Group Members: Franklin Young and Jenny Bui
Title: Gotta Catch Em All: Analyzing the First 721 Pokemon of the Pokedex
Topic/Data Set: The topic will be on analyzing 721 Pokemon in the first six generations and their 21 variables ranging from Type to Generation. Data is taken from Kaggle.
Description: Our project will explore the 721 Pokemon in the first six generations and their 21 variables ranging from Type to Generation. Before we begin the analysis, there are some background information to discuss. Pokemon Generation was first released in 1996 in Japan. Since 1996, a new Generation has been released every two to three years. Generation 6 was released in 2013. It is important to recognize that during this time period, the popularity of Pokemon fluctuated. In each generation, a completely new set of Pokemon and new characteristics are introduced. Our dataset covers the time frame of 1996 to 2013.
library(readr)
library(corrplot)## Warning: package 'corrplot' was built under R version 3.4.2## corrplot 0.84 loadedlibrary(ggplot2)
library(dplyr)## Warning: package 'dplyr' was built under R version 3.4.2##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(RColorBrewer)
library(rpart)
library(rpart.plot)
library(class)
library(e1071)
Pokemon <- read_csv("~/Downloads/datasetpokemon.csv")## Parsed with column specification:
## cols(
## .default = col_character(),
## Number = col_integer(),
## Total = col_integer(),
## HP = col_integer(),
## Attack = col_integer(),
## Defense = col_integer(),
## Sp_Atk = col_integer(),
## Sp_Def = col_integer(),
## Speed = col_integer(),
## Generation = col_integer(),
## Pr_Male = col_double(),
## Height_m = col_double(),
## Weight_kg = col_double(),
## Catch_Rate = col_integer()
## )## See spec(...) for full column specifications.print(Pokemon) ## # A tibble: 721 x 23
## Number Name Type_1 Type_2 Total HP Attack Defense Sp_Atk
## <int> <chr> <chr> <chr> <int> <int> <int> <int> <int>
## 1 1 Bulbasaur Grass Poison 318 45 49 49 65
## 2 2 Ivysaur Grass Poison 405 60 62 63 80
## 3 3 Venusaur Grass Poison 525 80 82 83 100
## 4 4 Charmander Fire <NA> 309 39 52 43 60
## 5 5 Charmeleon Fire <NA> 405 58 64 58 80
## 6 6 Charizard Fire Flying 534 78 84 78 109
## 7 7 Squirtle Water <NA> 314 44 48 65 50
## 8 8 Wartortle Water <NA> 405 59 63 80 65
## 9 9 Blastoise Water <NA> 530 79 83 100 85
## 10 10 Caterpie Bug <NA> 195 45 30 35 20
## # ... with 711 more rows, and 14 more variables: Sp_Def <int>,
## # Speed <int>, Generation <int>, isLegendary <chr>, Color <chr>,
## # hasGender <chr>, Pr_Male <dbl>, Egg_Group_1 <chr>, Egg_Group_2 <chr>,
## # hasMegaEvolution <chr>, Height_m <dbl>, Weight_kg <dbl>,
## # Catch_Rate <int>, Body_Style <chr>Hypothesis Number 1
Is there a relationship between Generation and Pokemon’s stats such as Attack and Total? We want to learn if there exists a relationship between stats and Generation. In order to test this hypothesis, we will first test the correlation between stats in the data frame. Afterward, we will test the hypothesis with a decision tree to show the accuracy of our predictions. If our accuracy is weak, we will also create regression analysis to gain more insight so we can better answer our hypothesis.
Correlation Plots Between Numerical Characteristics.
library(corrplot)
Pokemon1 <- data.frame(Pokemon)
Pokemon1 <- Pokemon1[, c(5, 6, 7, 8, 9, 10, 11)]
P <- cor(Pokemon1)
col1 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "white", "cyan", "#007FFF", "blue", "#00007F"))
col2 <- colorRampPalette(c("#67001F", "#B2182B", "#D6604D", "#F4A582", "#FDDBC7", "#FFFFFF", "#D1E5F0", "#92C5DE", "#4393C3", "#2166AC", "#053061"))
col3 <- colorRampPalette(c("red", "white", "blue"))
col4 <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "#7FFF7F", "cyan", "#007FFF", "blue", "#00007F"))
wb <- c("white", "black")
par(ask=TRUE)corrplot(P, method ="number", title = "Correlation Between Stats")
corrplot(P, title = "Correlation Between Stats")
corrplot(P, order = "original", addCoef.col = "grey", title="Correlation Between Stats")
From the correlation plots, there are two characteristics with an inverse correlation, which is Speed and Defense. Additionally, there is a high positive correlation between Total and other stats such as HP, Attack, and Speed. Total is the total amount of experience required to reach the highest level of a Pokemon. The stats with very high correlation is worth investigating. Total and Attack have the highest positive correlation at 0.73. Total and Speed Attack have the second highest positive correlation at 0.71. Moving forward with our hypothesis, we will focus on these stats (Total, Attack, and Speed Attack) because they have the highest positive correlation.
Pokemon_ <- read_csv("~/Downloads/datasetpokemon.csv")## Parsed with column specification:
## cols(
## .default = col_character(),
## Number = col_integer(),
## Total = col_integer(),
## HP = col_integer(),
## Attack = col_integer(),
## Defense = col_integer(),
## Sp_Atk = col_integer(),
## Sp_Def = col_integer(),
## Speed = col_integer(),
## Generation = col_integer(),
## Pr_Male = col_double(),
## Height_m = col_double(),
## Weight_kg = col_double(),
## Catch_Rate = col_integer()
## )## See spec(...) for full column specifications.library(ggplot2)
generationdistribution <- ggplot(Pokemon_, aes(x=Pokemon_$Generation)) + geom_bar(stat="count", fill="yellow") + labs(x='Generation', y='Count', title='Count of Pokemon in Each Generation')
generationdistribution
This is a distribution of all Pokemon across 6 Generation. From the graph, we can conlcude that Generation 6 has the lowest count of Pokemon. Generation 1, 3, and 5 have over 150 Pokemon. Whereas, Generation 2, 4, and 6 have relatively less Pokemon.
Distribution of Total by Generation. (Please remember that the following 3 graphs, the colors are only indicating different Generations.)
colnames(Pokemon_) <- make.names(names(Pokemon_))
ggplot(Pokemon_, aes(x=Total, fill=Generation)) +
facet_wrap(~Generation) +
geom_histogram(color="darkred") +
theme(legend.position = 'center') +
labs(x='Total Stats', y='Count', title = 'Distribution of Total Stats by Generation')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
From the Distribution of Total Stats by Generation, we can observe that there is a normal distribution across all Generation except Generation 5 because it has a bimodal distribution. Additionally, we can say that most Pokemon in Generation 1 to 6 have Total Stats below 600.
Distribution of Attack by Generation
colnames(Pokemon_) <- make.names(names(Pokemon_))
ggplot(Pokemon_, aes(x=Attack, fill=Generation)) +
facet_wrap(~Generation) +
geom_histogram(color="pink") +
theme(legend.position = 'none') +
labs(x='Attack', y='Count', title = 'Distribution of Attack by Generation')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
From this distribution, we can observe that Generation 1 has the most normal distribution shape with a clear mode. Generation 2, 3, and 6 have a distribution that is skewed to the right. There is a tail for Pokemon with relatively high Attack.
Distribution of Speed Attack by Generation
ggplot(Pokemon_, aes(x=Sp_Atk, fill=Generation)) + facet_wrap(~Generation) +
geom_histogram(color="yellow") +
theme(legend.position = 'none') +
labs(x='Speed Attack', y='Count', title = 'Distribution of Speed Attack by Generation') ## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
From the distribution, we can observe that the general distribution across all Generations is normally distributed when observing Speed Attack.
Scatter Plot of the Distribution of Total Stats by Attack based on Generation
plot1 <-ggplot(Pokemon_, aes(x=Total, y=Attack, color=Generation)) + geom_point() + labs(x='Total Stats', y='Attack', title = 'Plot of Total Stats by Attack based on Generation')
plot1 
The scatter plot suggests that there may be no relationship between Total Stats and Attack and Generation because the scatter plot has a highly dispersed distribution. However, the plot accurately shows the positive correlation between Attack and Total. As Attack points increases, Total Stats also increases.
Scatter Plot of the Distribution of Total and Speed Attack based on Generation
plot1 <-ggplot(Pokemon_, aes(x=Total, y=Sp_Atk, color=Generation)) + geom_point() + labs(x='Total', y='Sp_Atk', title = 'Plot of Total Stats by Speed Attack based on Generation')
plot1 
The scatter plot suggests that there may be no relationship between Speed Attack and Total Stats based on Generation because the scatter plot is highly dispersed distribution. However, the scatter plot does accurately show the positive correlation between Total Stats and Speed Attack. As Total Stats increases, Speed Attack also increases.
Decision Tree
Attack <- as.numeric(Pokemon_$Attack)
Total <- as.numeric(Pokemon_$Total)
SpeedAttack <- as.numeric(Pokemon_$Sp_Atk)
tree_classifier <- rpart(Pokemon_$Generation ~ Total, data = Pokemon_, method = 'class', control = rpart.control(maxdepth = 20, minsplit = 100))
summary(tree_classifier)## Call:
## rpart(formula = Pokemon_$Generation ~ Total, data = Pokemon_,
## method = "class", control = rpart.control(maxdepth = 20,
## minsplit = 100))
## n= 721
##
## CP nsplit rel error xerror xstd
## 1 0.02477876 0 1.0000000 1.017699 0.01909828
## 2 0.01000000 1 0.9752212 1.042478 0.01837928
##
## Variable importance
## Total
## 100
##
## Node number 1: 721 observations, complexity param=0.02477876
## predicted class=5 expected loss=0.7836338 P(node) =1
## class counts: 151 100 135 107 156 72
## probabilities: 0.209 0.139 0.187 0.148 0.216 0.100
## left son=2 (43 obs) right son=3 (678 obs)
## Primary splits:
## Total < 250.5 to the left, improve=4.572532, (0 missing)
##
## Node number 2: 43 observations
## predicted class=2 expected loss=0.6744186 P(node) =0.05963939
## class counts: 6 14 13 6 0 4
## probabilities: 0.140 0.326 0.302 0.140 0.000 0.093
##
## Node number 3: 678 observations
## predicted class=5 expected loss=0.7699115 P(node) =0.9403606
## class counts: 145 86 122 101 156 68
## probabilities: 0.214 0.127 0.180 0.149 0.230 0.100rpart.plot(tree_classifier)
title("Prediction Generation on Total")
Attack <- as.numeric(Pokemon_$Attack)
Total <- as.numeric(Pokemon_$Total)
SpeedAttack <- as.numeric(Pokemon_$Sp_Atk)
tree_classifier2 <- rpart(Pokemon_$Generation ~ Total + Attack, data = Pokemon_, method = 'class', control = rpart.control(maxdepth = 20, minsplit = 60))
summary(tree_classifier2)## Call:
## rpart(formula = Pokemon_$Generation ~ Total + Attack, data = Pokemon_,
## method = "class", control = rpart.control(maxdepth = 20,
## minsplit = 60))
## n= 721
##
## CP nsplit rel error xerror xstd
## 1 0.02477876 0 1.0000000 1.008850 0.01933792
## 2 0.01000000 1 0.9752212 1.014159 0.01919518
##
## Variable importance
## Total Attack
## 93 7
##
## Node number 1: 721 observations, complexity param=0.02477876
## predicted class=5 expected loss=0.7836338 P(node) =1
## class counts: 151 100 135 107 156 72
## probabilities: 0.209 0.139 0.187 0.148 0.216 0.100
## left son=2 (43 obs) right son=3 (678 obs)
## Primary splits:
## Total < 250.5 to the left, improve=4.572532, (0 missing)
## Attack < 84.5 to the left, improve=2.965793, (0 missing)
## Surrogate splits:
## Attack < 22.5 to the left, agree=0.945, adj=0.07, (0 split)
##
## Node number 2: 43 observations
## predicted class=2 expected loss=0.6744186 P(node) =0.05963939
## class counts: 6 14 13 6 0 4
## probabilities: 0.140 0.326 0.302 0.140 0.000 0.093
##
## Node number 3: 678 observations
## predicted class=5 expected loss=0.7699115 P(node) =0.9403606
## class counts: 145 86 122 101 156 68
## probabilities: 0.214 0.127 0.180 0.149 0.230 0.100rpart.plot(tree_classifier2)
title("Prediction Generation on Total, Attack")
Attack <- as.numeric(Pokemon_$Attack)
Total <- as.numeric(Pokemon_$Total)
SpeedAttack <- as.numeric(Pokemon_$Sp_Atk)
tree_classifier3 <- rpart(Pokemon_$Generation ~ Total + Attack + SpeedAttack, data = Pokemon_, method = 'class', control = rpart.control(maxdepth = 20, minsplit = 60))
summary(tree_classifier3)## Call:
## rpart(formula = Pokemon_$Generation ~ Total + Attack + SpeedAttack,
## data = Pokemon_, method = "class", control = rpart.control(maxdepth = 20,
## minsplit = 60))
## n= 721
##
## CP nsplit rel error xerror xstd
## 1 0.02477876 0 1.0000000 1.067257 0.01758262
## 2 0.01179941 1 0.9752212 1.040708 0.01843310
## 3 0.01061947 5 0.9274336 1.046018 0.01827045
## 4 0.01002950 6 0.9168142 1.044248 0.01832507
## 5 0.01000000 9 0.8867257 1.044248 0.01832507
##
## Variable importance
## Total Attack SpeedAttack
## 57 27 16
##
## Node number 1: 721 observations, complexity param=0.02477876
## predicted class=5 expected loss=0.7836338 P(node) =1
## class counts: 151 100 135 107 156 72
## probabilities: 0.209 0.139 0.187 0.148 0.216 0.100
## left son=2 (43 obs) right son=3 (678 obs)
## Primary splits:
## Total < 250.5 to the left, improve=4.572532, (0 missing)
## Attack < 84.5 to the left, improve=2.965793, (0 missing)
## SpeedAttack < 115.5 to the left, improve=2.694889, (0 missing)
## Surrogate splits:
## SpeedAttack < 29.5 to the left, agree=0.950, adj=0.163, (0 split)
## Attack < 22.5 to the left, agree=0.945, adj=0.070, (0 split)
##
## Node number 2: 43 observations
## predicted class=2 expected loss=0.6744186 P(node) =0.05963939
## class counts: 6 14 13 6 0 4
## probabilities: 0.140 0.326 0.302 0.140 0.000 0.093
##
## Node number 3: 678 observations, complexity param=0.01179941
## predicted class=5 expected loss=0.7699115 P(node) =0.9403606
## class counts: 145 86 122 101 156 68
## probabilities: 0.214 0.127 0.180 0.149 0.230 0.100
## left son=6 (475 obs) right son=7 (203 obs)
## Primary splits:
## Total < 492 to the left, improve=3.668560, (0 missing)
## SpeedAttack < 115.5 to the left, improve=2.395716, (0 missing)
## Attack < 111 to the left, improve=2.336745, (0 missing)
## Surrogate splits:
## SpeedAttack < 96 to the left, agree=0.798, adj=0.325, (0 split)
## Attack < 97.5 to the left, agree=0.788, adj=0.291, (0 split)
##
## Node number 6: 475 observations, complexity param=0.01179941
## predicted class=5 expected loss=0.76 P(node) =0.6588072
## class counts: 108 61 97 54 114 41
## probabilities: 0.227 0.128 0.204 0.114 0.240 0.086
## left son=12 (435 obs) right son=13 (40 obs)
## Primary splits:
## Total < 482.5 to the left, improve=2.814785, (0 missing)
## SpeedAttack < 54.5 to the left, improve=1.908587, (0 missing)
## Attack < 84.5 to the left, improve=1.677121, (0 missing)
## Surrogate splits:
## SpeedAttack < 122.5 to the left, agree=0.918, adj=0.025, (0 split)
##
## Node number 7: 203 observations
## predicted class=4 expected loss=0.7684729 P(node) =0.2815534
## class counts: 37 25 25 47 42 27
## probabilities: 0.182 0.123 0.123 0.232 0.207 0.133
##
## Node number 12: 435 observations, complexity param=0.01179941
## predicted class=1 expected loss=0.7770115 P(node) =0.6033287
## class counts: 97 58 92 51 96 41
## probabilities: 0.223 0.133 0.211 0.117 0.221 0.094
## left son=24 (177 obs) right son=25 (258 obs)
## Primary splits:
## SpeedAttack < 53.5 to the left, improve=2.611125, (0 missing)
## Total < 329.5 to the right, improve=2.413972, (0 missing)
## Attack < 84.5 to the left, improve=1.218174, (0 missing)
## Surrogate splits:
## Total < 329.5 to the left, agree=0.717, adj=0.305, (0 split)
## Attack < 24.5 to the left, agree=0.598, adj=0.011, (0 split)
##
## Node number 13: 40 observations
## predicted class=5 expected loss=0.55 P(node) =0.0554785
## class counts: 11 3 5 3 18 0
## probabilities: 0.275 0.075 0.125 0.075 0.450 0.000
##
## Node number 24: 177 observations, complexity param=0.01179941
## predicted class=5 expected loss=0.7175141 P(node) =0.2454924
## class counts: 47 18 31 19 50 12
## probabilities: 0.266 0.102 0.175 0.107 0.282 0.068
## left son=48 (20 obs) right son=49 (157 obs)
## Primary splits:
## Attack < 43.5 to the left, improve=2.9525500, (0 missing)
## Total < 302.5 to the left, improve=1.1299440, (0 missing)
## SpeedAttack < 30.5 to the right, improve=0.9809067, (0 missing)
##
## Node number 25: 258 observations, complexity param=0.0100295
## predicted class=3 expected loss=0.7635659 P(node) =0.3578363
## class counts: 50 40 61 32 46 29
## probabilities: 0.194 0.155 0.236 0.124 0.178 0.112
## left son=50 (228 obs) right son=51 (30 obs)
## Primary splits:
## Total < 470.5 to the left, improve=1.975112, (0 missing)
## Attack < 97.5 to the right, improve=1.927243, (0 missing)
## SpeedAttack < 99.5 to the right, improve=1.389027, (0 missing)
##
## Node number 48: 20 observations
## predicted class=3 expected loss=0.55 P(node) =0.02773925
## class counts: 3 3 9 3 2 0
## probabilities: 0.150 0.150 0.450 0.150 0.100 0.000
##
## Node number 49: 157 observations, complexity param=0.01061947
## predicted class=5 expected loss=0.6942675 P(node) =0.2177531
## class counts: 44 15 22 16 48 12
## probabilities: 0.280 0.096 0.140 0.102 0.306 0.076
## left son=98 (20 obs) right son=99 (137 obs)
## Primary splits:
## Attack < 49.5 to the left, improve=1.432856, (0 missing)
## Total < 328.5 to the left, improve=1.398573, (0 missing)
## SpeedAttack < 45.5 to the left, improve=1.299995, (0 missing)
## Surrogate splits:
## Total < 261 to the left, agree=0.879, adj=0.05, (0 split)
##
## Node number 50: 228 observations, complexity param=0.0100295
## predicted class=3 expected loss=0.754386 P(node) =0.3162275
## class counts: 47 39 56 25 37 24
## probabilities: 0.206 0.171 0.246 0.110 0.162 0.105
## left son=100 (134 obs) right son=101 (94 obs)
## Primary splits:
## Attack < 59.5 to the right, improve=1.922705, (0 missing)
## Total < 308.5 to the right, improve=1.921607, (0 missing)
## SpeedAttack < 94.5 to the right, improve=1.577188, (0 missing)
## Surrogate splits:
## Total < 349 to the right, agree=0.746, adj=0.383, (0 split)
## SpeedAttack < 94.5 to the left, agree=0.601, adj=0.032, (0 split)
##
## Node number 51: 30 observations
## predicted class=5 expected loss=0.7 P(node) =0.04160888
## class counts: 3 1 5 7 9 5
## probabilities: 0.100 0.033 0.167 0.233 0.300 0.167
##
## Node number 98: 20 observations
## predicted class=1 expected loss=0.55 P(node) =0.02773925
## class counts: 9 2 4 2 3 0
## probabilities: 0.450 0.100 0.200 0.100 0.150 0.000
##
## Node number 99: 137 observations
## predicted class=5 expected loss=0.6715328 P(node) =0.1900139
## class counts: 35 13 18 14 45 12
## probabilities: 0.255 0.095 0.131 0.102 0.328 0.088
##
## Node number 100: 134 observations
## predicted class=3 expected loss=0.6940299 P(node) =0.185853
## class counts: 27 23 41 15 20 8
## probabilities: 0.201 0.172 0.306 0.112 0.149 0.060
##
## Node number 101: 94 observations, complexity param=0.0100295
## predicted class=1 expected loss=0.787234 P(node) =0.1303745
## class counts: 20 16 15 10 17 16
## probabilities: 0.213 0.170 0.160 0.106 0.181 0.170
## left son=202 (72 obs) right son=203 (22 obs)
## Primary splits:
## Total < 308.5 to the right, improve=2.505856, (0 missing)
## SpeedAttack < 84 to the right, improve=2.424867, (0 missing)
## Attack < 47.5 to the left, improve=1.831175, (0 missing)
## Surrogate splits:
## Attack < 32.5 to the right, agree=0.798, adj=0.136, (0 split)
## SpeedAttack < 55.5 to the right, agree=0.787, adj=0.091, (0 split)
##
## Node number 202: 72 observations
## predicted class=1 expected loss=0.7361111 P(node) =0.0998613
## class counts: 19 14 11 8 8 12
## probabilities: 0.264 0.194 0.153 0.111 0.111 0.167
##
## Node number 203: 22 observations
## predicted class=5 expected loss=0.5909091 P(node) =0.03051318
## class counts: 1 2 4 2 9 4
## probabilities: 0.045 0.091 0.182 0.091 0.409 0.182rpart.plot(tree_classifier3)
title("Prediction Generation on Total, Attack, and Speed Attack")
treeprediction1 <- predict(tree_classifier, Pokemon_, type = 'class')
treeprediction2 <- predict(tree_classifier2, Pokemon_, type = 'class')
treeprediction3 <- predict(tree_classifier3, Pokemon_, type = 'class')The first decision tree shows our model attempting to predict Generation by Total Stats. The second decision tree shows our model attempting to predict Generation by Total Stats and Attack. The third decision tree shows our model attempting to predict Generation by Total Stats, Attack, and Speed Attack.
Testing Model Accuracy
accuracy <- function(predictions, ground_truth) {
mean(predictions == ground_truth)
}
accuracy(treeprediction1, Pokemon_$Generation)## [1] 0.2357836accuracy(treeprediction2, Pokemon_$Generation)## [1] 0.2357836accuracy(treeprediction3, Pokemon_$Generation)## [1] 0.3051318Our three models’ accuracy is not high enough to be significant. The first prediction accuracy is 23.5%, the second prediction accuracy is 23.5%, and the third prediction accuracy is 30.5%. Because the accuracy is considerably low, we do not have any support or point of direction in terms of the relationship between Generation and Total Stats and Attack and Speed Attack. But based upon the scatter plot of Total Stats and Attack based on Generation and the scatter plot of Total Stats and Speed Attack based on Generation, there was a lot of dispersion across all Generation given a positive correlation among all stats.
Generation 1 Regression
library(corrplot)
x <- (Pokemon_$Attack)
y <- (Pokemon_$Total)
plot(x,y)
new_model <- lm(y~x, data=Pokemon_, which(c(Pokemon_$Generation == "1")))
title("Generation 1 Regression")
abline(new_model)
summary(new_model)##
## Call:
## lm(formula = y ~ x, data = Pokemon_, subset = which(c(Pokemon_$Generation ==
## "1")))
##
## Residuals:
## Min 1Q Median 3Q Max
## -163.732 -53.326 -3.083 52.546 212.891
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 224.5279 17.5970 12.76 <2e-16 ***
## x 2.5162 0.2278 11.04 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 74.21 on 149 degrees of freedom
## Multiple R-squared: 0.4502, Adjusted R-squared: 0.4465
## F-statistic: 122 on 1 and 149 DF, p-value: < 2.2e-16Generation 2 Regression
x <- (Pokemon_$Attack)
y <- (Pokemon_$Total)
plot(x,y)
new_model <- lm(y~x, data=Pokemon_, which(c(Pokemon_$Generation == "2")))
title("Generation 2 Regression")
abline(new_model)
summary(new_model)##
## Call:
## lm(formula = y ~ x, data = Pokemon_, subset = which(c(Pokemon_$Generation ==
## "2")))
##
## Residuals:
## Min 1Q Median 3Q Max
## -136.72 -54.74 -11.03 60.53 285.38
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 228.6105 22.1967 10.299 < 2e-16 ***
## x 2.6014 0.3004 8.659 9.76e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 84.95 on 98 degrees of freedom
## Multiple R-squared: 0.4335, Adjusted R-squared: 0.4277
## F-statistic: 74.98 on 1 and 98 DF, p-value: 9.764e-14Generation 3 Regression
x <- (Pokemon_$Attack)
y <- (Pokemon_$Total)
plot(x,y)
new_model <- lm(y~x, data=Pokemon_, which(c(Pokemon_$Generation == "3")))
title("Generation 3 Regression")
abline(new_model)
summary(new_model)##
## Call:
## lm(formula = y ~ x, data = Pokemon_, subset = which(c(Pokemon_$Generation ==
## "3")))
##
## Residuals:
## Min 1Q Median 3Q Max
## -213.180 -54.305 -5.478 49.671 242.422
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 198.0745 17.6194 11.24 <2e-16 ***
## x 2.7901 0.2227 12.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 78.3 on 133 degrees of freedom
## Multiple R-squared: 0.5414, Adjusted R-squared: 0.5379
## F-statistic: 157 on 1 and 133 DF, p-value: < 2.2e-16Generation 4 Regression
x <- (Pokemon_$Attack)
y <- (Pokemon_$Total)
plot(x,y)
new_model <- lm(y~x, data=Pokemon_, which(c(Pokemon_$Generation == "4")))
title("Generation 4 Regression")
abline(new_model)
summary(new_model)##
## Call:
## lm(formula = y ~ x, data = Pokemon_, subset = which(c(Pokemon_$Generation ==
## "4")))
##
## Residuals:
## Min 1Q Median 3Q Max
## -216.864 -61.804 -1.131 53.968 182.490
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 227.4237 22.1120 10.29 <2e-16 ***
## x 2.7155 0.2567 10.58 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 82.12 on 105 degrees of freedom
## Multiple R-squared: 0.516, Adjusted R-squared: 0.5113
## F-statistic: 111.9 on 1 and 105 DF, p-value: < 2.2e-16Generation 5 Regression
x <- (Pokemon_$Attack)
y <- (Pokemon_$Total)
plot(x,y)
new_model <- lm(y~x, data=Pokemon_, which(c(Pokemon_$Generation == "5")))
title("Generation 5 Regression")
abline(new_model)
summary(new_model)##
## Call:
## lm(formula = y ~ x, data = Pokemon_, subset = which(c(Pokemon_$Generation ==
## "5")))
##
## Residuals:
## Min 1Q Median 3Q Max
## -132.826 -54.214 -5.366 45.088 184.131
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 226.5813 17.3425 13.06 <2e-16 ***
## x 2.4583 0.2019 12.18 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 73.24 on 154 degrees of freedom
## Multiple R-squared: 0.4905, Adjusted R-squared: 0.4872
## F-statistic: 148.3 on 1 and 154 DF, p-value: < 2.2e-16Generation 6 Regression
x <- (Pokemon_$Attack)
y <- (Pokemon_$Total)
plot(x,y)
new_model <- lm(y~x, data=Pokemon_, which(c(Pokemon_$Generation == "6")))
title("Generation 6 Regression")
abline(new_model)
summary(new_model)##
## Call:
## lm(formula = y ~ x, data = Pokemon_, subset = which(c(Pokemon_$Generation ==
## "6")))
##
## Residuals:
## Min 1Q Median 3Q Max
## -129.386 -57.096 6.184 49.251 164.826
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 189.821 26.346 7.205 5.28e-10 ***
## x 3.307 0.343 9.642 1.78e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 73.88 on 70 degrees of freedom
## Multiple R-squared: 0.5705, Adjusted R-squared: 0.5643
## F-statistic: 92.97 on 1 and 70 DF, p-value: 1.778e-14R-squared is a statistical measure of how close the data are to the fitted regression line. If 0% r-squared is produced, then the model explains none of the variability of the response data around its mean. However, for each Generation (1-6), there is high r-squared. In Generation 1, the r-squared of the model was 44.6%. This means that the 44.6% of the variability in Total Stats can be explained by Attack in Generation 1.
In Generation 2, the r-squared of the model was 44.6%. This means that the 42.7% of the variability in Total Stats can be explained by Attack in Generation 2. In Generation 3, the r-squared of the model was 44.6%. This means that the 53.7% of the variability in Total Stats can be explained by Attack in Generation 3. In Generation 4, the r-squared of the model was 44.6%. This means that the 51.1 % of the variability in Total Stats can be explained by Attack in Generation 4.
In Generation 5, the r-squared of the model was 48.7%. This means that the 48.7% of the variability in Total Stats can be explained by Attack in Generation 5. In Generation 6, the r-squared of the model was 48.7%. This means that the 56.4% of the variability in Total Stats can be explained by Attack in Generation 6. Because of the moderately high r-squared values throughout all the Generations being modeled on Total Stats against Attack, our ending statement is that stats may not be a good indicator of Generation due to each Generation having strong correlational patterns between stats. In other words, stats such as Total Stats and Attack may not be a good indicator of which among the six Generations are being observed. On the other hand, the regressions do suggest a strong relationship between Total Stats and Attack.
Hypothesis Number 2
Additionally for hypothesis number 2, we will explore whether we can predict Legendary Status of Pokemon based on Catch Rate or Total Stats. Our question is: Is there a relationship between Legendary Status and Catch Rate? Total Stats? In order to test this hypothesis, we must first visualize the data at hand. Then, we will use a decision tree to test the accuracy of our prediction model.
plot2 <-ggplot(Pokemon_, aes(x=Catch_Rate, y=Total, color=isLegendary)) + geom_point() + labs(x='Catch Rate', y='Total', title = 'Plot of Total Stats by Catch Rate based on Legendary Status')
plot2 
##Based on the plot, we can observe the dispersion. There are a large proportion of non-Legendary status Pokemon. Additionally, Legendary Status Pokemon have low catch rates and high total stats. There could be evidence or reason to believe that Legendary Status has a relationship with Total Stats and Catch Rate.
Testing for Legendary Status and Catch Rate
Catch <- as.numeric(Pokemon_$Catch_Rate)
tree_classifier <- rpart(Pokemon_$isLegendary ~ Catch, data = Pokemon_, method = 'class', control = rpart.control(maxdepth = 10, minsplit = 100))
summary(tree_classifier)## Call:
## rpart(formula = Pokemon_$isLegendary ~ Catch, data = Pokemon_,
## method = "class", control = rpart.control(maxdepth = 10,
## minsplit = 100))
## n= 721
##
## CP nsplit rel error xerror xstd
## 1 0.7391304 0 1.0000000 1.0000000 0.14266102
## 2 0.0100000 1 0.2608696 0.2608696 0.07467724
##
## Variable importance
## Catch
## 100
##
## Node number 1: 721 observations, complexity param=0.7391304
## predicted class=False expected loss=0.06380028 P(node) =1
## class counts: 675 46
## probabilities: 0.936 0.064
## left son=2 (671 obs) right son=3 (50 obs)
## Primary splits:
## Catch < 9 to the right, improve=64.73806, (0 missing)
##
## Node number 2: 671 observations
## predicted class=False expected loss=0.005961252 P(node) =0.9306519
## class counts: 667 4
## probabilities: 0.994 0.006
##
## Node number 3: 50 observations
## predicted class=True expected loss=0.16 P(node) =0.06934813
## class counts: 8 42
## probabilities: 0.160 0.840rpart.plot(tree_classifier)
title("Predicting Legendary using Total")
treeprediction1 <- predict(tree_classifier, Pokemon_, type = 'class')
accuracy <- function(predictions, ground_truth) {
mean(predictions == ground_truth)
}
accuracy(treeprediction1, Pokemon_$isLegendary)## [1] 0.9833564We used decision trees to investigate if our hypothesis of predicting Legendary status using catch rate was correct. We figured that Legendaries, due to their rarity, would be more difficult for players to catch. We found that catch rate reflects a trend by characterizing most legendary pokemon. With an accuracy score of 98%, we found a strong connection between the catch rate of a pokemon and its status as a legendary pokemon. Pokemon with a catch rate of 9 or less were placed in the right bucket. Additionally, our model has a 98.3% accuracy rate, which significantly reinforces our prediction model.
Testing for Legendary Status and Total
Total <- as.numeric(Pokemon_$Total)
tree_classifier <- rpart(Pokemon_$isLegendary ~ Total, data = Pokemon_, method = 'class', control = rpart.control(maxdepth = 10, minsplit = 100))
summary(tree_classifier)## Call:
## rpart(formula = Pokemon_$isLegendary ~ Total, data = Pokemon_,
## method = "class", control = rpart.control(maxdepth = 10,
## minsplit = 100))
## n= 721
##
## CP nsplit rel error xerror xstd
## 1 0.673913 0 1.000000 1.000000 0.14266102
## 2 0.010000 1 0.326087 0.326087 0.08331487
##
## Variable importance
## Total
## 100
##
## Node number 1: 721 observations, complexity param=0.673913
## predicted class=False expected loss=0.06380028 P(node) =1
## class counts: 675 46
## probabilities: 0.936 0.064
## left son=2 (660 obs) right son=3 (61 obs)
## Primary splits:
## Total < 573.5 to the left, improve=63.50742, (0 missing)
##
## Node number 2: 660 observations
## predicted class=False expected loss=0 P(node) =0.9153953
## class counts: 660 0
## probabilities: 1.000 0.000
##
## Node number 3: 61 observations
## predicted class=True expected loss=0.2459016 P(node) =0.08460472
## class counts: 15 46
## probabilities: 0.246 0.754rpart.plot(tree_classifier)
title("Predicting Legendary using Total")
treeprediction1 <- predict(tree_classifier, Pokemon_, type = 'class')
accuracy <- function(predictions, ground_truth) {
mean(predictions == ground_truth)
}
accuracy(treeprediction1, Pokemon_$isLegendary)## [1] 0.9791956