← All Data Visualization with AI modules

Module 4 — Association, Correlation & Regression

Weeks 7–8 · graduate statistics · adaptive competencies DV07–DV08

Move from scatterplot reasoning to fitted models, residual diagnostics, leverage, and defensible model claims.

Statistics focuscorrelation, covariance, confounding, simple linear regression, residuals, leverage, heteroscedasticity

R/tool focusInline browser R labs; optional desktop RStudio/Positron for capstone; cor(); ggplot2 scatterplots; lm(); broom; fitted/residual plots

Interactive assignmentCorrelation/causation trap gallery, residual diagnosis cards, regression diagnostic packet

Interactive reading

Predict before reveal

A correlation of 0.82 between study time and exam score proves that more study time causes higher scores. What is wrong?

Correlation is association, not causation. Confounders, selection effects, measurement issues, and study design must be considered before causal language is justified.

Confounding lab

The confounding lab needs JavaScript.

Correlation and causation gallery

The causation gallery needs JavaScript.

Residual diagnosis cards

The residual diagnosis cards need JavaScript.

AI-output audit

This AI audit needs JavaScript.

Hands-on visual lab

Move one observation out of twenty-five and watch the fitted slope follow it. Leverage is a property of the predictor alone, so a point can dominate a model before you have looked at its outcome. Then run the browser-R lab below without leaving QuantegyAI.

This visual lab needs JavaScript.

GeoGebra lab

Use GeoGebra to connect scatterplot geometry, fitted lines, and residual distances before relying on R model output.

Interactive Math with AI / GeoGebra strand

Embedded GeoGebra applet loading…

R lab

R / Quarto / Shiny workflow

Fit `lm()`, use `broom::tidy()`, create fitted and residual plots, and write a model-appropriateness note.

# Suggested R workflow scaffold
library(tidyverse)
# 1. Import or construct the dataset
# 2. Verify summaries before visualizing
# 3. Build the ggplot2 visualization
# 4. Write the statistical interpretation and limitation note
# 5. Log any AI assistance and corrections

Module 4 Capstone

The inline Module 4 capstone submission and AI grader need JavaScript.

Adaptive reflection

What I know / where I go next

I can tell a descriptive claim from an associational one and both from a causal one. I can name a lurking variable that would produce a relationship I am about to report. I can read a residual plot for curvature, non-constant variance, and influence. I can say what a fitted line does and does not license me to predict. I can state the causal boundary of my capstone's headline relationship.

Mastery check loading…

Capstone connection Add this module’s evidence to your capstone readiness tracker. If your explanation depends on AI, include the prompt, output, verification method, and final correction.