Course: GRE Math Question Bank In the form of 5 Practice Tests
The Practice Test 1 chapter provides a concise, practical set of exercises that introduce core R techniques for data analysis, visualization, and statistical modeling. It begins with a data analysis task using a hypothetical sales_data file to demonstrate how to compute total revenue by adding a derived column and summing it. The visualization section uses the built-in mtcars dataset to show how ggplot2 creates clear scatter plots for mpg versus horsepower. Statistical modeling is introduced through linear regression examples that predict mpg from hp and wt, with instructions to fit models and inspect summaries. Each example pairs a clear task statement with runnable R code, promoting hands-on learning and reproducibility. The sequence—from loading and cleaning data to plotting and modeling—reinforces the typical workflow in applied data science. Reflection prompts encourage learners to consider how these components interact to produce analytical insight. Subsequent practice tests (2–5) expand on these themes, adding filtering with dplyr, diagnostics for regression models, and simple prediction examples. The material also includes GRE-style quantitative and verbal examples to connect statistical practice with standardized test skills. Throughout, emphasis is placed on interpretation of outputs (coefficients, R-squared, residuals) rather than mere code execution. Learners are urged to adapt snippets to their own datasets and to inspect assumptions before trusting model results. Overall, the chapter balances technical detail with pedagogical guidance to build transferable R skills for analysis and communication.Lesson
Topic: Practice Tests — Data Analysis, Visualization, and Statistical Modeling in R
Learning Outcomes
- Load and inspect CSV and built-in datasets in R (read.csv, data(), head(), summary()).
- Create derived columns and compute aggregate metrics (mutate-like operations and sum()).
- Visualize relationships using ggplot2 and base R plotting functions.
- Fit linear regression models with lm(), interpret coefficients, R-squared, and p-values.
- Use dplyr for filtering and cleaning, and run basic model diagnostics (residual plots).
Conceptual Explanation
These practice tests are structured to follow a standard analysis pipeline: data ingestion, cleaning, exploration, visualization, modeling, and evaluation. The first practical exercise computes total revenue by creating a transaction-level revenue column and summing it; this exemplifies feature engineering and aggregation. Visualization examples (scatter plots, bar charts) use ggplot2 for layered, labeled figures that support interpretation. Linear models show how to quantify relationships and make predictions; summary() outputs guide decisions about model fit and statistical significance. Diagnostics (residual plots, leverage) are emphasized so models are not accepted uncritically. Combining dplyr and ggplot2 makes workflows readable and reproducible, and small prediction examples illustrate how to apply models to new observations. Throughout, students should record assumptions and verify them (linearity, independence, homoscedasticity) before relying on results.
| Section | Task | Representative R Example |
|---|---|---|
| Data Analysis | Compute total revenue from sales_data |
|
| Data Visualization | Scatter plot mpg vs hp |
|
| Statistical Modeling | Predict mpg from hp and wt |
|
Bilingual (EN → বাংলা)
-
EN: Compute total revenue by multiplying quantity and unit price, then sum.
বাংলা: পরিমাণ এবং ইউনিট মূল্যের গুণফল হিসেবে মোট আয় হিসাব করুন, তারপর সবগুলো যোগ করুন। -
EN: Use ggplot2 to create clear scatter plots with labels and theme.
বাংলা: লেবেল এবং থিম সহ স্পষ্ট স্ক্যাটার প্লট তৈরি করতে ggplot2 ব্যবহার করুন। -
EN: Fit a linear regression with lm() and inspect coefficients and R-squared.
বাংলা: lm() দিয়ে লিনিয়ার রিগ্রেশন ফিট করুন এবং কোফিশিয়েন্ট ও R-squared পরীক্ষা করুন। -
EN: Always check residuals and model assumptions before interpretation.
বাংলা: ব্যাখ্যার আগে সর্বদা রেসিডুয়াল এবং মডেল অনুমানগুলো পরীক্ষা করুন।
Important Notes
- Code examples are minimal templates — adjust variable names and paths to your dataset.
- Interpretation matters: statistical significance does not imply practical significance.
- Missing values must be handled explicitly (na.omit, filter(!is.na(...)), imputation).
- For reproducibility, set seeds when performing random sampling or partitioning (set.seed()).
- Use par(mfrow = c(2,2)) or ggplot2 diagnostic plots to evaluate model fit visually.
Exercises
True / False
- Creating a new column with quantity * price_per_unit is a valid way to compute per-transaction revenue.
- R-squared always indicates that the model is the correct choice for prediction.
Answer
True — multiplying quantity and unit price yields transaction revenue; summing gives total revenue.
Answer
False — R-squared measures explained variance; it does not prove causation or guarantee predictive generalization.
Fill in the Blanks
- To read a CSV file in R we use ____.
- In ggplot2, the function to add points to a scatter plot is ____.
Answer
read.csv()
Answer
geom_point()
Multiple Choice Questions (MCQ)
| Q# | Question | Choices | Answer |
|---|---|---|---|
| 1 | Which function fits a linear model in base R? | A) glm(), B) lm(), C) lmer(), D) nls() |
AnswerB) lm() |
| 2 | Which ggplot2 layer adds a smoothed regression line? | A) geom_bar(), B) geom_smooth(), C) geom_histogram(), D) geom_boxplot() |
AnswerB) geom_smooth() |
Matching
Match the R object to its typical use:
| Item | Use |
|---|---|
| A. ggplot | 1. Model diagnostics |
| B. lm() | 2. Plotting |
| C. summary() | 3. Summarize model results |
Answer
A → 2 (ggplot = plotting), B → (lm() = model fitting), C → 3 (summary() shows model output).
Descriptive
Explain why residual plots are important after fitting a linear model.
Answer
Residual plots reveal patterns that violate model assumptions (non-linearity, heteroscedasticity, non-normal errors). If residuals show structure, coefficients and p-values may be biased or misleading, and corrective actions (transformations, different model families, or adding predictors) may be needed.
Creative
Design a 3-step mini-project using a dataset of your choice that incorporates the key elements from these practice tests.
Answer
Step 1: Ingest and clean — load CSV, handle NAs, convert dates. Step 2: Explore and visualize — compute summary statistics, create scatter and bar plots with ggplot2 to detect relationships and outliers. Step 3: Model and evaluate — fit an lm() model with relevant predictors, check summary and residual diagnostics, produce predictions for a holdout set and report RMSE and interpretation of coefficients.
Activities, Vocabulary, Homework, Practice Task
Activities
- Run the three core examples (revenue calculation, ggplot scatter, lm regression) on your machine and save outputs as scripts.
- Modify one example to include another predictor and document changes in R-squared and coefficients.
Answer
Expected deliverable: a zip or GitHub gist containing the R scripts, a brief README describing dataset adjustments, and screenshots or exported plots showing results.
Vocabulary
- Aggregate
- Feature engineering
- Homoscedasticity
- R-squared
- Residual
Answer
Definitions: Aggregate = combine values (e.g., sum); Feature engineering = create new variables; Homoscedasticity = constant variance of errors; R-squared = proportion variance explained; Residual = observed minus predicted value.
Homework
- Apply the revenue calculation pattern to a dataset with returns/refunds and compute net revenue.
- Fit an lm() model predicting mpg using cyl, hp, and wt; report and interpret coefficients and R-squared.
Answer
Homework checklist: cleaned data, script with comments, model summary output, short write-up (≤ 300 words) interpreting effects and potential limitations.
Practice Task
Using a sample dataset (mtcars or your own), create a small report (one page) that includes: data summary, one visualization, one fitted model, and three interpretable takeaways.
Answer
Report structure: Title, Methods (data and code reference), Results (table of summary stats, plot image, model summary excerpt), Conclusions (3 bullet takeaways), and Suggestions for further analysis.