Bivariate Data Analysis: Free Course

About this course

Bivariate analysis asks how two measurements vary together. This course moves from scatter plots to correlation, regression and residual analysis while keeping interpretation tied to the observed data. Study the complete public source playlist from Khan Academy in English, with all 16 recordings available in the on-site classroom. Lessons retain their original titles and source order, including worked examples, introductions and repeated entries.

Course at a glance

What you’ll learn

• Describe the direction, form and strength of a scatter plot.
• Interpret correlation and a regression line in context.
• Calculate residuals and examine residual plots.
• Explain how outliers and sampling scope affect conclusions.

Skills you’ll gain

• Scatter plots
• Correlation
• Linear regression
• Residual analysis

Course Overview

Start by describing the direction, form and strength of a relationship before calculating a coefficient. The correlation lessons develop both calculation and intuition, while regression adds a fitted line for predicting one variable from another. Slope and intercept are interpreted in the units and context of the original measurements. Residuals then show what the fitted line leaves unexplained. Their plots, standard deviation and connection with the coefficient of determination provide several complementary ways to evaluate the model. The course also includes survey generalizability and examples of how removing an outlier affects a fitted relationship. Those lessons are a reminder that a numerical fit alone does not establish causal meaning or justify predictions for every population. Keep the observed range, sampling context and unusual points visible when describing a result.

How to study the course

• Videos 1–4: this part of the source list includes “Constructing a scatter plot” through “Calculating correlation coefficient r”. Define the question and the observations. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 5–8: this part of the source list includes “Example: Correlation coefficient intuition” through “Calculating the equation of a regression line”. Check the assumptions behind a method. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 9–12: this part of the source list includes “Interpreting slope of regression line” through “Residual plots”. Connect a calculation with a plain-language interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 13–16: this part of the source list includes “R-squared or coefficient of determination” through “Impact of removing outliers on regression lines”. Describe uncertainty and limits of a conclusion. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, analysts and readers who want to understand the specific statistical methods in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Basic arithmetic and familiarity with tables and graphs are helpful. More advanced probability or inference topics assume the prerequisite methods shown in the recordings.

Put the lessons into practice

Use a small fictional table of paired observations to draw a scatter plot and fit or reproduce a simple regression line. Interpret its slope with units, calculate residuals and inspect their pattern. Repeat the fit after removing one unusual observation. Explain the change without presenting the removal as automatically justified, and identify a prediction that would go beyond the observed data.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.