library(dplyr)
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library(purrr)
library(tidyverse)
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library(ggthemes)
library(ggrepel)
data_path <- "C:/Users/shanata/Downloads/smoking_driking_dataset_Ver01.csv"
data <-  read.csv(data_path)

ANOVA

data |>
  ggplot() +
  geom_boxplot(mapping = aes(y = hemoglobin, x = sex)) +
  labs(x = "Gender",
       y = "Hemoglobin levels") +
  theme_minimal()

#### Null hypothesis:

categorical variable: Gender continous variable : Hemoglobin levels

H0 : The average hemoglobin levels is same across both the genders.

m <- aov(hemoglobin ~ sex, data = data)
summary(m)
##                 Df  Sum Sq Mean Sq F value Pr(>F)    
## sex              1 1115932 1115932  804956 <2e-16 ***
## Residuals   991344 1374326       1                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Results:

With such a small p-value, we can conclude that there is a statistically significant difference in mean hemoglobin levels between the two genders. In other words, the average hemoglobin levels are not the same for both genders.

Linaer Regression

Independent variable: Weight Dependent variable : waistline

Trying to predict waistline based on weight.

data |>
  ggplot(mapping = aes(x = weight, y =waistline)) +
  geom_point(size = 2, color = 'darkblue') +
  theme_minimal()

We can see that they have a linear relationship

model <- lm(waistline ~ weight, data)
model$coefficients
## (Intercept)      weight 
##  43.0497113   0.6033692

Interpretations of coefficients:

  1. If weight is 0, the expected waistline is 43 cm
  2. For every unit increase in weight the waistline is expected to increase by 0.6 cm

Hypothesis Testing:

Null Hypothesis (H0): There is no relationship between weight and waistline. Alternative Hypothesis (H1): There is a significant relationship between weight and waistline.

summary_model <- summary(model)

p_value_weight <- summary_model$coefficients["weight", "Pr(>|t|)"]

alpha <- 0.05

if (p_value_weight < alpha) {
  cat("Reject the null hypothesis: There is a significant relationship between weight and waistline.\n")
} else {
  cat("Fail to reject the null hypothesis: There is no significant relationship between weight and waistline.\n")
}
## Reject the null hypothesis: There is a significant relationship between weight and waistline.

Results:

Therefore, we can conclude that there is a significant relationship between weight and waistline.

Diagnostic Plots:

par(mfrow=c(2,2))  

plot(model, which = 1)


plot(model, which = 2)


plot(model, which = 3)


plot(model, which = 4)

par(mfrow=c(1,1))

Multiple variables:

I want to find out how gender affects the waistline and weight relationship

data_grouped <-
  data |>
  group_by(sex) |>
  summarise(mean_waistline = mean(waistline))

data |>
  ggplot() +
  facet_wrap(vars(sex), labeller = label_both) +
  geom_point(mapping = aes(x = weight, y = waistline)) +
  geom_hline(data =data_grouped,
             mapping = aes(yintercept = mean_waistline),
             color = 'darkorange', linetype = 'dashed') +
  labs(title = "Waistline wrt weight",
       x = "weight", y = "waistline") +
  theme_minimal()

model <- lm(waistline ~ weight + sex,data)
model$coefficients
## (Intercept)      weight     sexMale 
##  42.1779396   0.6249516  -0.9303926

Results;

When considering only weight as an independent variable, a one-unit increase in weight is associated with a 0.625 centimeter increase in waistline, assuming sex is held constant.

When comparing males (sexMale = 1) to females (sexMale = 0) with all other factors held constant, males tend to have a waistline that is 0.930 centimeters smaller than females.

Trying to smoking and Drinking status

model <- lm(waistline ~ weight + sex + SMK_stat_type_cd+ DRK_YN,data)
model$coefficients
##      (Intercept)           weight          sexMale SMK_stat_type_cd 
##       42.4950483        0.6306037       -0.2701830       -0.0695271 
##          DRK_YNY 
##       -1.8278168

Results:

Weight (0.631): For each additional kilogram in weight, waistline is expected to increase by approximately 0.631 centimeters.

SexMale (-0.270): On average, males tend to have a waistline approximately 0.270 centimeters smaller than females, controlling for other variables.

SMK_stat_type_cd (-0.070): Differences in smoking status are associated with a 0.070 centimeter reduction in waistline, on average, when other factors are held constant.

DRK_YNY (-1.828): Individuals with different drinking habits tend to have a waistline difference of approximately 1.828 centimeters, on average, controlling for all other predictors.