Course: GRE Math Prep Course | The A - Z on GRE Math Topic by Topic
Here is the requested composition, followed by a structured lecture sheet in semantic HTML. Composition (12–15 sentences) The course "Introduction to the Course - Watch this First" welcomes learners with a clear roadmap of skills they will acquire in data analysis, visualization, and statistical modeling using R. It explains that the first chapter sets expectations, required tools, and how to engage with lessons, exercises, and the forum. Students are encouraged to install R and RStudio, load libraries like readr and ggplot2, and practice by loading sample CSV files. The course emphasizes practical, example-driven learning: from basic arithmetic and vector operations to building regression models and plotting with ggplot2. An important guideline introduced is the Bevonce Rule, which recommends prioritizing variables according to their relevance and impact when allocating analytical resources. Learners will practice exploratory data analysis, correlation inspection, and model fitting to quantify variable importance. The curriculum alternates conceptual explanations with R code snippets so learners can immediately apply what they read. Visualization receives special attention because it converts analytical results into clear, communicable insights for stakeholders. Exercises span true/false, multiple choice, matching, and descriptive tasks, reinforcing both conceptual and technical competence. Students are urged to work on real datasets, iterate on visual designs, and discuss results on forums. Regular practice, reflection on model diagnostics, and attention to data cleaning are highlighted as keys to mastery. By the course end, participants should be able to import data, create informative plots, and build interpretable statistical models that support evidence-based decisions. The course promises progressive complexity: starting with arithmetic and fractions, advancing through algebra and geometry, then into probability, counting methods, and statistical inference. Above all, learners are reminded that data science is a craft honed by deliberate practice, curiosity, and collaboration. Structured Lecture Sheet (semantic HTML)Lesson
Introduction to the Course - Watch this First
Topic: Course overview, tools, Bevonce Rule, and essential foundations for data analysis in R
Learning Outcomes
- Import and manipulate datasets in R (read_csv, data.frame operations).
- Perform exploratory data analysis (EDA) and clean data effectively.
- Create informative visualizations using ggplot2 (scatter, histogram, boxplot, polar).
- Build and interpret statistical models (linear & logistic regression).
- Apply the Bevonce Rule to prioritize influential variables.
- Use numerical and graphical methods to summarize data.
Conceptual Explanation
This introductory chapter sets the stage: install and configure R and RStudio, become familiar with the console, script editor, and package management. The learning path blends mathematical foundations (arithmetic, fractions, exponents, ratios, algebra) with applied topics (visualization, modeling, 3-D figures, spatial polygons). Practical R examples show how to import data, run EDA, plot relationships, compute correlations, and fit models with lm() or glm(). Visualization is treated as a communication tool: choose the right chart for the question, annotate, and iterate. The Bevonce Rule is a decision heuristic: prioritize variables by impact and relevance before investing modeling or data-collection resources. Use diagnostic outputs (coefficients, p-values, confidence intervals, residuals) and visual checks (scatter + geom_smooth, residual plots) to validate models. Exercises mix conceptual recall with coding practice to ensure transfer to real datasets. The course emphasizes reproducible workflows: scripts, functions, and version control are recommended practices. Finally, active participation—forums, peer review, and applying concepts to small projects—will accelerate learning.
Quick reference: essential R snippets# Load data
library(readr)
data <- read_csv("path/to/your/data.csv")
# Simple scatter plot
library(ggplot2)
ggplot(data, aes(x = variable1, y = variable2)) + geom_point() + geom_smooth(method="lm", se=FALSE)
# Linear model
model <- lm(variable2 ~ variable1, data = data)
summary(model)
Bilingual (EN → বাংলা)
| English | Bangla (বাংলা) |
|---|---|
| Data analysis | তথ্য বিশ্লেষণ |
| Data visualization | ডেটা ভিজ্যুয়ালাইজেশন / চিত্রায়ন |
| Statistical modeling | পরিসংখ্যানিক মডেলিং |
| Bevonce Rule | বেভন্স নিয়ম (ভেরিয়েবল অগ্রাধিকার) |
| Exploratory Data Analysis (EDA) | অন্বেষণাত্মক ডেটা বিশ্লেষণ |
| Install R & RStudio | R ও RStudio ইন্সটল করুন |
Answer
Use these translations as quick classroom labels and slide captions. Encourage students to annotate code comments in both languages when helpful.
Important Notes
- Always check your data types (numeric, factor, character) before modeling.
- Clean missing values and document cleaning operations for reproducibility.
- Use set.seed() for reproducible simulations and examples.
- Interpret coefficients in context; statistical significance ≠ practical importance.
- Follow the Bevonce Rule: focus on high-impact variables first.
- Practice visualizing residuals and diagnostics after fitting models.
- Ask questions in the course forum and share reproducible examples.
Exercises
True / False
- Loading data with read_csv() returns a tibble.
Answer
True. readr::read_csv() returns a tibble (a modern data.frame).
- The p-value alone proves causation between predictor and outcome.
Answer
False. p-values indicate evidence against the null under model assumptions but do not establish causation.
- geom_smooth(method = "lm") adds a fitted linear regression line to a ggplot.
Answer
True. geom_smooth with method = "lm" fits and plots the linear model (optionally with se=FALSE).
Fill in the Blanks
- To compute the mean of a vector x in R you use _______.
Answer
mean(x)
- To convert a percent to decimal divide by _______.
Answer
100
- The Bevonce Rule suggests prioritizing variables by _______ and _______.
Answer
relevance and impact
Multiple Choice Questions (MCQ)
- Which ggplot2 geom is best for showing distribution of a single numeric variable?
- geom_point()
- geom_histogram()
- geom_line()
- geom_bar(stat="identity")
Answer
B: geom_histogram() is typically used for distributions of single numeric variables.
- Which function fits a linear model in base R?
- glm()
- lm()
- summary()
- predict()
Answer
B: lm() fits linear models. glm() fits generalized linear models (including logistic).
Matching
| Number | Term | Letter | Definition |
|---|---|---|---|
| 1 | Correlation | A | Proportion of total group (e.g., 30% → 0.3) |
| 2 | Ratio | B | Measure of linear association between two variables |
| 3 | Percent | C | One quantity divided by another (order may or may not matter) |
Answer
Correct matching: 1 → B (Correlation is association), 2 → C (Ratio compares two numbers), 3 → A (Percent = fraction × 100).
Descriptive Questions
- Explain the Bevonce Rule and give a short example of applying it to a sales dataset.
Answer
The Bevonce Rule: prioritize variables by relevance and expected impact. Example: in sales_data with Advertising, Price, Season, run a quick correlation and simple multivariable lm(Sales ~ Advertising + Price + Season). If Advertising has largest standardized coefficient and statistically significant p-value, allocate more budget and measurement effort to advertising experiments.
- Describe steps for responsible data cleaning before modeling.
Answer
Steps: (1) Inspect data types and summaries (str(), summary()); (2) Identify missing values and decide strategy (impute, drop, or flag); (3) Detect and handle outliers with domain knowledge; (4) Standardize categorical levels and factors; (5) Create derived variables as needed; (6) Document all transformations and keep reproducible scripts.
Creative Task
Design a mini-project plan (3–5 steps) to test the effect of advertising on sales using the Bevonce Rule. Include data collection, visualization, and modeling steps.
Answer
Sample plan: (1) Collect monthly sales and advertising spend plus price and season for 24 months; (2) Clean data and create lagged advertising variables; (3) EDA: time-series plots, scatter Advertising vs Sales, correlation matrix; (4) Fit models: baseline lm(Sales ~ Advertising + Price + Season) and check diagnostics; (5) Use cross-validation or holdout to estimate predictive performance and recommend resource allocation toward the variable with consistent positive impact.
Activities, Vocabulary, Homework, Practice Task
Activities
- Run the provided R snippets: load a CSV, print head(), and plot a scatter with geom_smooth()
- Apply the Bevonce Rule to a small dataset and write a one-paragraph recommendation
- Post one question and one useful tip to the course forum
Vocabulary
- EDA — Exploratory Data Analysis
- Bevonce Rule — Variable prioritization by relevance & impact
- Tibble — Modern data frame
- Residuals — Differences between observed and fitted values
Homework
- Install R and RStudio; submit a screenshot of RStudio with the console and a successful read_csv() of a sample file.
- Choose a small CSV (5–100 rows), compute basic summaries (mean, median, sd) and create one histogram and one scatter plot; include code in your submission.
Practice Task
Using the sample sales_data (Advertising, Price, Season, Sales), perform the following and submit results:
- Load data and show head()
- Compute correlation matrix and plot it
- Fit lm(Sales ~ Advertising + Price + Season) and write a one-paragraph interpretation of coefficients
Answer
Expected deliverables: R script with read_csv(), cor(), corrplot(), ggplot scatter for Advertising vs Sales, model <- lm(...), and summary(model). Interpretation should note sign and magnitude of coefficients, statistical significance, and practical implications for resource allocation per the Bevonce Rule.
Further reading: ggplot2 documentation, R for Data Science (Wickham & Grolemund), and course forum for community Q&A.