Odevdeneme
Selman ŞİŞMAN
2025-10-23
Simpson Paradoksunu Keşfetmek – Palmer Penguins Örneği
library(dplyr)## Warning: package 'dplyr' was built under R version 4.4.3##
## 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(tidyr)## Warning: package 'tidyr' was built under R version 4.4.3#install.packages("palmerpenguins")library(palmerpenguins)## Warning: package 'palmerpenguins' was built under R version 4.4.3Verinin boyutlarını inceleme
glimpse(penguins)## Rows: 344
## Columns: 8
## $ species <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adel…
## $ island <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgerse…
## $ bill_length_mm <dbl> 39.1, 39.5, 40.3, NA, 36.7, 39.3, 38.9, 39.2, 34.1, …
## $ bill_depth_mm <dbl> 18.7, 17.4, 18.0, NA, 19.3, 20.6, 17.8, 19.6, 18.1, …
## $ flipper_length_mm <int> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190, 186…
## $ body_mass_g <int> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 3475, …
## $ sex <fct> male, female, female, NA, female, male, female, male…
## $ year <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007…dim(penguins)## [1] 344 8Eksik verilere bakma
is.na(penguins)## species island bill_length_mm bill_depth_mm flipper_length_mm
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## [344,] FALSE FALSE FALSEcolSums(is.na(penguins))## species island bill_length_mm bill_depth_mm
## 0 0 2 2
## flipper_length_mm body_mass_g sex year
## 2 2 11 0Değişken adlarını türkçeleştirme
penguenler <- penguins %>%
rename(tur = species,
ada = island,
gaga_uzunlugu = bill_length_mm,
gaga_derinligi = bill_depth_mm,
yuzgec_uzunlugu = flipper_length_mm,
vucut_kutlesi = body_mass_g,
cinsiyet = sex,
yil = year)Eksik verileri çıkarma
penguenlerclean <- na.omit(penguenler)clean dataya bakış
dim(penguenlerclean)## [1] 333 8glimpse(penguenlerclean)## Rows: 333
## Columns: 8
## $ tur <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adelie…
## $ ada <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgersen,…
## $ gaga_uzunlugu <dbl> 39.1, 39.5, 40.3, 36.7, 39.3, 38.9, 39.2, 41.1, 38.6, …
## $ gaga_derinligi <dbl> 18.7, 17.4, 18.0, 19.3, 20.6, 17.8, 19.6, 17.6, 21.2, …
## $ yuzgec_uzunlugu <int> 181, 186, 195, 193, 190, 181, 195, 182, 191, 198, 185,…
## $ vucut_kutlesi <int> 3750, 3800, 3250, 3450, 3650, 3625, 4675, 3200, 3800, …
## $ cinsiyet <fct> male, female, female, female, male, female, male, fema…
## $ yil <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, …View(penguenlerclean)Yeni değişken oluşturma (bmi)
penguenlerclean <- penguenlerclean %>% mutate(bma = vucut_kutlesi / yuzgec_uzunlugu)##Türlere göre betimsel istatistikler
penguenlerclean1 <- penguenlerclean %>%
group_by(tur) %>%
summarise(ort = mean(bma),
ss = sd(bma),
min = min(bma),
maks = max(bma),
n = n())
glimpse(penguenlerclean1)## Rows: 3
## Columns: 6
## $ tur <fct> Adelie, Chinstrap, Gentoo
## $ ort <dbl> 19.48037, 19.04376, 23.41415
## $ ss <dbl> 2.179467, 1.598395, 1.881543
## $ min <dbl> 15.15544, 14.06250, 18.99038
## $ maks <dbl> 25.27174, 22.85714, 28.50679
## $ n <int> 146, 68, 119Kutu grafiği oluşturma
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.4.3ggplot(data = penguenlerclean, aes(x = tur, y = bma, fill = tur)) +
geom_boxplot(alpha = 0.8, outlier.shape = 21, outlier.fill = "white", outlier.color = "black") +
labs(title = "Penguen Turlerine Gore Vucut Kutlesi Dagılımı")
Yorum: Kutu grafiğibe bakıldığında gentoo penguenlerin vücut kütlelerinin ortalaması diğerlerine göre daha fazla olduğu görülmektedir.
Scatter Plot Oluşturma ve Regresyon Çizgisi
ggplot(data = penguenlerclean, aes(x = gaga_derinligi, y = gaga_uzunlugu)) +
geom_point(aes(color=tur), size = 2, alpha = 0.7) +
labs(title = "Gaga Uzunluğu ve Derinliği Arası",
x = "Gaga_Uzunluğu (mm)", y = "Gaga Derinliği (mm)") + theme_minimal() +
geom_smooth(method = "lm", se = TRUE, linewidth = 1)## `geom_smooth()` using formula = 'y ~ x'
Saçılım grafiği incelendiğinde Regresyon çizgisi soldan sağa aşağıya doğru seyretmektedir. Dolayısısıyla genel olarak gaga uzunluğu ile gaga derinliği arasında negatif ilişki olduğu görülebilir. Başka bir deyişle gaga uzunluğu arttıkça gaga derinliği azalmaktadır.
Tür Bazında Analiz
ggplot(penguenlerclean, aes(x = gaga_uzunlugu, y = gaga_derinligi, color = tur)) +
geom_point() +
geom_smooth(method = "lm", se = TRUE) +
facet_wrap(~tur) +
theme_minimal() +
labs(title = "Tur Bazında Gaga Uzunlugu ve Gaga Derinligi İliskisi\n",
x = "\nGaga Uzunlugu",
y = "Gaga Derinligi\n")## `geom_smooth()` using formula = 'y ~ x'
Grafik incelendiğinde gaga uzunluğu arttıkça gaga derinliğinin de arttığı görülmektedir.
adelie_model <- lm(gaga_derinligi ~ gaga_uzunlugu, data = penguenlerclean %>% filter(tur == "Adelie"))
chinstrap_model <- lm(gaga_derinligi ~ gaga_uzunlugu, data = penguenlerclean %>% filter(tur == "Chinstrap"))
gentoo_model <- lm(gaga_derinligi ~ gaga_uzunlugu, data = penguenlerclean %>% filter(tur == "Gentoo"))
summary(adelie_model)##
## Call:
## lm(formula = gaga_derinligi ~ gaga_uzunlugu, data = penguenlerclean %>%
## filter(tur == "Adelie"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1487 -0.7926 -0.0842 0.5550 3.4990
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.48771 1.37010 8.385 4.23e-14 ***
## gaga_uzunlugu 0.17668 0.03521 5.018 1.51e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.129 on 144 degrees of freedom
## Multiple R-squared: 0.1489, Adjusted R-squared: 0.1429
## F-statistic: 25.18 on 1 and 144 DF, p-value: 1.515e-06summary(chinstrap_model)##
## Call:
## lm(formula = gaga_derinligi ~ gaga_uzunlugu, data = penguenlerclean %>%
## filter(tur == "Chinstrap"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.65742 -0.46033 -0.01862 0.61473 1.69801
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.56914 1.55053 4.882 6.99e-06 ***
## gaga_uzunlugu 0.22221 0.03168 7.015 1.53e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8659 on 66 degrees of freedom
## Multiple R-squared: 0.4271, Adjusted R-squared: 0.4184
## F-statistic: 49.21 on 1 and 66 DF, p-value: 1.526e-09summary(gentoo_model)##
## Call:
## lm(formula = gaga_derinligi ~ gaga_uzunlugu, data = penguenlerclean %>%
## filter(tur == "Gentoo"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.57143 -0.52974 -0.04479 0.45417 2.96109
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.1210 1.0583 4.839 4.02e-06 ***
## gaga_uzunlugu 0.2076 0.0222 9.352 7.34e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7491 on 117 degrees of freedom
## Multiple R-squared: 0.4277, Adjusted R-squared: 0.4229
## F-statistic: 87.45 on 1 and 117 DF, p-value: 7.337e-16Regresyon katsayısı (eğim, gaga_uzunlugu için) = 0.22221. Yani gaga_uzunluğu 1 birim arttığında gaga_derinliği ort. 0.222 birim artıyor. Bu katsayı anlamlı: t = 7.015, p = 1.53e-09 (p << 0.001) → istatistiksel olarak güçlü bir ilişki.