QuantegyAI Module 6 (Canvas Weeks 11–12 | DV11–DV12 | Project 4)
Module 6 — Multivariate & Time-Series Visualization
Compare multivariate relationships and change over time.
Start with the statistical foundations for studying several variables together and observations ordered over time.
Module 6 is a guided path: 19 short pages, with a guided check on all but three of them.
Start Module 6 with the introduction →
6 checkpoints
2 interactive visual labs
2 Project 4 evidence items
45–60 minutes
Recorded checkpoint coverage0%
Start with the five prediction checks.
Multivariate lensfacets, heatmaps, pair plots, residual plots, and standardization
Time-series lenstrend, seasonality, smoothing, aggregation, indexing, and rate of change
Evidence workflowInline browser R labs → audit AI → defend the final visual; optional desktop RStudio/Positron for extended work
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Begin with the prediction checks. The map will distinguish practice evidence from demonstrated mastery.
Next best action: prediction checks →Module overviewView full topics and learning outcomes
What students will cover
- Multivariate structure: relationships among several variables, correlation matrices, pair plots, facets, heatmaps, and residual plots.
- Standardized values: how measurement units affect numerical spread, how \(z\)-scores express distance from a mean, and how to label original and standardized axes.
- Clustering and grouping: distance, scaling, cluster sensitivity, and the difference between a useful grouping visual and an unsupported category claim.
- Time-series visualization: trend, seasonality, smoothing windows, moving averages, indexed series, rate of change, and the visual consequences of aggregation.
- AI audit: checking AI-generated multivariate and time-series claims for scale errors, over-smoothed patterns, omitted variables, and unsupported causal language.
Student learning outcomes
- Choose among facets, heatmaps, pair plots, correlation matrices, residual plots, and time-series views based on the statistical question.
- Explain how standardization expresses observations relative to each variable’s center and spread.
- Interpret positive, negative, and zero standardized values without confusing them with original measurement units.
- Compare raw and standardized multivariate views and state what each preserves, distorts, or discards.
- Use smoothing or aggregation on a time series only after naming the window, unit, and pattern that may be hidden.
- Audit an AI-generated multivariate or time-series claim and revise it into defensible statistical language.
- Write a final visual defense that names the omitted dimensions, scaling choices, time unit, and one limitation.
Module 6 · Step 1 of 6 · Watch8 min
Interactive reading: association, regression and time series
This reading uses quick prediction checks before the explanation is revealed. Work each prompt before opening the answer; the goal is to defend multivariate and time-series choices instead of accepting attractive graphics at face value.
Correlation and causation
A strong correlation between two variables proves that changing one variable causes the other to change. True or false?
False. Correlation describes an association, not proof of causation. As the introduction explains, a strong relationship does not prove that changing one variable causes the other to change. A confounding variable can help explain why they move together.
Regression residuals
A residual is the observed response minus the predicted response. True or false?
True. As introduced earlier, \(\text{residual}=y-\hat{y}\). A positive residual means the observed response is above the prediction; a negative residual means it is below.
Scatterplots
A scatterplot can be used to visualize the relationship between two quantitative variables. True or false?
True. A scatterplot places one quantitative variable on each axis and shows each paired observation as a point. It helps reveal direction, shape, and outliers in the relationship.
- Time order carries information: rows of a time series are not interchangeable. Reordering them destroys the pattern, which is not true of a plain sample.
- Serial dependence: a value is often related to the values just before it. Today’s enrolment is informative about tomorrow’s.
- Lag: the number of time steps between two observations. A lag-1 comparison sets each value beside the one immediately before it.
- Autocorrelation: the correlation of a series with its own lagged values. The autocorrelation function summarises it across several lags.
- Why it matters: methods that assume independent observations can report intervals that are far too narrow on dependent data, so the uncertainty looks smaller than it is.
- Different rows is not independence: each observation occupying its own row says nothing about whether the observations are related.
Observations collected at different times must be independent of one another. True or false?
False. A value today may be related to earlier values. The introduction calls this serial dependence; autocorrelation describes relationships across time lags.
- What smoothing is: Smoothing replaces a noisy time-series with a less variable curve, often by averaging nearby values or fitting a trend.
- Noise vs. signal: Time-series data often contain random fluctuation, but the “noisy original” may also contain real short-term changes that are meaningful.
- Smoothing reduces variability: A smoothed line can make long-term trends easier to see by reducing random ups and downs.
- Smoothing can distort the data: It may hide peaks, sudden changes, seasonality, outliers, or structural breaks. Therefore, it is not automatically more accurate or “more truthful.”
- Bias–variance tradeoff: Smoothing lowers variance but can introduce bias, especially if the smoothing is too strong or the method is inappropriate.
- Choice of smoothing method matters: Moving averages, LOESS, splines, and other methods can produce different results from the same data.
- The original data still matter: The raw series shows what was actually observed; the smoothed line is a model-based or method-based summary.
A smoothed time-series line is always more truthful than the noisy original because it removes random fluctuation. True or false?
False. Smoothing can reveal trend by reducing noise, but it can also hide abrupt changes, seasonal cycles, and meaningful local variation. The window choice is an analytic decision. A defensible time-series graphic states the time unit, smoothing rule, window size, and what the smoothing may hide.
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Module 6 · Step 2 of 6 · Guided8 min
Raw and standardized values
Compare original measurements with their positions relative to each variable’s mean and standard deviation.
The standardization lab needs JavaScript.
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Module 6 · Step 3 of 6 · Guided10 min
Choose the view that preserves the evidence
Match each statistical question to the representation that answers it, then audit the shortcuts proposed by AI.
Open the DV11 representation-choice lab · about 10 minutes
Your task Match all six questions to the view that answers them. Ask what each view preserves and what it throws away before you choose.
Lab complete when the score box reads 6 / 6 and you can say why the runner-up view fails for each question.
The representation lab needs JavaScript.
Open the multivariate AI-output audit · about 10 minutes
AI-output audit
Your task Rule Accept, Modify, or Reject on all six AI proposals. Modify is for a proposal whose diagnosis is right but whose action needs discipline.
Lab complete when every proposal has a verdict and the audit table below the cards is filled in — that table lists recommended revisions. Add only the work you actually carried out to your Project 4 project log.
This AI audit needs JavaScript.
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Module 6 · Step 4 of 6 · Challenge10 min
Interpret smoothing and temporal variation
A weekly series carrying trend, an annual cycle, and noise. Smoothing is a filter, not a cleaning step: widen the window far enough and the seasonality you were asked to report disappears by construction. Then run the browser-R lab below without leaving QuantegyAI.
Open the DV12 smoothing tradeoff lab · about 10 minutes
This visual lab needs JavaScript.
Open the three browser-R activities
Starter: understand moving-average endpoints
Optional starter practice. Your task Compare 12 fixed synthetic weekly values with a centred three-week moving average. Explain why the endpoint averages are undefined and what smoothing hides.
Lab complete when the output contains the raw values and their moving averages, and your interpretation identifies the trend, the window and a pattern the smoother can hide. Undefined endpoint averages must not be described as missing raw observations.
DV11: investigate multivariate structure
Required evidence activity; supplied lab route. Your task Compare raw and standardized views of five simulated variables across 40 campuses. Read the correlation matrix with the pair plot, choose a view, and explain the scaling, relationship and limitations.
Lab complete when your interpretation identifies an association, examines its shape in a suitable plot, explains raw versus standardized units and states a limitation.
DV12: investigate seasonal time series
Required evidence activity; supplied lab route. Your task Use 104 simulated weeks with trend, a 52-week cycle and noise. Compare the raw series with its five-week smoother; justify the window, time unit and aggregation, report undefined endpoints, and identify a pattern smoothing could hide.
Lab complete when your interpretation uses the raw and smoothed output to distinguish trend from the designed seasonal cycle, justify the window and identify a hidden-pattern risk. Report any undefined endpoints.
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Module 6 · Step 5 of 6 · Independent15–20 min
Module 6 evidence: explain and evaluate the visual analysis
Complete Canvas Project 4 evidence items DV11 and DV12. Each item autosaves, and the shared AI grader responds to the statistical defense—not surface polish.
Where do I get my data?
The starter is a fixed synthetic fixture; Labs A and B use simulated data. Their source is the supplied script, not collected campus records. External retrieval is not applicable. Preserve the script version and seeds with your evidence.
For the time-series half of DV12: R Lab already holds week and visits in its editor, 12 weeks with a trend and noise. Run it to compare raw values with the three-week moving average and defend what the smoother hides. That series carries no seasonal component, so use R Lab B when your defence has to name seasonality.
For the multivariate half of DV11: R Lab A already holds the designed campus data frame in its editor: five variables across 40 campuses with the structure built in. Open it and press Run: it prints the raw and standardized views, the correlation matrix, a pair plot, and one complementary visual — exactly what a facet, heatmap, pair-plot or correlation-matrix defence needs.
For the seasonal half of DV12: R Lab B already holds the season data frame in its editor, 104 weeks with a 52-week cycle, for trend, seasonality and a smoothing window. Open it and press Run: it draws the raw series with the 5-week moving average over it. Both Lab A and Lab B are drawn with set.seed(), so describe them as simulated rather than collected.
Rather not write R? The standardized values lab and the smoothing tradeoff lab both report numbers you can quote directly in your defence.
Prefer your own dataset? You can use any built-in R dataset (run data() to list them) or add your own CSV under Your data in the R lab (files up to 500 MB stay in your browser). But you don't need to — the R lab dataset is ready to go.
Open the DV11 and DV12 Project 4 evidence checklists
Your task Open each card, read the worked exemplar, then tick each check once your own work satisfies it and paste your note or link.
Module 6 evidence complete when both cards read complete — that is 2 of the 4 Project 4 evidence items. Continue to Module 7 for DV13 and DV14. The shared Project_4_Canvas_Packet.zip is eligible to download on the Project 4 page when all four items are download-eligible. Evidence completion and download eligibility are separate: completed evidence or the applicable earned-credit policy can make an item eligible. This includes newly earned credit, not only historical credit. Module 6 credit alone does not unlock the whole four-item ZIP; DV13 and DV14 must also be eligible. Unticked boxes still mean evidence is incomplete, even when earned credit permits download.
Project 4 evidence items: DV11 Multivariate Structure Defense · DV12 Time-Series Story
Open the submission decision check
The Module 6 submission decision check needs JavaScript.
Open the Module 6 AI-feedback workspace
Submit the Module 6 workspace for AI feedback
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Capstone writing autosaves as you work.
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Module 6 · Step 6 of 6 · Evidence gate8 min
Review concepts and save the mastery assessment
Review the concepts and complete the four-question mastery assessment. Saving its result does not complete the evidence checklists or verify a Canvas submission.
Adaptive reflection
What I know / where I go next
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Module 6 record
Your saved Module 6 record needs JavaScript. You can also see it on your skills dashboard report card.
Project 4 connection Complete DV11 and DV12 here, then continue to Module 7 for DV13 and DV14. The shared Project 4 packet follows Module 7. If your explanation depends on AI, include the prompt, output, verification method, and final correction.