Course (Part 762)

Course: Pass the Praxis 7001: 7002 Rdg, 7003 Math, 7004 SS, 7005 Sci

Introduction — Short Composition

Data analysis is an essential modern skill that transforms raw facts into actionable knowledge, and R is a leading tool for that work. This introductory chapter outlines the core pipeline: collecting relevant data, cleaning it to remove errors, exploring its patterns, fitting statistical models, and finally visualizing results for communication. R and RStudio together provide a reproducible, scriptable environment that makes every step auditable and repeatable. Starting with built‑in datasets such as mtcars helps learners practice basic commands like data(), head(), and summary() to inspect structure and distributions. Exploratory visualizations using ggplot2—scatter plots, histograms, and boxplots—reveal relationships and guide modeling choices. Simple models like linear regression (lm()) introduce concepts of coefficients, R‑squared, and residual diagnostics. Emphasis on data cleaning—handling missing values, outliers, and type conversions—prepares data for meaningful inference. Good analysis couples quantitative output with clear graphics and concise interpretation of model results. Iteration is intrinsic: insights from models often prompt additional cleaning or feature engineering. Throughout, practice and project work accelerate mastery more than passive reading. Students should learn to question data provenance and assumptions behind every analytic step. By the end of the introduction, learners will be ready to perform basic EDA, fit simple models, and produce publication‑quality plots. The next chapter will focus on data wrangling techniques that are essential before advanced modeling.

Lesson

Topic: Introduction to Data Analysis with R — pipeline, EDA, visualization, and basic modeling

Learning Outcomes

• Understand the five core components of a data analysis workflow: collection, cleaning, exploration, modeling, and visualization.
• Install R and RStudio; load a dataset and inspect its structure with head(), str(), and summary().
• Create basic ggplot2 visualizations (scatter plot, histogram, boxplot) and interpret them.
• Fit a simple linear regression model using lm(), read the summary(), and visualize the regression line.
• Document findings, check model diagnostics, and iterate on preprocessing steps.

Conceptual Explanation

Data analysis in practice is an iterative pipeline where raw data becomes insight through a sequence of steps. Begin by collecting or loading data, then clean it (handle NAs, correct types, remove duplicates). Explore the cleaned data using descriptive statistics and visual plots to discover distributions, correlations, and anomalies. Build simple statistical models (e.g., linear regression) to quantify relationships and generate predictions; evaluate models via summary statistics and residual diagnostics. Finally, create clear visualizations and succinct interpretations to communicate results. R supports each stage with dedicated functions and packages—dplyr for manipulation, ggplot2 for plotting, and base/stats for modeling—making the process reproducible and scriptable. Reproducibility and clear reporting are as important as technical correctness.

Bilingual (EN → বাংলা)

English: Data analysis is a sequence of steps—collection, cleaning, exploration, modeling, and visualization—that turns raw data into actionable insights. R provides tools to perform each step reproducibly.

বাংলা: ডাটা বিশ্লেষণ হল এক ধাপে সম্পন্ন প্রক্রিয়া — সংগ্রহ, পরিস্কার, অন্বেষণ, মডেলিং এবং ভিজ্যুয়ালাইজেশন — যা কাঁচা ডাটাকে ব্যবহারযোগ্য অন্তর্দৃষ্টিতে পরিণত করে। R প্রতিটি ধাপ পুনরুত্পাদনযোগ্যভাবে সম্পাদন করার সরঞ্জাম দেয়।

Important Notes

• Always record data provenance: where the data came from and any preprocessing steps.
• Check assumptions of any statistical model (linearity, homoscedasticity, normality of residuals) before interpreting results.
• Prefer tidy, well‑documented scripts and R Markdown for reproducible reports.
• Visualization should support conclusions—label axes, add units, and include summaries (e.g., regression lines with confidence bands).

Core data analysis pipeline (compact table)

Step	Purpose	Typical R tools / functions
Data Collection	Gather or load raw data	read.csv(), readr::read_csv(), data()
Data Cleaning	Handle NAs, types, duplicates	dplyr::filter(), mutate(), tidyr::drop_na()
Exploration (EDA)	Summaries & visual patterns	summary(), ggplot2::geom_histogram(), geom_boxplot()
Modeling	Quantify relationships / predict	lm(), glm(), caret
Visualization & Reporting	Communicate results	ggplot2, RMarkdown

Starter R Examples (copyable)

# Load example data
data(mtcars)
# Quick inspection
head(mtcars)
summary(mtcars)
# Basic ggplot2 scatter
library(ggplot2)
ggplot(mtcars, aes(x = hp, y = mpg)) +
  geom_point() +
  labs(title = "Horsepower vs. MPG", x = "Horsepower", y = "Miles Per Gallon")
# Fit a simple linear model
model <- lm(mpg ~ hp, data = mtcars)
summary(model)
# Scatter with regression line
ggplot(mtcars, aes(x = hp, y = mpg)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, color = "blue")

Exercises

Types: True / False / Fill in the Blanks / MCQ / Matching / Descriptive / Creative

True / False

1. Linear regression only applies to normally distributed dependent variables.
   Answer

   False — Linear regression requires assumptions about residuals (e.g., approximate normality), not that the dependent variable itself is strictly normally distributed.

2. ggplot2’s geom_smooth(method = "lm") adds a fitted linear model line.
   Answer

   True — It adds a regression line; set se = TRUE to include confidence band.

Fill in the Blanks

1. The R function to read a CSV file is ______.
   Answer

   read.csv() (or readr::read_csv()).

2. To calculate the mean while ignoring NA values, use ______.
   Answer

   mean(x, na.rm = TRUE).

Multiple Choice Questions (MCQ)

1. Which ggplot2 layer maps aesthetics (like x and y)?
   • A) geom_point()
   • B) labs()
   • C) aes()
   • D) theme()
   Answer

   C) aes() defines aesthetic mappings.

2. Which R function fits a linear model?
   • A) glm()
   • B) lm()
   • C) nls()
   • D) predict()
   Answer

   B) lm() fits linear models (use glm() for generalized models).

Matching

Match the R function (left) to its purpose (right).

Function	Purpose
read.csv()	Load CSV file into a data.frame
ggplot()	Create layered plots
lm()	Fit linear regression models
dplyr::filter()	Subset rows by condition

Answer

read.csv() → Load CSV; ggplot() → Create layered plots; lm() → Fit linear regression; filter() → Subset rows.

Descriptive Questions

1. Explain why data cleaning is essential before modeling.
   Answer

   Data cleaning removes or corrects errors (missing values, inconsistent types, duplicates, outliers) that can bias estimates, violate model assumptions, or cause functions to fail. It ensures the model receives accurate, consistent inputs and that the results are interpretable and reproducible.

2. List three diagnostics you would check after fitting a linear model and why.
   Answer

   1. Residual vs fitted plot — to detect non‑linearity or heteroscedasticity.
   2. Normal Q‑Q plot of residuals — to assess approximate normality of residuals.
   3. Leverage / Cook’s distance — to identify influential observations that unduly affect estimates.

Creative Tasks

1. Design a mini project: choose a public dataset, write three research questions, and outline an R plan (data load, cleaning, EDA, model, visualization).
   Answer

   Example plan: Dataset — Gapminder world data; Questions — (1) How has life expectancy changed by continent since 1950? (2) What predictors (GDP per capita, education) explain current life expectancy? (3) Are trends linear or accelerating? Plan — load with read_csv(), clean NA years, compute continent summaries, EDA with line plots & faceting, fit lm(lifeExp ~ gdpPercap + schooling), diagnostics, and create final faceted plots and a short R Markdown report.

Activities, Vocabulary, Homework, Practice Task

Activities

1. Hands‑on: Run the provided mtcars code, create an mpg vs hp scatter, fit lm(mpg ~ hp), and save a PNG of the plot.
2. Group: Compare two cleaning strategies (drop NA vs mean imputation) and report the effect on model coefficients.

Answer

See starter R examples above. Use ggsave() to save plots. Document changes in coefficients and R‑squared when imputing vs dropping NA.

Vocabulary

• EDA: Exploratory Data Analysis
• Residual: Observed minus predicted value
• Homoscedasticity: Constant variance of residuals
• R‑squared: Proportion of variance explained

Answer

Definitions: EDA = summarize & visualize; residual = y - ŷ; homoscedasticity = no pattern in residual spread; R‑squared = model explanatory power (0–1).

Homework

1. Install R and RStudio; run the starter script; export your scatter+regression image and attach a one‑paragraph interpretation.
2. Find a CSV dataset (public) and prepare a one‑page EDA: three plots and two modeling attempts (linear/logistic or transform), report findings.

Answer

Submit an R Markdown file showing code, plots, model summaries, and a short interpretation paragraph highlighting assumptions checked and any limitations.

Practice Task

Using the mtcars dataset, test whether weight (wt) or horsepower (hp) is a stronger predictor of mpg. Fit models mpg ~ wt, mpg ~ hp, and mpg ~ wt + hp. Compare R‑squared and AIC, and display a concise interpretation (3–5 sentences).

Answer

Example steps: fit the three models, examine summary() for R‑squared and AIC(). Typically, both wt and hp are significant; the combined model often increases R‑squared and reduces AIC, indicating improved fit. Check multicollinearity (e.g., cor(mtcars$wt, mtcars$hp)), and interpret coefficients with units (e.g., each 1 unit increase in wt corresponds to Δ mpg after adjusting for hp).