SkyLimit Tech Hub: Data Science Training Center

Course 5: Basic Statistical Modeling in R

Statistical modeling in R provides a foundation for analyzing data relationships and making predictions. By using statistical models, data scientists can uncover patterns, estimate trends, and predict future values based on historical data. This course introduces learners to the fundamentals of statistical modeling, focusing on linear regression, data preparation, model evaluation, and practical applications. Designed for those with basic R knowledge, it equips students to build, interpret, and evaluate statistical models over one week.

Objective: By the end of the course, learners will be proficient in fitting linear regression models, preparing data, evaluating model performance, and visualizing results using R and ggplot2 for effective data analysis.

Scope: The course covers core statistical modeling concepts, including linear regression with lm(), data preparation with dplyr, model diagnostics, and visualization with ggplot2, using datasets like mtcars.

Day 1: Introduction to Statistical Modeling

Introduction: Statistical modeling in R provides a foundation for analyzing data relationships and making predictions. By using statistical models, data scientists can uncover patterns, estimate trends, and predict future values based on historical data. This is an essential skill for anyone working with data, as models help interpret complex datasets and provide actionable insights. Understanding the fundamentals of statistical modeling empowers professionals to approach data science tasks with a structured and informed perspective.

Objective: The goal of this session is to introduce learners to basic statistical modeling concepts, focusing on linear regression. Learners will learn how to fit linear regression models using R and how to interpret the results. By the end of this session, learners should be able to apply simple linear regression techniques to their data and understand the meaning of the model outputs, including coefficients, p-values, and R-squared values.

Scope of the Lesson: This lesson will introduce the core concepts of statistical modeling in R, with a specific focus on linear regression. Topics covered include: Introduction to Statistical Models, Fitting Linear Regression Models using lm(), Interpreting Model Summaries, and Assumptions of Linear Models.

Background Information: In statistical modeling, linear regression is used to estimate the relationships among variables. It’s a foundational model in statistics and data science. A simple linear regression model assumes a straight-line relationship between a dependent variable (y) and one independent variable (x). When you run a linear regression in R, the lm() function fits this model, and the summary() function provides key statistics to help you evaluate the model.

Simple Code Examples:

# Load necessary libraries
library(ggplot2)

# Load dataset: mtcars
data(mtcars)

# Fit a simple linear regression model: predicting mpg from horsepower (hp)
model <- lm(mpg ~ hp, data = mtcars)

# Summary of the model
summary(model)

Interpretation of the Example Code: We load the ggplot2 package and the mtcars dataset. The lm() function fits a simple linear regression model, predicting mpg from hp. The summary() function displays the model’s statistical output, including coefficients, p-values, and R-squared.

Supplemental Information:

Discussion Points:

  • How does linear regression model the relationship between dependent and independent variables?
  • What is the role of the p-value in determining the significance of the model’s coefficients?
  • Why is R-squared important, and what does it tell us about the model’s fit to the data?
  • What assumptions must be checked when using linear regression, and how can they affect the model results?
  • How can you use linear regression in real-world data science projects, such as predicting sales or customer behavior?

Day 2: Preparing Data for Modeling

Introduction: Preparing data is a crucial step in statistical modeling. Clean, well-structured data ensures that models are accurate, interpretable, and reliable. Without proper preparation, the model’s performance and validity can be compromised.

Objective: The goal of this lesson is to understand how to prepare data for statistical modeling by addressing common issues such as missing values, categorical variables, and scaling. Learners will also explore how to check assumptions like linearity and normality that impact model performance.

Scope of the Lesson: This lesson covers handling missing values, encoding categorical variables, scaling numeric variables, and checking model assumptions.

Background Information: Data preparation is essential to improve model performance. Missing data can be handled by removing rows or imputing values. Categorical variables are converted to factors, and numeric variables may need scaling.

Simple Code Examples:

# Load necessary libraries
library(dplyr)

# Example data: mtcars dataset
data(mtcars)

# 1. Handling Missing Values
clean_data <- mtcars %>% filter(!is.na(mpg))

# 2. Encoding Categorical Variables
clean_data$cyl <- as.factor(clean_data$cyl)

# 3. Scaling Numeric Variables
clean_data$mpg <- scale(clean_data$mpg)

# 4. Checking Model Assumptions
model <- lm(mpg ~ hp + wt, data = clean_data)
plot(model)

Interpretation of the Example Code: The code removes missing values, converts cyl to a factor, scales mpg, and checks model assumptions using diagnostic plots.

Supplemental Information:

Discussion Points:

  • Why is it important to handle missing data before fitting a statistical model?
  • How does encoding categorical variables into factors impact model performance?
  • Why is scaling numeric variables important for regression?
  • What tools can be used to check model assumptions?
  • How do assumptions like linearity impact regression results?

Day 3: Linear Regression in R

Introduction: Linear regression is a statistical technique used to model relationships between a dependent variable and one or more independent variables. It is widely applied for prediction and inference.

Objective: The goal of this session is to understand how to fit a linear regression model using R, interpret results, and generate predictions.

Scope of the Lesson: Learners will explore fitting linear models, multiple regression, interpreting coefficients, predicting with models, and model diagnostics.

Background Information: Linear regression models relationships using lm(). Coefficients, p-values, and R-squared provide insights into model performance.

Simple Code Examples:

# Load necessary library
library(dplyr)

# Example data: mtcars dataset
data(mtcars)

# 1. Fit a simple linear regression model
model_simple <- lm(mpg ~ wt, data = mtcars)

# 2. View summary of the model
summary(model_simple)

# 3. Fit a multiple linear regression model
model_multiple <- lm(mpg ~ wt + hp + drat, data = mtcars)

# 4. View summary of the multiple regression model
summary(model_multiple)

# 5. Generate predictions for new data
new_data <- data.frame(wt = c(3.0, 3.5), hp = c(120, 150), drat = c(3.9, 4.1))
predictions <- predict(model_multiple, newdata = new_data)

# 6. Check model diagnostics
plot(model_multiple)

Interpretation of the Example Code: The code fits simple and multiple regression models, generates predictions, and checks diagnostics.

Supplemental Information:

Discussion Points:

  • How do coefficients help understand predictor impacts?
  • What are the assumptions of linear regression?
  • Why interpret p-values for coefficients?
  • How can predict() be used for forecasting?
  • How do you decide which predictors to include?

Day 4: Model Evaluation and Visualization

Introduction: Evaluating regression models is crucial for understanding their reliability. Visualization aids in interpreting results and diagnosing issues.

Objective: The goal is to evaluate regression models using R-squared, residuals, and diagnostic plots, and visualize predictions with ggplot2.

Scope of the Lesson: Covers model evaluation metrics, diagnostic plots, visualization with ggplot2, and model improvement.

Background Information: R-squared measures variance explained, residuals highlight errors, and diagnostic plots check assumptions.

Simple Code Examples:

# Load necessary libraries
library(ggplot2)

# Example data: mtcars dataset
data(mtcars)

# Fit a linear regression model
model <- lm(mpg ~ wt + hp + drat, data = mtcars)

# 1. View model summary
summary(model)

# 2. Generate residuals
residuals <- resid(model)

# 3. Plot residuals
plot(model)

# 4. Visualize predictions vs actual values
predictions <- predict(model, newdata = mtcars)
ggplot(mtcars, aes(x = mpg, y = predictions)) +
  geom_point() +
  geom_abline(slope = 1, intercept = 0, color = "red") +
  labs(title = "Observed vs Predicted Values", x = "Observed mpg", y = "Predicted mpg")

# 5. Visualize residuals
ggplot(mtcars, aes(x = predictions, y = residuals)) +
  geom_point() +
  geom_hline(yintercept = 0, color = "red") +
  labs(title = "Residuals vs Fitted Values", x = "Predicted mpg", y = "Residuals")

Interpretation of the Example Code: The code evaluates a model using summary(), residuals, and diagnostic plots, and visualizes predictions and residuals with ggplot2.

Supplemental Information:

Discussion Points:

  • How does R-squared measure model performance?
  • When should diagnostic plots be used?
  • How do residual plots detect model issues?
  • Why visualize predictions and residuals?
  • How would you improve a model with residual issues?

Day 5: Capstone Modeling Project

Introduction: The capstone project applies all course concepts through a full data analysis pipeline, from cleaning to modeling and visualization.

Objective: The objective is to complete a modeling project covering data preparation, modeling, evaluation, visualization, and reporting.

Scope of the Lesson: Includes loading datasets, data cleaning, modeling with lm(), evaluation, visualization with ggplot2, and reporting.

Background Information: A typical modeling workflow involves cleaning data, fitting models, evaluating performance, and visualizing results.

Simple Code Example:

# Load necessary libraries
library(ggplot2)

# Load dataset
data(mtcars)

# 1. Data Cleaning
mtcars_clean <- filter(mtcars, !is.na(mpg))

# 2. Fit Linear Regression Model
model <- lm(mpg ~ wt + hp + drat, data = mtcars_clean)

# 3. Model Summary
summary(model)

# 4. Diagnostic Plots
plot(model)

# 5. Create Predictions
predictions <- predict(model, newdata = mtcars_clean)

# 6. Visualize Predictions vs Actual Values
ggplot(mtcars_clean, aes(x = mpg, y = predictions)) +
  geom_point() +
  geom_abline(slope = 1, intercept = 0, color = "red") +
  labs(title = "Observed vs Predicted Values", x = "Observed mpg", y = "Predicted mpg")

# 7. Visualize Residuals
residuals <- resid(model)
ggplot(mtcars_clean, aes(x = predictions, y = residuals)) +
  geom_point() +
  geom_hline(yintercept = 0, color = "red") +
  labs(title = "Residuals vs Fitted Values", x = "Predicted mpg", y = "Residuals")

Interpretation of the Example Code: The code demonstrates a full modeling pipeline, from cleaning to visualization, using the mtcars dataset.

Supplemental Information:

Discussion Points:

  • How can you handle missing values in real datasets?
  • What diagnostic checks would you perform for low R-squared?
  • How do residual plots identify model issues?
  • What are the advantages of visualizing predictions and residuals?

Daily Quiz

Practice Lab

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Exercise

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