mtcars
## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
shapiro.test(mtcars$mpg)
##
## Shapiro-Wilk normality test
##
## data: mtcars$mpg
## W = 0.94756, p-value = 0.1229
shapiro.test(mtcars$wt)
##
## Shapiro-Wilk normality test
##
## data: mtcars$wt
## W = 0.94326, p-value = 0.09265
library(ggpubr)
## Loading required package: ggplot2
ggscatter(
mtcars,
x = "wt",
y = "mpg"
)
#correlation
cor(mtcars$wt, mtcars$mpg)
## [1] -0.8676594
#using penguin dataset
# Load required libraries
library(palmerpenguins)
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, union
# Load dataset
data("penguins")
# View first rows
head(penguins)
## # A tibble: 6 × 8
## species island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g
## <fct> <fct> <dbl> <dbl> <int> <int>
## 1 Adelie Torgersen 39.1 18.7 181 3750
## 2 Adelie Torgersen 39.5 17.4 186 3800
## 3 Adelie Torgersen 40.3 18 195 3250
## 4 Adelie Torgersen NA NA NA NA
## 5 Adelie Torgersen 36.7 19.3 193 3450
## 6 Adelie Torgersen 39.3 20.6 190 3650
## # ℹ 2 more variables: sex <fct>, year <int>
# Keep only Gentoo penguins and remove missing values
gentoo <- penguins %>%
filter(species == "Gentoo") %>%
select(bill_depth_mm, flipper_length_mm, bill_length_mm) %>%
na.omit()
# Model 1: bill depth as a function of flipper length
model_flipper <- lm(bill_depth_mm ~ flipper_length_mm, data = gentoo)
# Model 2: bill depth as a function of bill length
model_bill <- lm(bill_depth_mm ~ bill_length_mm, data = gentoo)
# Summaries
summary(model_flipper)
##
## Call:
## lm(formula = bill_depth_mm ~ flipper_length_mm, data = gentoo)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.64831 -0.48630 0.01715 0.39824 2.12406
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.236854 2.114995 -3.895 0.000162 ***
## flipper_length_mm 0.106908 0.009734 10.983 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6972 on 121 degrees of freedom
## Multiple R-squared: 0.4992, Adjusted R-squared: 0.4951
## F-statistic: 120.6 on 1 and 121 DF, p-value: < 2.2e-16
summary(model_bill)
##
## Call:
## lm(formula = bill_depth_mm ~ bill_length_mm, data = gentoo)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.55952 -0.52572 -0.06658 0.46041 2.95390
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.25101 1.05481 4.978 2.15e-06 ***
## bill_length_mm 0.20484 0.02216 9.245 1.02e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7543 on 121 degrees of freedom
## Multiple R-squared: 0.4139, Adjusted R-squared: 0.4091
## F-statistic: 85.46 on 1 and 121 DF, p-value: 1.016e-15
# Compare R-squared values
summary(model_flipper)$r.squared
## [1] 0.4992319
summary(model_bill)$r.squared
## [1] 0.4139429
#Regression diagnostics
# Load libraries
library(palmerpenguins)
library(dplyr)
# Load data
data("penguins")
# Filter Gentoo penguins
gentoo <- penguins %>%
filter(species == "Gentoo") %>%
select(bill_depth_mm, flipper_length_mm, bill_length_mm) %>%
na.omit()
# Linear model: bill depth ~ flipper length
model_flipper <- lm(bill_depth_mm ~ flipper_length_mm, data = gentoo)
# Linear model: bill depth ~ bill length
model_bill <- lm(bill_depth_mm ~ bill_length_mm, data = gentoo)
# Model summaries
summary(model_flipper)
##
## Call:
## lm(formula = bill_depth_mm ~ flipper_length_mm, data = gentoo)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.64831 -0.48630 0.01715 0.39824 2.12406
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.236854 2.114995 -3.895 0.000162 ***
## flipper_length_mm 0.106908 0.009734 10.983 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6972 on 121 degrees of freedom
## Multiple R-squared: 0.4992, Adjusted R-squared: 0.4951
## F-statistic: 120.6 on 1 and 121 DF, p-value: < 2.2e-16
summary(model_bill)
##
## Call:
## lm(formula = bill_depth_mm ~ bill_length_mm, data = gentoo)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.55952 -0.52572 -0.06658 0.46041 2.95390
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.25101 1.05481 4.978 2.15e-06 ***
## bill_length_mm 0.20484 0.02216 9.245 1.02e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7543 on 121 degrees of freedom
## Multiple R-squared: 0.4139, Adjusted R-squared: 0.4091
## F-statistic: 85.46 on 1 and 121 DF, p-value: 1.016e-15
# Extract R-squared values
r2_flipper <- summary(model_flipper)$r.squared
r2_bill <- summary(model_bill)$r.squared
r2_flipper
## [1] 0.4992319
r2_bill
## [1] 0.4139429
# Compare predictors
# i have to check if (r2_flipper > r2_bill)
# Flipper length is the better predictor of bill depth
# ANOVA: Do daily ozone measurements differ by month?
# ANOVA
data("airquality")
library(ggplot2)
# Convert Month into factor
airquality$Month <- factor(airquality$Month)
# Boxplot
ggplot(airquality, aes(x = Month, y = Ozone)) +
geom_boxplot()
## Warning: Removed 37 rows containing non-finite outside the scale range
## (`stat_boxplot()`).
# Check normality
shapiro.test(airquality$Ozone)
##
## Shapiro-Wilk normality test
##
## data: airquality$Ozone
## W = 0.87867, p-value = 2.79e-08
# Data are not normal, so use Kruskal-Wallis test
kruskal.test(Ozone ~ Month, data = airquality)
##
## Kruskal-Wallis rank sum test
##
## data: Ozone by Month
## Kruskal-Wallis chi-squared = 29.267, df = 4, p-value = 6.901e-06
# Pairwise comparison to see which months differ
pairwise.wilcox.test(airquality$Ozone,
airquality$Month)
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
## Warning in wilcox.test.default(xi, xj, paired = paired, ...): cannot compute
## exact p-value with ties
##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: airquality$Ozone and airquality$Month
##
## 5 6 7 8
## 6 0.5775 - - -
## 7 0.0003 0.0848 - -
## 8 0.0011 0.1295 1.0000 -
## 9 0.4744 1.0000 0.0060 0.0227
##
## P value adjustment method: holm