash + Handed + Bkfst. + Veg. + Cell, family = "binomial",
## data = newSurvey_Data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6385 -0.0003 0.0000 0.0000 3.6307
##
## Coefficients: (2 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -10.068307 44.175084 -0.228 0.8197
## Math -0.001621 0.015001 -0.108 0.9139
## Verbal 0.025386 0.016321 1.555 0.1198
## WT 0.042106 0.074344 0.566 0.5711
## HT 1.565239 1.003456 1.560 0.1188
## Compu -0.019821 0.012555 -1.579 0.1144
## TV -0.005010 0.021288 -0.235 0.8140
## Phone -0.019954 0.026209 -0.761 0.4465
## Shoe 3.359734 1.433091 2.344 0.0191 *
## Smoke 6.943374 5.106434 1.360 0.1739
## Sibs -0.080017 0.500364 -0.160 0.8729
## MomHT -0.856080 0.545248 -1.570 0.1164
## DadHT -1.783086 1.000987 -1.781 0.0749 .
## Black 6.602588 5.027849 1.313 0.1891
## Blue 0.407550 2.321548 0.176 0.8606
## Green -6.076506 3.991131 -1.523 0.1279
## Orange -4.850944 54.471558 -0.089 0.9290
## Red -2.521779 4.089201 -0.617 0.5374
## Pink -20.920471 47.894804 -0.437 0.6623
## Yellow -2.650880 75.638244 -0.035 0.9720
## Purple NA NA NA NA
## Credits 0.144409 0.818371 0.176 0.8599
## Year2 2.379161 2.681244 0.887 0.3749
## Year3 3.115139 3.941677 0.790 0.4293
## Year4 2.713674 5.340098 0.508 0.6113
## Yearother 4.402872 49.096366 0.090 0.9285
## Live -0.336637 1.917102 -0.176 0.8606
## Exer 0.029214 0.022863 1.278 0.2013
## Sleep 1.855716 1.265886 1.466 0.1427
## Age 1.490188 1.356972 1.098 0.2721
## MomAge -0.039140 0.294517 -0.133 0.8943
## DadAge 0.039431 0.288537 0.137 0.8913
## Pierced -14.156565 7.138689 -1.983 0.0474 *
## Closed_Eyes -8.381756 5.074489 -1.652 0.0986 .
## Normal_Eyes -4.583463 3.158740 -1.451 0.1468
## Eyeglasses NA NA NA NA
## Earned 0.303608 0.324196 0.936 0.3490
## Cash -0.034572 0.023289 -1.485 0.1377
## Handed 1.805666 3.117667 0.579 0.5625
## Bkfst. -8.753697 5.143991 -1.702 0.0888 .
## Veg. 2.591541 1.905665 1.360 0.1739
## Cell -1.859158 2.392098 -0.777 0.4370
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 474.066 on 360 degrees of freedom
## Residual deviance: 41.129 on 321 degrees of freedom
## AIC: 121.13
##
## Number of Fisher Scoring iterations: 14Given our results, we found that Shoe Size and Percsing were the best predictors for gender. We came to this conclusion because their values are statistically significant, indicating there is some correlation between them in some way.