week 11
Saisree Mucharla
2024-11-07
# Load necessary libraries
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors# Load the data
obesity <- read.csv("C://Users//saisr//Downloads//statistics using R//obesity.csv")
head(obesity)## Gender Age Height Weight family_history_with_overweight FAVC FCVC NCP
## 1 Female 21 1.62 64.0 yes no 2 3
## 2 Female 21 1.52 56.0 yes no 3 3
## 3 Male 23 1.80 77.0 yes no 2 3
## 4 Male 27 1.80 87.0 no no 3 3
## 5 Male 22 1.78 89.8 no no 2 1
## 6 Male 29 1.62 53.0 no yes 2 3
## CAEC SMOKE CH2O SCC FAF TUE CALC MTRANS
## 1 Sometimes no 2 no 0 1 no Public_Transportation
## 2 Sometimes yes 3 yes 3 0 Sometimes Public_Transportation
## 3 Sometimes no 2 no 2 1 Frequently Public_Transportation
## 4 Sometimes no 2 no 2 0 Frequently Walking
## 5 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 6 Sometimes no 2 no 0 0 Sometimes Automobile
## NObeyesdad
## 1 Normal_Weight
## 2 Normal_Weight
## 3 Normal_Weight
## 4 Overweight_Level_I
## 5 Overweight_Level_II
## 6 Normal_Weight# Checking for missing values
sum(is.na(obesity))## [1] 0Converting Categorical Variables to Factors
# Convert categorical variables to factors if necessary
obesity$Gender <- as.factor(obesity$Gender)
obesity$family_history_with_overweight <- as.factor(obesity$family_history_with_overweight)
obesity_clean <- na.omit(obesity)
# Select only numeric columns for correlation
numeric_data <- obesity_clean %>% select_if(is.numeric)
# Calculate the correlation matrix
cor_matrix <- cor(numeric_data)
# Check the structure of the dataset
str(obesity_clean)## 'data.frame': 2111 obs. of 17 variables:
## $ Gender : Factor w/ 2 levels "Female","Male": 1 1 2 2 2 2 1 2 2 2 ...
## $ Age : num 21 21 23 27 22 29 23 22 24 22 ...
## $ Height : num 1.62 1.52 1.8 1.8 1.78 1.62 1.5 1.64 1.78 1.72 ...
## $ Weight : num 64 56 77 87 89.8 53 55 53 64 68 ...
## $ family_history_with_overweight: Factor w/ 2 levels "no","yes": 2 2 2 1 1 1 2 1 2 2 ...
## $ FAVC : chr "no" "no" "no" "no" ...
## $ FCVC : num 2 3 2 3 2 2 3 2 3 2 ...
## $ NCP : num 3 3 3 3 1 3 3 3 3 3 ...
## $ CAEC : chr "Sometimes" "Sometimes" "Sometimes" "Sometimes" ...
## $ SMOKE : chr "no" "yes" "no" "no" ...
## $ CH2O : num 2 3 2 2 2 2 2 2 2 2 ...
## $ SCC : chr "no" "yes" "no" "no" ...
## $ FAF : num 0 3 2 2 0 0 1 3 1 1 ...
## $ TUE : num 1 0 1 0 0 0 0 0 1 1 ...
## $ CALC : chr "no" "Sometimes" "Frequently" "Frequently" ...
## $ MTRANS : chr "Public_Transportation" "Public_Transportation" "Public_Transportation" "Walking" ...
## $ NObeyesdad : chr "Normal_Weight" "Normal_Weight" "Normal_Weight" "Overweight_Level_I" ...Linear Model
# Build a linear regression model
model <- lm(Height ~ Age + Gender + family_history_with_overweight, data = obesity_clean)
# Summarize the model
summary(model)##
## Call:
## lm(formula = Height ~ Age + Gender + family_history_with_overweight,
## data = obesity_clean)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.17580 -0.05189 -0.00244 0.05001 0.21488
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.6390004 0.0065367 250.738 < 2e-16 ***
## Age -0.0014332 0.0002481 -5.777 8.74e-09 ***
## GenderMale 0.1123323 0.0030973 36.268 < 2e-16 ***
## family_history_with_overweightyes 0.0497674 0.0040930 12.159 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07075 on 2107 degrees of freedom
## Multiple R-squared: 0.4259, Adjusted R-squared: 0.4251
## F-statistic: 521.1 on 3 and 2107 DF, p-value: < 2.2e-16Insights
Intercept: The intercept is 1.639, which means when Age, Gender, and family_history_with_overweight are all zero, the estimated Height is 1.639.
Age: The coefficient for Age is -0.0014332. This means that for every 1-year increase in Age, the model predicts a decrease in Height by 0.00143 units.The t-value is -5.777, which indicates this effect is statistically significant (p-value = 8.74e-09), meaning age has a significant impact on height.
GenderMale: The coefficient for GenderMale is 0.1123323. This means that being male is associated with an increase in height by 0.1123 units, compared to being female. This difference is statistically significant with a very low p-value (< 2e-16).
family_history_with_overweightyes: The coefficient for family_history_with_overweightyes is 0.0497674. This indicates that having a family history of overweight is associated with an increase in height by 0.0498 units, holding all other factors constant.
Residual standard error: This is the standard deviation of the residuals. A smaller value indicates a better fit.
R-squared: This means that about 42.6% of the variance in Height is explained by the model. This is not an exceptionally high R-squared, suggesting that other factors might influence height that are not captured by the model.
Adjusted R-squared: This adjusts the R-squared value for the number of predictors in the model. Since it’s very close to the R-squared value, we can conclude that adding more predictors wouldn’t significantly improve the fit.
F-statistic: with p-value < 2.2e-16. This indicates that the overall model is statistically significant.
Diagnosing the Model
# Plot residuals vs fitted values
plot(model, which = 1)
Issues with residual vs fitted model
Non-constant Variance of Residuals: The Residuals vs Fitted plot shows a funnel shape, indicating that the variance of the residuals increases with the fitted values. This violates the assumption of homoscedasticity, which is a key assumption of linear regression.
# Check for normality of residuals
plot(model, which = 2)
Issues with Q-Q plot
Non-normality of Residuals: The Q-Q plot shows a clear deviation from the straight line, indicating that the residuals are not normally distributed. This opposes one of the key assumptions of linear regression.
# Check for Cook's distance (influence)
plot(model, which = 4)
Issues with Cook’s distance
Influential Points: The Cook’s Distance plot reveals several points with high Cook’s distances, exceeding the threshold. These points have a significant impact on the regression model and may be distorting the results.
Interpret Coefficients
- here interpreting age from this dataset
# Get the coefficient for Age
coef(model)["Age"]## Age
## -0.001433217Insights
- The negative sign of the coefficient suggests a small but significant decrease in height with age, which could reflect a general trend such as slight height reduction with aging.
- As people age, especially after reaching adulthood, they might experience a decrease in height due to natural physiological changes like compression of spinal discs and changes in posture.