Week 15 — Readings & Resources

Your primary reading is Chapter 15 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 10 items (4 readings and 6 videos). Allow 78–92 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (18–21 min total)

• Least Squares Regression — Math is Fun
• Inference on the Slope (An Example) — jbstatistics
• The Effects of Outliers and Extrapolation on Regression (2.4) — Simple Learning Pro

① Fitting the line and reading its slope

Chapter 15, Section “Fit the least-squares line: the line with the smallest squared misses” · Session 1, Segment 1, “The least-squares line and its slope” · Remember: the least-squares line makes the squared misses as small as possible, and its slope is the predicted change in y for each one-unit increase in x.

• The Main Ideas of Fitting a Line to Data (The Main Ideas of Least Squares and Linear Regression.) — StatQuest with Josh Starmer — a calm, picture-first walk through the least-squares idea: measure how far each point sits from a line, square those misses, and turn the line until their total is as small as it can be. This builds on Week 4's work with scatterplots and correlation. (video, 9 min) (captions: creator)
• Least Squares Regression — Math is Fun — read the steps and the worked example that predicts ice-cream sales from hours of sunshine, then the short part on outliers. It computes the slope and intercept by hand; in this course a spreadsheet does that step for you. (reading, 5–8 min)
• Regression: Crash Course Statistics #32 — CrashCourse — a lively build of a hypothetical model that relates likes and comments on a trending video, framed as one member of a bigger family of models. Parts that go beyond a single straight line can be skimmed; use it while completing the Week-15 module overview. (video, 13 min) (captions: creator)

② How well does the line fit? r squared and residual plots

Chapter 15, Section “Read a residual plot: band, curve, or fan” · Session 1, Segment 2, “Residuals, r squared, and residual plots” · Remember: r squared is a share of variation, not a share of points, and a residual plot should look like a shapeless band.

• R-squared, Clearly Explained!!! — StatQuest with Josh Starmer — what r-squared measures and why it is a share of the variation in y, not a share of the points on the line. (video, 11 min) (captions: creator)
• Regression Analysis: How Do I Interpret R-squared and Assess the Goodness-of-Fit? — Minitab Blog — read what r-squared is, its key limitations, and the section on why a high r-squared is not always good; the point matches the chapter's warning that r-squared never replaces a look at the residual plot. Skip the product demo. (reading, 8–12 min)
• Simple Linear Regression: Checking Assumptions with Residual Plots — jbstatistics — a careful tour of the linearity, constant-spread, and normality checks, each read from a residual plot on a small real dataset. (video, 8 min) (captions: creator)
• Regression Analysis — Seeing Theory — an interactive page: drag points in the Ordinary Least Squares panel and watch the line and its squared misses change, then try the Correlation panel. Skip the Analysis of Variance panel, which this course does not cover. (reading, 6–10 min)

③ Is the slope real, and where does the line stop?

Chapter 15, Section “Test the slope: from the sample line to the population line” · Session 2, Segment 3, “Inference for the slope and its limits” · Remember: test whether the population slope could be 0 with t = b₁ ⁄ SE(b₁) on n − 2 degrees of freedom, and predict only inside the observed range of x.

• Inference on the Slope (An Example) — jbstatistics — one worked example that builds a confidence interval for the slope and runs the t test of a zero slope, the same two steps as the penguin example. (video, 7 min) (captions: creator)
• The Effects of Outliers and Extrapolation on Regression (2.4) — Simple Learning Pro — a short look at how one unusual point can pull a regression line, and why a prediction beyond the observed x values deserves no trust. (video, 6 min) (captions: automatic)

Optional one-stop reference (free online reference)

• 4.4.4. How can I tell if a model fits my data? — NIST/SEMATECH e-Handbook of Statistical Methods — a free government reference. Read the opening argument that r-squared is not enough and that residual plots are the main check; skip the numerical methods that follow. (reading, 5–8 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

Provenance: Built with The Course Maker · samples.thecoursemaker.com