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Test.tex
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% Options for packages loaded elsewhere
\PassOptionsToPackage{unicode}{hyperref}
\PassOptionsToPackage{hyphens}{url}
%
\documentclass[
]{article}
\author{}
\date{\vspace{-2.5em}}
\usepackage{amsmath,amssymb}
\usepackage{lmodern}
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\begin{document}
Ovdje neki uvod i razrada null vrijednosti ako napravimo
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{read.csv}\NormalTok{(}\StringTok{\textquotesingle{}./vgsales.csv\textquotesingle{}}\NormalTok{)}
\FunctionTok{library}\NormalTok{(tidyverse)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## Warning: package 'tidyverse' was built under R version 4.1.2
\end{verbatim}
\begin{verbatim}
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
\end{verbatim}
\begin{verbatim}
## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.6 v dplyr 1.0.7
## v tidyr 1.1.4 v stringr 1.4.0
## v readr 2.1.1 v forcats 0.5.1
\end{verbatim}
\begin{verbatim}
## Warning: package 'ggplot2' was built under R version 4.1.2
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## Warning: package 'forcats' was built under R version 4.1.2
\end{verbatim}
\begin{verbatim}
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
\end{verbatim}
\#\#1. Pitanje: Jesu li u Japanu RPG igre značajno prodavanije od FPS
igara? Možete li pronaći neki žanr koji je značajno popularniji u Europi
nego u Japanu?
\#Jesu li u Japanu RPG igre značajno prodavanije od FPS igara?
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# Pogledajmo prvo podatke koje imam o Japanu prije same uspostave testa}
\CommentTok{\# Za usporedbu po žanrovima koristiti ćemo udio prodaje žanra u Japanu od ukupnih prodaja u Japanu.}
\NormalTok{JPGenreSales }\OtherTok{=}\NormalTok{ data[}\FunctionTok{c}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{9}\NormalTok{)]}
\NormalTok{JapanProfitByGenre }\OtherTok{=}\NormalTok{ JPGenreSales }\SpecialCharTok{\%\textgreater{}\%} \FunctionTok{group\_by}\NormalTok{(Genre) }\SpecialCharTok{\%\textgreater{}\%}
\FunctionTok{summarise}\NormalTok{(}\AttributeTok{PercentageOfGenreInMarket =} \FunctionTok{sum}\NormalTok{(JP\_Sales) }\SpecialCharTok{/} \FunctionTok{sum}\NormalTok{(JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sales))}
\FunctionTok{barplot}\NormalTok{(JapanProfitByGenre}\SpecialCharTok{$}\NormalTok{PercentageOfGenreInMarket, }
\AttributeTok{names.arg =}\NormalTok{ JapanProfitByGenre}\SpecialCharTok{$}\NormalTok{Genre, }
\AttributeTok{las =} \DecValTok{2}\NormalTok{, }
\AttributeTok{cex.names =} \FloatTok{0.8}\NormalTok{,}
\AttributeTok{main =} \StringTok{"Popularnost žanrova u Japanu"}\NormalTok{,}
\AttributeTok{ylab =} \StringTok{"Udio prodaje žanra od ukupne prodaje u Japana"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-2-1.pdf}
Na prvi pogled izgleda kao da su RPG igre znatno dominantan žanr u
Japanu te svakako popularnije od FPS igri. Uvjerimo se u to
prikazivanjem podataka pomoću dodatnih grafova te zatim provjerimo
t-testom.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{JP\_FPSData }\OtherTok{=}\NormalTok{ JPGenreSales[JPGenreSales}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Shooter"} \SpecialCharTok{\&}\NormalTok{ JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sale }\SpecialCharTok{\textgreater{}} \DecValTok{0}\NormalTok{, ]}
\NormalTok{JP\_RPGData }\OtherTok{=}\NormalTok{ JPGenreSales[JPGenreSales}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Role{-}Playing"} \SpecialCharTok{\&}\NormalTok{ JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sales }\SpecialCharTok{\textgreater{}} \DecValTok{0}\NormalTok{, ]}
\FunctionTok{boxplot}\NormalTok{(JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales, JP\_RPGData}\SpecialCharTok{$}\NormalTok{JP\_Sales,}
\AttributeTok{names =} \FunctionTok{c}\NormalTok{(}\StringTok{"FPS sales"}\NormalTok{, }\StringTok{"RPG sales"}\NormalTok{),}
\AttributeTok{main =} \StringTok{"Prodaja FPS i RPG igara u Japanu"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-3-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{b }\OtherTok{=} \FunctionTok{seq}\NormalTok{(}\FunctionTok{min}\NormalTok{(JP\_RPGData}\SpecialCharTok{$}\NormalTok{JP\_Sales) }\SpecialCharTok{{-}} \FloatTok{0.2}\NormalTok{,}\FunctionTok{max}\NormalTok{(JP\_RPGData}\SpecialCharTok{$}\NormalTok{JP\_Sales) }\SpecialCharTok{+} \FloatTok{0.2}\NormalTok{,}\FloatTok{0.2}\NormalTok{)}
\NormalTok{h1 }\OtherTok{=} \FunctionTok{hist}\NormalTok{(JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{breaks =}\NormalTok{ b, }\AttributeTok{plot =} \ConstantTok{FALSE}\NormalTok{)}
\NormalTok{h2 }\OtherTok{=} \FunctionTok{hist}\NormalTok{(JP\_RPGData}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{breaks =}\NormalTok{ b, }\AttributeTok{plot =} \ConstantTok{FALSE}\NormalTok{)}
\NormalTok{JP\_RPGFPSdata }\OtherTok{\textless{}{-}} \FunctionTok{t}\NormalTok{(}\FunctionTok{cbind}\NormalTok{(h1}\SpecialCharTok{$}\NormalTok{counts, h2}\SpecialCharTok{$}\NormalTok{counts))}
\FunctionTok{barplot}\NormalTok{(JP\_RPGFPSdata, }\AttributeTok{beside=}\ConstantTok{TRUE}\NormalTok{, }\AttributeTok{col =} \FunctionTok{c}\NormalTok{(}\StringTok{"red"}\NormalTok{, }\StringTok{"green"}\NormalTok{),}
\AttributeTok{main =} \StringTok{"Prodaja FPS i RPG igara u Japanu"}\NormalTok{)}
\FunctionTok{legend}\NormalTok{(}\StringTok{"topright"}\NormalTok{, }\AttributeTok{fill =} \FunctionTok{c}\NormalTok{(}\StringTok{"red"}\NormalTok{, }\StringTok{"green"}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\StringTok{"FPS igre"}\NormalTok{, }\StringTok{"RPG igre"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-3-2.pdf}
Nažalost podatci sadrže ogroman broj niskoprodavanih igrica te time je
svaka imalo uspješna igrica ``outlier''. Posljedica je jako nečitljiv
box-and-whisker graf i gotovo nevidljivi outlieri na bar grafu. Zato
ćemo iz naših podataka izbaciti najnižih i najviših 10\% vrijednosti.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{JP\_FPSq }\OtherTok{\textless{}{-}} \FunctionTok{quantile}\NormalTok{(JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{probs =} \FunctionTok{c}\NormalTok{(.}\DecValTok{1}\NormalTok{, .}\DecValTok{90}\NormalTok{))}
\NormalTok{JP\_RPGq }\OtherTok{\textless{}{-}} \FunctionTok{quantile}\NormalTok{(JP\_RPGData}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{probs =} \FunctionTok{c}\NormalTok{(.}\DecValTok{1}\NormalTok{, .}\DecValTok{90}\NormalTok{))}
\NormalTok{JP\_FPSDataTrimmed }\OtherTok{=}\NormalTok{ JPGenreSales[JPGenreSales}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Shooter"}
\SpecialCharTok{\&}\NormalTok{ JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sales }\SpecialCharTok{\textgreater{}=}\NormalTok{ JP\_FPSq[}\DecValTok{1}\NormalTok{] }\SpecialCharTok{\&}\NormalTok{ JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sales }\SpecialCharTok{\textless{}=}\NormalTok{ JP\_FPSq[}\DecValTok{2}\NormalTok{], ]}
\NormalTok{JP\_RPGDataTrimmed }\OtherTok{=}\NormalTok{ JPGenreSales[JPGenreSales}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Role{-}Playing"}
\SpecialCharTok{\&}\NormalTok{ JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sales }\SpecialCharTok{\textgreater{}=}\NormalTok{ JP\_RPGq[}\DecValTok{1}\NormalTok{] }\SpecialCharTok{\&}\NormalTok{ JPGenreSales}\SpecialCharTok{$}\NormalTok{JP\_Sales }\SpecialCharTok{\textless{}=}\NormalTok{ JP\_RPGq[}\DecValTok{2}\NormalTok{], ]}
\NormalTok{bTrimmed }\OtherTok{=} \FunctionTok{seq}\NormalTok{(}\FunctionTok{min}\NormalTok{(JP\_RPGDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales) }\SpecialCharTok{{-}} \FloatTok{0.05}\NormalTok{,}\FunctionTok{max}\NormalTok{(JP\_RPGDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales) }\SpecialCharTok{+} \FloatTok{0.05}\NormalTok{,}\FloatTok{0.05}\NormalTok{)}
\FunctionTok{boxplot}\NormalTok{(JP\_FPSDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales, JP\_RPGDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales,}
\AttributeTok{names =} \FunctionTok{c}\NormalTok{(}\StringTok{"FPS sales"}\NormalTok{, }\StringTok{"RPG sales"}\NormalTok{),}
\AttributeTok{main =} \StringTok{"Prodaja FPS i RPG igara u Japanu"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-4-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{h1Trimmed }\OtherTok{=} \FunctionTok{hist}\NormalTok{(JP\_FPSDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{breaks =}\NormalTok{ bTrimmed, }\AttributeTok{plot =} \ConstantTok{FALSE}\NormalTok{)}
\NormalTok{h2Trimmed }\OtherTok{=} \FunctionTok{hist}\NormalTok{(JP\_RPGDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{breaks =}\NormalTok{ bTrimmed, }\AttributeTok{plot =} \ConstantTok{FALSE}\NormalTok{)}
\NormalTok{JP\_RPGFPSdataTrimmed }\OtherTok{\textless{}{-}} \FunctionTok{t}\NormalTok{(}\FunctionTok{cbind}\NormalTok{(h1Trimmed}\SpecialCharTok{$}\NormalTok{counts, h2Trimmed}\SpecialCharTok{$}\NormalTok{counts))}
\FunctionTok{barplot}\NormalTok{(JP\_RPGFPSdataTrimmed, }\AttributeTok{beside=}\ConstantTok{TRUE}\NormalTok{, }\AttributeTok{col =} \FunctionTok{c}\NormalTok{(}\StringTok{"red"}\NormalTok{, }\StringTok{"green"}\NormalTok{),}
\AttributeTok{main =} \StringTok{"Prodaja FPS i RPG igara u Japanu"}\NormalTok{,)}
\FunctionTok{legend}\NormalTok{(}\StringTok{"topright"}\NormalTok{, }\AttributeTok{fill =} \FunctionTok{c}\NormalTok{(}\StringTok{"red"}\NormalTok{, }\StringTok{"green"}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\StringTok{"FPS igre"}\NormalTok{, }\StringTok{"RPG igre"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-4-2.pdf}
Iz novih grafova možemo pretpostaviti nekoliko stvari: U Japanu izlazi
puno više novih RPG nego FPS igri. U prosjeku RPG igre se prodaju više
od FPS igri. RPG igre imaju puno više jako uspješnih outliera te su oni
i znatno uspješniji od FPS outliera. Potvrdimo sada pretpostavku
popularnosti t-testom.
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\#Postavimo t{-}test na sljedeći način:}
\CommentTok{\#H0 {-} d = 0 {-}{-} srednje vrijednosti prodaje RPG i FPS igri su jednake}
\CommentTok{\#H1 {-} d \textgreater{} 0 {-}{-} srednje vrijednosti prodaje RPG i FPS igri nisu jednake }
\CommentTok{\#također koristiti ćemo alfa=0.01 da bismo dobili 99\% interval povjerenja}
\CommentTok{\#pretpostavljamo različite varijance prodaje igri unutar žanrova}
\FunctionTok{t.test}\NormalTok{(JP\_RPGData}\SpecialCharTok{$}\NormalTok{JP\_Sales, JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales, }
\AttributeTok{alternative=}\StringTok{"greater"}\NormalTok{,}
\AttributeTok{paired=}\ConstantTok{FALSE}\NormalTok{,}
\AttributeTok{var.equal=}\ConstantTok{FALSE}\NormalTok{,}
\AttributeTok{conf.level=}\FloatTok{0.99}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Welch Two Sample t-test
##
## data: JP_RPGData$JP_Sales and JP_FPSData$JP_Sales
## t = 9.4633, df = 1301, p-value < 2.2e-16
## alternative hypothesis: true difference in means is greater than 0
## 99 percent confidence interval:
## 0.176123 Inf
## sample estimates:
## mean of x mean of y
## 0.3348954 0.1012698
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{qt}\NormalTok{(}\AttributeTok{p=}\FloatTok{0.01}\NormalTok{, }\AttributeTok{df=}\DecValTok{1301}\NormalTok{, }\AttributeTok{lower.tail=}\ConstantTok{FALSE}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## [1] 2.329218
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{qt}\NormalTok{(}\AttributeTok{p=}\FloatTok{0.00001}\NormalTok{, }\AttributeTok{df=}\DecValTok{1301}\NormalTok{, }\AttributeTok{lower.tail=}\ConstantTok{FALSE}\NormalTok{) }\CommentTok{\#t{-}vrijednost potrebna za odbacivanje na 99.999\% intervalu povjerenja}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## [1] 4.280668
\end{verbatim}
Iz rezultata možemo zaključiti sljedeće: Na temelju jako male
p-vrijednost znamo da je ovo jako ekstreman slučaj tj. jako je mala
šansa ovakvog uzorka u slučaju H0. P-vrijednost podupire hipotezu H1. Na
temelju jako velike t-vrijednosti koja se nalazi daleko iznad kritične
vrijednosti odbacivanja možemo odbaciti H0 u korist H1. Zaključujemo da
su RPG igre prodavanije od FPS igri.
\#Možete li pronaći neki žanr koji je značajno popularniji u Europi nego
u Japanu?
Prije nego krenemo na rješavanje samog pitanja moramo razriješiti
problem popularnosti. Kako je Europsko tržište znatno veće nego Japan
moramo odabrati model koji će dobro opisati ``popularnost'' žanrova
neovisno o populaciji potrošača. Model koji smo izabrali za grafički
prikaz problema jest udio potrošača žanra od ukupnih potrošača regije.
npr. popularnost RPG igara u Japanu odredit ćemo tako da broj prodaja
RPG igara Japana podijelimo s brojem prodaje svih žanrova Japana.
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\#Prikažimo prvo podatke grafički bar grafovima}
\NormalTok{EUGenreSales }\OtherTok{=}\NormalTok{ data[}\FunctionTok{c}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{8}\NormalTok{)]}
\NormalTok{EuropeProfitByGenre }\OtherTok{=}\NormalTok{ EUGenreSales }\SpecialCharTok{\%\textgreater{}\%} \FunctionTok{group\_by}\NormalTok{(Genre) }\SpecialCharTok{\%\textgreater{}\%}
\FunctionTok{summarise}\NormalTok{(}\AttributeTok{PercentageOfGenreInMarket =} \FunctionTok{sum}\NormalTok{(EU\_Sales) }\SpecialCharTok{/} \FunctionTok{sum}\NormalTok{(EUGenreSales}\SpecialCharTok{$}\NormalTok{EU\_Sales))}
\FunctionTok{par}\NormalTok{(}\AttributeTok{mfrow=}\FunctionTok{c}\NormalTok{(}\DecValTok{1}\NormalTok{,}\DecValTok{2}\NormalTok{))}
\FunctionTok{barplot}\NormalTok{(EuropeProfitByGenre}\SpecialCharTok{$}\NormalTok{PercentageOfGenreInMarket, }
\AttributeTok{names.arg =}\NormalTok{ EuropeProfitByGenre}\SpecialCharTok{$}\NormalTok{Genre, }
\AttributeTok{las =} \DecValTok{2}\NormalTok{, }
\AttributeTok{cex.names =} \FloatTok{0.8}\NormalTok{,}
\AttributeTok{main =} \StringTok{"Popularnost žanrova u Europi"}\NormalTok{,}
\AttributeTok{ylab =} \StringTok{"Udio prodaje žanra od ukupne prodaje u Europi"}\NormalTok{)}
\FunctionTok{barplot}\NormalTok{(JapanProfitByGenre}\SpecialCharTok{$}\NormalTok{PercentageOfGenreInMarket, }
\AttributeTok{names.arg =}\NormalTok{ JapanProfitByGenre}\SpecialCharTok{$}\NormalTok{Genre, }
\AttributeTok{las =} \DecValTok{2}\NormalTok{, }
\AttributeTok{cex.names =} \FloatTok{0.8}\NormalTok{,}
\AttributeTok{main =} \StringTok{"Popularnost žanrova u Japanu"}\NormalTok{,}
\AttributeTok{ylab =} \StringTok{"Udio prodaje žanra od ukupne prodaje u Japana"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-6-1.pdf}
Možemo uočiti nekoliko žanrova za koje možemo pretpostaviti da su
popularniji u Europi nego u Japanu prema izabranom modelu. To su
žanrovi: Action, Racing, Shooter, Sports. Prikažimo dodatne pomoćne
grafove za žanr Shooter.
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\#Odmah ćemo koristiti srezane podatke}
\NormalTok{EU\_FPSData }\OtherTok{=}\NormalTok{ EUGenreSales[EUGenreSales}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Shooter"} \SpecialCharTok{\&}\NormalTok{ EUGenreSales}\SpecialCharTok{$}\NormalTok{EU\_Sales }\SpecialCharTok{\textgreater{}} \DecValTok{0}\NormalTok{, ]}
\NormalTok{EU\_FPSq }\OtherTok{\textless{}{-}} \FunctionTok{quantile}\NormalTok{(EU\_FPSData}\SpecialCharTok{$}\NormalTok{EU\_Sales, }\AttributeTok{probs =} \FunctionTok{c}\NormalTok{(.}\DecValTok{1}\NormalTok{, .}\DecValTok{90}\NormalTok{))}
\NormalTok{EU\_FPSDataTrimmed }\OtherTok{=}\NormalTok{ EUGenreSales[EUGenreSales}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Shooter"}
\SpecialCharTok{\&}\NormalTok{ EUGenreSales}\SpecialCharTok{$}\NormalTok{EU\_Sales }\SpecialCharTok{\textgreater{}=}\NormalTok{ EU\_FPSq[}\DecValTok{1}\NormalTok{] }\SpecialCharTok{\&}\NormalTok{ EUGenreSales}\SpecialCharTok{$}\NormalTok{EU\_Sales }\SpecialCharTok{\textless{}=}\NormalTok{ EU\_FPSq[}\DecValTok{2}\NormalTok{], ]}
\FunctionTok{boxplot}\NormalTok{(EU\_FPSDataTrimmed}\SpecialCharTok{$}\NormalTok{EU\_Sales, JP\_FPSDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales,}
\AttributeTok{names =} \FunctionTok{c}\NormalTok{(}\StringTok{"EU FPS sales"}\NormalTok{, }\StringTok{"Japan FPS sales"}\NormalTok{),}
\AttributeTok{main =} \StringTok{"Prodaja FPS igri u EU i Japanu"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-7-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{bJPvEU }\OtherTok{=} \FunctionTok{seq}\NormalTok{(}\FunctionTok{min}\NormalTok{(JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales) }\SpecialCharTok{{-}} \FloatTok{0.05}\NormalTok{,}\FunctionTok{max}\NormalTok{(JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales)}\SpecialCharTok{{-}}\FloatTok{0.6}\NormalTok{,}\FloatTok{0.05}\NormalTok{)}
\NormalTok{h1 }\OtherTok{=} \FunctionTok{hist}\NormalTok{(JP\_FPSDataTrimmed}\SpecialCharTok{$}\NormalTok{JP\_Sales, }\AttributeTok{breaks =}\NormalTok{ bJPvEU, }\AttributeTok{plot =} \ConstantTok{FALSE}\NormalTok{)}
\NormalTok{h2 }\OtherTok{=} \FunctionTok{hist}\NormalTok{(EU\_FPSDataTrimmed}\SpecialCharTok{$}\NormalTok{EU\_Sales, }\AttributeTok{breaks =}\NormalTok{ bJPvEU, }\AttributeTok{plot =} \ConstantTok{FALSE}\NormalTok{)}
\NormalTok{JPEU\_FPSdataTrimmed }\OtherTok{\textless{}{-}} \FunctionTok{t}\NormalTok{(}\FunctionTok{cbind}\NormalTok{(h1}\SpecialCharTok{$}\NormalTok{counts, h2}\SpecialCharTok{$}\NormalTok{counts))}
\FunctionTok{barplot}\NormalTok{(JPEU\_FPSdataTrimmed, }\AttributeTok{beside=}\ConstantTok{TRUE}\NormalTok{, }\AttributeTok{col =} \FunctionTok{c}\NormalTok{(}\StringTok{"red"}\NormalTok{, }\StringTok{"green"}\NormalTok{),}
\AttributeTok{main =} \StringTok{"Prodaja FPS igri u EU i Japanu"}\NormalTok{)}
\FunctionTok{legend}\NormalTok{(}\StringTok{"topright"}\NormalTok{, }\AttributeTok{fill =} \FunctionTok{c}\NormalTok{(}\StringTok{"red"}\NormalTok{, }\StringTok{"green"}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\StringTok{"FPS prodaja u Japanu"}\NormalTok{, }\StringTok{"FPS prodaja u EU"}\NormalTok{))}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-7-2.pdf}
Prikazani grafovi potvrđuju da su FPS igre popularnije u Europi nego
Japanu i po broju naslova i po prodajama. No potvrdimo to t-testom.
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\#Kako bismo dobili podatke koji bolje prikazuju popularnost unutar same regije, vrijednosti prodaje FPS igara unutar regije podijelit ćemo s prosječnim brojem prodaje igara unutar te regije}
\NormalTok{NonBisaedEUFPSData }\OtherTok{=}\NormalTok{ EU\_FPSData}\SpecialCharTok{$}\NormalTok{EU\_Sales }\SpecialCharTok{/} \FunctionTok{mean}\NormalTok{(data}\SpecialCharTok{$}\NormalTok{EU\_Sales)}
\NormalTok{NonBiasedJPFPSDATA }\OtherTok{=}\NormalTok{ JP\_FPSData}\SpecialCharTok{$}\NormalTok{JP\_Sales }\SpecialCharTok{/} \FunctionTok{mean}\NormalTok{(data}\SpecialCharTok{$}\NormalTok{JP\_Sales)}
\CommentTok{\#Postavimo t{-}test na sljedeći način:}
\CommentTok{\#H0 {-} d = 0 {-}{-} srednje vrijednosti prodaje FPS igri unutar EU i Japana su jednake}
\CommentTok{\#H1 {-} d \textgreater{} 0 {-}{-} srednje vrijednosti prodaje FPS igri unutar EU i Japana nisu jednake }
\CommentTok{\#također koristiti ćemo alfa=0.01 da bismo dobili 99\% interval povjerenja}
\CommentTok{\#pretpostavljamo različite varijance prodaje igri unutar žanrova}
\FunctionTok{t.test}\NormalTok{(NonBisaedEUFPSData, NonBiasedJPFPSDATA, }
\AttributeTok{alternative=}\StringTok{"greater"}\NormalTok{,}
\AttributeTok{paired=}\ConstantTok{FALSE}\NormalTok{,}
\AttributeTok{var.equal=}\ConstantTok{FALSE}\NormalTok{,}
\AttributeTok{conf.level=}\FloatTok{0.99}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Welch Two Sample t-test
##
## data: NonBisaedEUFPSData and NonBiasedJPFPSDATA
## t = 4.0421, df = 1208.4, p-value = 2.816e-05
## alternative hypothesis: true difference in means is greater than 0
## 99 percent confidence interval:
## 0.2856255 Inf
## sample estimates:
## mean of x mean of y
## 1.976083 1.301976
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{qt}\NormalTok{(}\AttributeTok{p=}\FloatTok{0.0001}\NormalTok{, }\AttributeTok{df=}\DecValTok{1301}\NormalTok{, }\AttributeTok{lower.tail=}\ConstantTok{FALSE}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## [1] 3.729643
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{qt}\NormalTok{(}\AttributeTok{p=}\FloatTok{0.00001}\NormalTok{, }\AttributeTok{df=}\DecValTok{1301}\NormalTok{, }\AttributeTok{lower.tail=}\ConstantTok{FALSE}\NormalTok{) }\CommentTok{\#t{-}vrijednost potrebna za odbacivanje na 99.999\% intervalu povjerenja}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## [1] 4.280668
\end{verbatim}
Iz rezultata možemo zaključiti sljedeće: Na temelju jako male
p-vrijednost znamo da je ovo jako ekstreman slučaj tj. jako je mala
šansa ovakvog uzorka u slučaju H0. P-vrijednost podupire hipotezu H1. Na
temelju jako velike t-vrijednosti (nalazi se između intervala povjerenja
99.99\% i 99.999\%) koja se nalazi iznad kritične vrijednosti
odbacivanja možemo odbaciti H0 u korist H1. Zaključujemo da su FPS igre
prodavanije u EU nego Japanu.
\#\#2. Pitanje: Promatrajući prodaju u Sjevernoj Americi, jesu li neki
žanrovi značajno popularniji?
Gledamo prvo podatke koje imamo o Sjevernoj Americi prije testa. Za
usporedbu po žanrovima koristiti ćemo udio prodaje žanrova u Americi od
ukupne prodaje u Americi.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{NAGenreSales }\OtherTok{=}\NormalTok{ data[}\FunctionTok{c}\NormalTok{(}\DecValTok{5}\NormalTok{,}\DecValTok{7}\NormalTok{)]}
\NormalTok{NAProfitByGenre }\OtherTok{=}\NormalTok{ NAGenreSales }\SpecialCharTok{\%\textgreater{}\%} \FunctionTok{group\_by}\NormalTok{(Genre) }\SpecialCharTok{\%\textgreater{}\%}
\FunctionTok{summarise}\NormalTok{(}\AttributeTok{PercentageOfGenreInMarket =} \FunctionTok{sum}\NormalTok{(NA\_Sales) }\SpecialCharTok{/} \FunctionTok{sum}\NormalTok{(NAGenreSales}\SpecialCharTok{$}\NormalTok{NA\_Sales))}
\FunctionTok{barplot}\NormalTok{(NAProfitByGenre}\SpecialCharTok{$}\NormalTok{PercentageOfGenreInMarket, }
\AttributeTok{names.arg =}\NormalTok{ NAProfitByGenre}\SpecialCharTok{$}\NormalTok{Genre, }
\AttributeTok{las =} \DecValTok{2}\NormalTok{, }
\AttributeTok{cex.names =} \FloatTok{0.8}\NormalTok{,}
\AttributeTok{main =} \StringTok{"Popularnost zanrova u Americi"}\NormalTok{,}
\AttributeTok{ylab =} \StringTok{"Udio prodaje zanra od ukupne prodaje u Sjevernoj Americi"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-9-1.pdf}
Odokativno vidimo da su prodavaniji žanrovi Action, Shooter i Sports, te
da se žanrovi Strategy,Adventure i Puzzle slabije prodaju, tj. možemo
pretpostaviti da varijance neće biti iste kod različitih žanrova.
Da bi smo odgovorili na ovo pitanje u potpunosti koristiti ćemo ANOVA
test, tj. metodu s kojom testiramo sredine više populacija, u našem
slučaju žanrova. Jedan od glavnih ciljeva analize varijance je
ustanoviti jesu li upravo te razlike između grupa samo posljedica
slučajnosti ili je statistički značajna. U našem slučaju koristimo
jednofaktorsku varijantu jer smatramo da popularnost proizlazi iz
prodanosti određenih žanrova.
Pretpostavke ANOVA-e su:
\begin{itemize}
\tightlist
\item
nezavisnost pojedinih podataka u uzorcima,
\item
normalna razdioba podataka,
\item
homogenost varijanci među populacijama.
\end{itemize}
Analizom varijance testiramo: \[ \begin{aligned}
H_0 & : \mu_1 = \mu_2 = \ldots = \mu_k \\
H_1 & : \neg H_0.
\end{aligned} \]
Provjeru normalnost ćemo napraviti prikazom histograma svakog žanra.
Gdje je žanr varijabla koja određuje grupu, a prodaja je zavisna
varijabla.
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{require}\NormalTok{(nortest)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## Loading required package: nortest
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# Iz sljedećih histograma vidimo da podaci nisu normalno distribuirani}
\FunctionTok{hist}\NormalTok{(data}\SpecialCharTok{$}\NormalTok{NA\_Sales[data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{\textquotesingle{}Action\textquotesingle{}}\NormalTok{],}\AttributeTok{main=}\StringTok{\textquotesingle{}Broj prodanih primjeraka Action žanra iz ne transformiranih podataka\textquotesingle{}}\NormalTok{, }\AttributeTok{xlab=}\StringTok{\textquotesingle{}Value\textquotesingle{}}\NormalTok{,}\AttributeTok{ylab=}\StringTok{\textquotesingle{}Frequency\textquotesingle{}}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/test pretpostavki - normalnost-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{hist}\NormalTok{(data}\SpecialCharTok{$}\NormalTok{NA\_Sales[data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{\textquotesingle{}Adventure\textquotesingle{}}\NormalTok{],}\AttributeTok{main=}\StringTok{\textquotesingle{}Broj prodanih primjeraka Adventure žanra iz ne transformiranih podataka\textquotesingle{}}\NormalTok{, }\AttributeTok{xlab=}\StringTok{\textquotesingle{}Value\textquotesingle{}}\NormalTok{,}\AttributeTok{ylab=}\StringTok{\textquotesingle{}Frequency\textquotesingle{}}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/test pretpostavki - normalnost-2.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-1.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-2.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-3.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-4.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-5.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-6.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-7.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-8.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-10-9.pdf}
Pošto podatci nisu u normalnoj distribuciji, koristeći log
transformaciju približavamo podatke normalnoj distribuciji. Radimo novi
stupac gdje ćemo imati vrijednosti prodanih primjeraka povećanih 100
puta da nemamo vrijednosti između 0 i 1, jer nam onda logaritamska
transformacija ima samo pozitivne vrijednosti
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{trimmedData }\OtherTok{\textless{}{-}}\NormalTok{ data[data}\SpecialCharTok{$}\NormalTok{NA\_Sales }\SpecialCharTok{!=} \DecValTok{0} \SpecialCharTok{\&}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{Year }\SpecialCharTok{!=} \StringTok{"N/A"} \SpecialCharTok{\&}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{Year }\SpecialCharTok{!=} \StringTok{"2020"}\NormalTok{,]}
\NormalTok{trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\OtherTok{\textless{}{-}} \FunctionTok{log}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales }\SpecialCharTok{*} \DecValTok{100}\NormalTok{)}
\FunctionTok{hist}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted[trimmedData}\SpecialCharTok{$}\NormalTok{Genre}\SpecialCharTok{==}\StringTok{\textquotesingle{}Action\textquotesingle{}}\NormalTok{],}\AttributeTok{main=}\StringTok{\textquotesingle{}Broj prodanih primjeraka Action žanra\textquotesingle{}}\NormalTok{,}\AttributeTok{xlab=}\StringTok{\textquotesingle{}Value\textquotesingle{}}\NormalTok{,}\AttributeTok{ylab=}\StringTok{\textquotesingle{}Frequency\textquotesingle{}}\NormalTok{, }\AttributeTok{breaks=}\DecValTok{20}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/histogrami normalnosti-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{hist}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted[trimmedData}\SpecialCharTok{$}\NormalTok{Genre}\SpecialCharTok{==}\StringTok{\textquotesingle{}Racing\textquotesingle{}}\NormalTok{],}\AttributeTok{main=}\StringTok{\textquotesingle{}Broj prodanih primjeraka Racing žanra\textquotesingle{}}\NormalTok{,}\AttributeTok{xlab=}\StringTok{\textquotesingle{}Value\textquotesingle{}}\NormalTok{,}\AttributeTok{ylab=}\StringTok{\textquotesingle{}Frequency\textquotesingle{}}\NormalTok{, }\AttributeTok{breaks=}\DecValTok{20}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/histogrami normalnosti-2.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{qqnorm}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted[trimmedData}\SpecialCharTok{$}\NormalTok{Genre}\SpecialCharTok{==}\StringTok{\textquotesingle{}Action\textquotesingle{}}\NormalTok{], }\AttributeTok{pch =} \DecValTok{1}\NormalTok{, }\AttributeTok{frame =} \ConstantTok{FALSE}\NormalTok{,}\AttributeTok{main=}\StringTok{\textquotesingle{}Action\textquotesingle{}}\NormalTok{)}
\FunctionTok{qqline}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted[trimmedData}\SpecialCharTok{$}\NormalTok{Genre}\SpecialCharTok{==}\StringTok{\textquotesingle{}Action\textquotesingle{}}\NormalTok{], }\AttributeTok{col =} \StringTok{"steelblue"}\NormalTok{, }\AttributeTok{lwd =} \DecValTok{2}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/histogrami normalnosti-3.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{qqnorm}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted[trimmedData}\SpecialCharTok{$}\NormalTok{Genre}\SpecialCharTok{==}\StringTok{\textquotesingle{}Racing\textquotesingle{}}\NormalTok{], }\AttributeTok{pch =} \DecValTok{1}\NormalTok{, }\AttributeTok{frame =} \ConstantTok{FALSE}\NormalTok{,}\AttributeTok{main=}\StringTok{\textquotesingle{}Racing\textquotesingle{}}\NormalTok{)}
\FunctionTok{qqline}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted[trimmedData}\SpecialCharTok{$}\NormalTok{Genre}\SpecialCharTok{==}\StringTok{\textquotesingle{}Racing\textquotesingle{}}\NormalTok{], }\AttributeTok{col =} \StringTok{"steelblue"}\NormalTok{, }\AttributeTok{lwd =} \DecValTok{2}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/histogrami normalnosti-4.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-1.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-2.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-3.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-4.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-5.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-6.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-7.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-8.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-9.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-10.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-11.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-12.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-13.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-14.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-15.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-16.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-17.pdf}
\includegraphics{Test_files/figure-latex/unnamed-chunk-11-18.pdf}
Provodimo Bartlettov test homogenosti varijanci među žanrovima i
nacrtajmo box plotove transformiranih podataka.
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{bartlett.test}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ trimmedData}\SpecialCharTok{$}\NormalTok{Genre)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Bartlett test of homogeneity of variances
##
## data: trimmedData$NA_Sales_adjusted by trimmedData$Genre
## Bartlett's K-squared = 98.682, df = 11, p-value = 3.256e-16
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# Graficki prikaz podataka}
\FunctionTok{boxplot}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ trimmedData}\SpecialCharTok{$}\NormalTok{Genre, }\AttributeTok{cex.axis =} \DecValTok{1}\NormalTok{, }\AttributeTok{las=}\DecValTok{2}\NormalTok{, }\AttributeTok{xlab=}\StringTok{""}\NormalTok{, }\AttributeTok{ylab=}\StringTok{"Log transformirani podaci prodaje primjeraka u Americi"}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/test pretpostavki - homogenost varijanci-1.pdf}
Zbog jako male p vrijednosti nam zapravo Bartlettov test sam sugerira da
su im varijance različite, no provedimo ANOVA test.
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# ANOVA Test}
\NormalTok{a }\OtherTok{=} \FunctionTok{aov}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ trimmedData}\SpecialCharTok{$}\NormalTok{Genre)}
\FunctionTok{summary}\NormalTok{(a)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## Df Sum Sq Mean Sq F value Pr(>F)
## trimmedData$Genre 11 487 44.31 26.63 <2e-16 ***
## Residuals 11875 19761 1.66
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# Linearni model}
\NormalTok{model }\OtherTok{=} \FunctionTok{lm}\NormalTok{(trimmedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ trimmedData}\SpecialCharTok{$}\NormalTok{Genre, }\AttributeTok{data =}\NormalTok{ trimmedData)}
\FunctionTok{summary}\NormalTok{(model)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Call:
## lm(formula = trimmedData$NA_Sales_adjusted ~ trimmedData$Genre,
## data = trimmedData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9260 -0.8466 -0.0465 0.8406 5.5709
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.74295 0.02567 106.867 < 2e-16 ***
## trimmedData$GenreAdventure -0.51320 0.06121 -8.385 < 2e-16 ***
## trimmedData$GenreFighting 0.09839 0.05919 1.662 0.096470 .
## trimmedData$GenreMisc -0.04369 0.04540 -0.962 0.335863
## trimmedData$GenrePlatform 0.18309 0.05254 3.485 0.000494 ***
## trimmedData$GenrePuzzle -0.56455 0.06670 -8.463 < 2e-16 ***
## trimmedData$GenreRacing -0.19399 0.04678 -4.147 3.39e-05 ***
## trimmedData$GenreRole-Playing -0.05737 0.05109 -1.123 0.261409
## trimmedData$GenreShooter 0.08503 0.04627 1.838 0.066123 .
## trimmedData$GenreSimulation -0.09751 0.05843 -1.669 0.095176 .
## trimmedData$GenreSports 0.06391 0.03968 1.611 0.107307
## trimmedData$GenreStrategy -0.66485 0.07511 -8.852 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.29 on 11875 degrees of freedom
## Multiple R-squared: 0.02407, Adjusted R-squared: 0.02317
## F-statistic: 26.63 on 11 and 11875 DF, p-value: < 2.2e-16
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{anova}\NormalTok{(model)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## Analysis of Variance Table
##
## Response: trimmedData$NA_Sales_adjusted
## Df Sum Sq Mean Sq F value Pr(>F)
## trimmedData$Genre 11 487.4 44.313 26.628 < 2.2e-16 ***
## Residuals 11875 19761.5 1.664
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
\end{verbatim}
Nakon provedenog ANOVA testa, zbog premalog p-valuea, zaključujemo da su
varijance različite, tj neki žanrovi su značajno popularniji, kao što
smo i očekivali.
No što ako provjeravamo točno one žanrove koje ``odokativno'' vidimo da
bi mogli imati istu popularnost. Provjerimo žanrove Strategy, Puzzle i
Adventure, je li ima značajno popularnijih? (znamo da su podaci normalno
distribuirani iz histograma provedenih prethodno)
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{adjustedData }\OtherTok{\textless{}{-}}\NormalTok{ data[(data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Strategy"} \SpecialCharTok{|}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Puzzle"} \SpecialCharTok{|}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Adventure"}\NormalTok{) }\SpecialCharTok{\&}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{NA\_Sales }\SpecialCharTok{!=} \DecValTok{0}\NormalTok{,]}
\NormalTok{adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\OtherTok{\textless{}{-}} \FunctionTok{log}\NormalTok{(adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales }\SpecialCharTok{*} \DecValTok{100}\NormalTok{)}
\FunctionTok{bartlett.test}\NormalTok{(adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ adjustedData}\SpecialCharTok{$}\NormalTok{Genre)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Bartlett test of homogeneity of variances
##
## data: adjustedData$NA_Sales_adjusted by adjustedData$Genre
## Bartlett's K-squared = 11.875, df = 2, p-value = 0.002639
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# ANOVA Test}
\NormalTok{a }\OtherTok{=} \FunctionTok{aov}\NormalTok{(adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ adjustedData}\SpecialCharTok{$}\NormalTok{Genre)}
\FunctionTok{summary}\NormalTok{(a)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## Df Sum Sq Mean Sq F value Pr(>F)
## adjustedData$Genre 2 5 2.520 1.61 0.2
## Residuals 1330 2082 1.565
\end{verbatim}
Nakon provedbe ANOVA testa vidimo da je p vrijednost 0.2 što znači da
prihvaćamo H0 hipotezu da su varijance jednake, tj. nema značajno
popularnijih žanrova od odabranih.
Idemo provjeriti i prethodno spomenute žanrove Action, Shooter i Sports.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{adjustedData }\OtherTok{\textless{}{-}}\NormalTok{ data[(data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Action"} \SpecialCharTok{|}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Shooter"} \SpecialCharTok{|}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{Genre }\SpecialCharTok{==} \StringTok{"Sports"}\NormalTok{) }\SpecialCharTok{\&}\NormalTok{ data}\SpecialCharTok{$}\NormalTok{NA\_Sales }\SpecialCharTok{!=} \DecValTok{0}\NormalTok{,]}
\NormalTok{adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\OtherTok{\textless{}{-}} \FunctionTok{log}\NormalTok{(adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales }\SpecialCharTok{*} \DecValTok{100}\NormalTok{)}
\FunctionTok{bartlett.test}\NormalTok{(adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ adjustedData}\SpecialCharTok{$}\NormalTok{Genre)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Bartlett test of homogeneity of variances
##
## data: adjustedData$NA_Sales_adjusted by adjustedData$Genre
## Bartlett's K-squared = 56.267, df = 2, p-value = 6.049e-13
\end{verbatim}
\begin{Shaded}
\begin{Highlighting}[]
\CommentTok{\# ANOVA Test}
\NormalTok{a }\OtherTok{=} \FunctionTok{aov}\NormalTok{(adjustedData}\SpecialCharTok{$}\NormalTok{NA\_Sales\_adjusted }\SpecialCharTok{\textasciitilde{}}\NormalTok{ adjustedData}\SpecialCharTok{$}\NormalTok{Genre)}
\FunctionTok{summary}\NormalTok{(a)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
## Df Sum Sq Mean Sq F value Pr(>F)
## adjustedData$Genre 2 6 3.181 1.918 0.147
## Residuals 5579 9251 1.658
\end{verbatim}
Dolazimo do istog zaključka kao i u prethodnom testu, tj. žanrovi
Action, Shooter i Sports su slične popularnosti.
\#\#3. Pitanje: Možemo li temeljem danih varijabli predvidjeti prodaju
neke videoigre?
Kako bi znali predvidjeti prodaju neke videoigre, možemo ispitati
različite varijable koje bi mogle znatno utjecati na broj prodanih
primjeraka u svijetu:
\begin{itemize}
\tightlist
\item
Platforma
\item
Žanr
\end{itemize}
Također, koristiti ćemo samo podatke zadnjih 5 godina u zadanim podacima
(\textgreater= 2012) kako bi vidjeli modernije trendove. Podatke koji
nemaju upisanu godinu cemo izbaciti.Pošto imamo samo 4 videoigre u
razdoblju (2017\textless=x\textless=2020) njih ćemo izbaciti.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{PredictionData }\OtherTok{=}\NormalTok{ data[}\FunctionTok{c}\NormalTok{(}\DecValTok{3}\NormalTok{,}\DecValTok{4}\NormalTok{,}\DecValTok{5}\NormalTok{,}\DecValTok{6}\NormalTok{,}\DecValTok{11}\NormalTok{)]}
\NormalTok{Last5YearData }\OtherTok{=}\NormalTok{ PredictionData[PredictionData}\SpecialCharTok{$}\NormalTok{Year }\SpecialCharTok{\textgreater{}=} \DecValTok{2012}\NormalTok{,]}
\NormalTok{Last5YearData }\OtherTok{=}\NormalTok{ Last5YearData[Last5YearData}\SpecialCharTok{$}\NormalTok{Year }\SpecialCharTok{\textless{}=} \DecValTok{2016}\NormalTok{,]}
\NormalTok{Last5YearData[Last5YearData}\SpecialCharTok{==}\StringTok{"N/A"}\NormalTok{] }\OtherTok{=} \ConstantTok{NA}
\NormalTok{Last5YearData }\OtherTok{=}\NormalTok{ Last5YearData[}\FunctionTok{complete.cases}\NormalTok{(Last5YearData}\SpecialCharTok{$}\NormalTok{Year),]}
\FunctionTok{boxplot}\NormalTok{(Global\_Sales}\SpecialCharTok{\textasciitilde{}}\NormalTok{Platform,Last5YearData)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-14-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{boxplot}\NormalTok{(Global\_Sales}\SpecialCharTok{\textasciitilde{}}\NormalTok{Genre,Last5YearData)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-14-2.pdf}
Zbog outliera s vrijednostima koje previše odstupaju od box-plota
izbacit cemo 5\% najvecih vrijednosti kako bi graf postao čitljiviji.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{TrimmedLast5YearData }\OtherTok{=}\NormalTok{ Last5YearData[Last5YearData}\SpecialCharTok{$}\NormalTok{Global\_Sales }\SpecialCharTok{\textless{}} \FunctionTok{quantile}\NormalTok{(Last5YearData}\SpecialCharTok{$}\NormalTok{Global\_Sales, }\FloatTok{0.95}\NormalTok{),]}
\FunctionTok{boxplot}\NormalTok{(}\AttributeTok{las =} \DecValTok{2}\NormalTok{,Global\_Sales}\SpecialCharTok{\textasciitilde{}}\NormalTok{Platform,TrimmedLast5YearData)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-15-1.pdf}
\begin{Shaded}
\begin{Highlighting}[]
\FunctionTok{boxplot}\NormalTok{(}\AttributeTok{las =} \DecValTok{2}\NormalTok{,}\AttributeTok{cex.names=}\NormalTok{.}\DecValTok{5}\NormalTok{,Global\_Sales}\SpecialCharTok{\textasciitilde{}}\NormalTok{Genre,TrimmedLast5YearData)}
\end{Highlighting}
\end{Shaded}
\includegraphics{Test_files/figure-latex/unnamed-chunk-15-2.pdf}
Iz ovih Box plot-ova možemo uvidjeti da se u modernije vrijeme najveća
prodaja primjeraka događa na konsolama PS3,PS4,X360 i XOne dok je
prodaja jako slaba na PSP-u i PSV-i. Od žanrova najprodavanije su
Platform,Shooter i Sports dok Adventure i Puzzle poprilično sigurno drže
zadnja mjesta.
Zbog ovoliko velikih razlika između platformi/žanrova smatramo da odabir
istih poprilično utječe na prodaju te se do neke mjere može predvidjeti.
Linearnom regresijom se predviđa vrijednost varijable izlaza Y
(Global\_Sales) obzirom na varijable unosa X (Genre,Platform).
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{lrmodel }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(Global\_Sales }\SpecialCharTok{\textasciitilde{}}\NormalTok{ Genre }\SpecialCharTok{+}\NormalTok{ Platform,TrimmedLast5YearData)}
\FunctionTok{summary}\NormalTok{(lrmodel)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Call:
## lm(formula = Global_Sales ~ Genre + Platform, data = TrimmedLast5YearData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.62678 -0.22882 -0.09646 0.06797 1.69579
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.25044 0.02224 11.260 < 2e-16 ***
## GenreAdventure -0.12318 0.02632 -4.681 3.01e-06 ***
## GenreFighting -0.03165 0.03928 -0.806 0.420552
## GenreMisc -0.03996 0.03192 -1.252 0.210715
## GenrePlatform 0.14519 0.04504 3.224 0.001281 **
## GenrePuzzle -0.07094 0.07348 -0.965 0.334437
## GenreRacing 0.00804 0.03914 0.205 0.837277
## GenreRole-Playing 0.05377 0.02412 2.230 0.025846 *
## GenreShooter 0.19331 0.03132 6.171 7.83e-10 ***
## GenreSimulation -0.08501 0.04822 -1.763 0.078025 .
## GenreSports 0.06954 0.02770 2.511 0.012100 *
## GenreStrategy -0.05711 0.04787 -1.193 0.233023
## PlatformDS -0.08927 0.06820 -1.309 0.190701
## PlatformPC -0.05388 0.03298 -1.634 0.102448
## PlatformPS3 0.09128 0.02705 3.375 0.000750 ***
## PlatformPS4 0.10526 0.02996 3.513 0.000451 ***
## PlatformPSP -0.15645 0.03549 -4.408 1.09e-05 ***
## PlatformPSV -0.10016 0.02792 -3.587 0.000341 ***
## PlatformWii 0.10574 0.05834 1.813 0.070020 .
## PlatformWiiU 0.07170 0.03838 1.868 0.061882 .
## PlatformX360 0.19303 0.03124 6.179 7.46e-10 ***
## PlatformXOne 0.11353 0.03442 3.299 0.000985 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.378 on 2582 degrees of freedom
## Multiple R-squared: 0.1231, Adjusted R-squared: 0.116
## F-statistic: 17.26 on 21 and 2582 DF, p-value: < 2.2e-16
\end{verbatim}
\(R^2\) od modela nam govori da je model zaslužan samo za 11.5\%
varijacije u podacima što nije pretežito velik broj, ali sudeći da je
bitnija kvaliteta igrice nego samo kategorizacija kod prodaje smatramo
ga prihvatljivim.
Dodavanjem Izdavača i godinu izdavanja u regresiju pretpostavljamo da će
se rezultat poboljšati. Ovdje ćemo zbog prevelikog broj koeficijenata u
ispisu samo ispisat platforme i žanr.
\begin{Shaded}
\begin{Highlighting}[]
\NormalTok{lrmodel }\OtherTok{=} \FunctionTok{lm}\NormalTok{(Global\_Sales }\SpecialCharTok{\textasciitilde{}}\NormalTok{ Platform }\SpecialCharTok{+}\NormalTok{ Genre }\SpecialCharTok{+}\NormalTok{ Year }\SpecialCharTok{+}\NormalTok{ Publisher,TrimmedLast5YearData)}
\FunctionTok{my.summary.lm}\NormalTok{(}\FunctionTok{summary}\NormalTok{(lrmodel), }\AttributeTok{my.rows=}\DecValTok{1}\SpecialCharTok{:}\DecValTok{22}\NormalTok{)}
\end{Highlighting}
\end{Shaded}
\begin{verbatim}
##
## Call:
## lm(formula = Global_Sales ~ Platform + Genre + Year + Publisher,
## data = TrimmedLast5YearData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.79200 -0.17261 -0.02958 0.08276 1.55052
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.15403 0.06604 2.332 0.019758 *
## PlatformDS -0.10219 0.06779 -1.507 0.131841
## PlatformPC -0.08570 0.03422 -2.504 0.012342 *
## PlatformPS3 0.12752 0.02690 4.741 2.26e-06 ***
## PlatformPS4 0.22572 0.03121 7.232 6.38e-13 ***
## PlatformPSP -0.09025 0.03784 -2.385 0.017143 *
## PlatformPSV 0.01532 0.02887 0.531 0.595670
## PlatformWii 0.01962 0.05407 0.363 0.716745
## PlatformWiiU -0.06006 0.03527 -1.703 0.088711 .
## PlatformX360 0.15224 0.03088 4.930 8.78e-07 ***
## PlatformXOne 0.11790 0.03515 3.354 0.000808 ***
## GenreAdventure -0.02315 0.02883 -0.803 0.422065
## GenreFighting 0.05013 0.03669 1.366 0.171941
## GenreMisc -0.04667 0.03049 -1.531 0.126017
## GenrePlatform 0.08888 0.04418 2.012 0.044366 *
## GenrePuzzle -0.15241 0.07472 -2.040 0.041485 *
## GenreRacing 0.07438 0.04801 1.549 0.121467
## GenreRole-Playing 0.08845 0.02412 3.668 0.000250 ***
## GenreShooter 0.13326 0.03100 4.298 1.79e-05 ***
## GenreSimulation -0.04879 0.04943 -0.987 0.323740
## GenreSports -0.01423 0.03032 -0.469 0.638810
## GenreStrategy -0.03178 0.04469 -0.711 0.477027
## ---