📈 Statistical Analysis with R – Descriptive, Predictive & Advanced Modeling Techniques

📊 Unlock the full potential of your data using R’s powerful statistical and machine learning tools—from simple metrics to sophisticated models.

🧲 Introduction – Perform Powerful Statistical & Machine Learning Analysis in R

R was created specifically for statistical computing and data analysis. Whether you’re summarizing a dataset, testing hypotheses, or building predictive models, R offers both built-in functions and advanced packages like caret, survival, forecast, and randomForest that empower data scientists and analysts to explore, model, and visualize data like never before.

This section introduces a broad set of statistical tools—ranging from descriptive statistics to time series forecasting, regression modeling, and machine learning techniques—that help you derive actionable insights from any dataset.

🎯 In This Guide, You’ll Learn:

• How to compute summary statistics like mean, median, mode, percentiles
• How to perform linear, logistic, and Poisson regression
• How to analyze distributions and run time series forecasts
• How to apply decision trees, random forests, and survival models

📘 Topics Covered

📊 R – Statistics Intro / Data Set

Start with sample datasets like mtcars, iris, or load external datasets using read.csv().

summary(mtcars)
str(iris)

Use summary() and str() to explore data structure and statistics.

🔢 R – Max, Min, Mean, Median, Mode

data <- c(10, 20, 30, 40, 50)
mean(data)       # Average
median(data)     # Middle value
max(data)        # Largest value
min(data)        # Smallest value

Use modeest::mfv() to calculate the mode.

📏 R – Percentiles

quantile(data, probs = c(0.25, 0.5, 0.75))  # Quartiles

Great for detecting outliers and understanding spread.

📈 R – Linear / Multiple Regression

model <- lm(mpg ~ wt + hp, data = mtcars)
summary(model)

Explore coefficients, p-values, and R² to assess model strength.

📉 R – Logistic / Poisson Regression

Logistic:

glm(vs ~ mpg + wt, family = binomial, data = mtcars)

Poisson:

glm(count ~ age + gender, family = poisson, data = df)

Ideal for classification or modeling count-based outcomes.

🧮 R – Normal / Binomial Distribution

dnorm(0, mean = 0, sd = 1)     # Normal PDF
rbinom(10, 5, 0.5)             # Random binomial values

Visualize with curve(), hist(), or ggplot2::stat_function().

🧪 R – ANCOVA / Nonlinear Least Squares

ANCOVA:

aov(Sepal.Length ~ Species + Petal.Width, data = iris)

NLS:

nls(y ~ a * exp(b * x), start = list(a = 1, b = 0.1), data = df)

Used for interaction effects and nonlinear modeling.

⏱️ R – Time Series Analysis

ts_data <- ts(AirPassengers, frequency = 12)
forecast::auto.arima(ts_data)

Use forecast, TTR, or tsibble packages for smoothing and forecasting.

🌲 R – Decision Tree / Random Forest

library(rpart)
tree_model <- rpart(Species ~ ., data = iris)

library(randomForest)
rf_model <- randomForest(Species ~ ., data = iris)

Great for modeling complex interactions and feature importance.

🧬 R – Survival Analysis

library(survival)
fit <- survfit(Surv(time, status) ~ gender, data = lung)
plot(fit)

Used in medical research and customer churn prediction.

✅ R – Chi-Square Test

chisq.test(table(mtcars$gear, mtcars$cyl))

Assesses relationships between categorical variables.

📌 Summary – Recap & Next Steps

📈 Statistical analysis in R allows you to move beyond summaries and dig deep into data relationships, variability, and predictions. Whether you’re performing regressions, classification, or survival modeling, R offers a robust toolbox to support every analytical need.

You can rapidly experiment, validate models, and communicate findings with powerful visualizations and statistical rigor. These tools are essential for academia, business intelligence, and scientific discovery.

🔍 Key Takeaways:

• Use R for everything from basic summaries to predictive modeling
• Run regressions, hypothesis tests, and machine learning workflows
• Explore advanced packages for survival, time series, and classification

⚙️ Real-World Relevance:
R is used extensively in healthcare, finance, marketing, and social sciences to turn data into decisions.

🎓 Next Steps:
Deepen your skills with packages like caret, mlr3, and tidymodels, and explore cross-validation, tuning, and ensemble learning.

❓ Frequently Asked Questions (FAQs)

Q1: Is R better than Python for statistics?
✅ R is purpose-built for statistical analysis and has more mature packages for modeling. Python is preferred for production ML pipelines.

Q2: Can I use R for machine learning?
✅ Yes! Use caret, randomForest, xgboost, and mlr3 for classification, regression, and model tuning.

Q3: What data formats work best for regression in R?
✅ Data frames with clean, numeric variables. Use na.omit() to remove missing values.

Q4: How do I check model performance?
✅ Use summary(), residual plots, confusionMatrix(), and cross-validation methods for evaluation.

Q5: Is R suitable for time series forecasting?
✅ Absolutely. R has forecast, prophet, and tsibble for seasonality, trend, and prediction modeling.