Week 15 — Readings & Resources · Linear Regression & Inference

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 8 — Fit and interpret a simple linear regression model, including inference for the slope.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: 4 short readings + 4 short videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 50–60 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① the least-squares line — slope & intercept → ② prediction & residuals (residual plots) → ③ r² (the share of variation explained) → ④ inference for the slope (is it significantly different from 0?).

A habit to start now: every resource below hands you a finished regression line or output. Your job all term is to read and interpret it — what does the slope mean in context? how much does r² explain? is the slope real? — not to re-derive the math. Keep the Week-4 question in your back pocket: a line still isn't a cause.

① The Least-Squares Line · Slope & Intercept

Maps to Lecture Segment 2. The line is ŷ = b₀ + b₁x: the slope is the per-one-unit-of-x change in ŷ (with units!), the intercept is ŷ when x = 0. The hat on ŷ means predicted, not observed.

Reading — "Simple Linear Regression | An Easy Introduction & Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/simple-linear-regression/
Why it's assigned: the cleanest plain-language version of the exact model we drew on the board — one straight line summarizing two quantitative variables, with a worked example and the regression output read piece by piece (slope, intercept, prediction). Read the "interpret" sections closely.
⏱ ~9 min

Video — "Interpreting slope of regression line" (Khan Academy)
🔗 https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/least-squares-regression/v/interpreting-slope-of-regression-line
Why it earns the click: a short, worked demonstration of stating a slope in context with units — exactly the deliverable from Segment 2 (not "the slope is 4," but "4 points per extra hour"). The companion intercept video sits right beside it in the same unit.
⏱ ~4 min

② Prediction & Residuals · Reading a Residual Plot

Maps to Lecture Segments 3 & 6. residual = observed − predicted (positive = above the line, negative = below). A good residual plot is a boring, patternless cloud around 0; a shape in it means a line was the wrong model.

Reading — "Introduction to residuals" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitative-data/regression-library/a/introduction-to-residuals
Why it's assigned: defines the residual as the vertical gap between an observed point and the line, with the sign convention (observed − predicted) we drilled in class — the foundation for both prediction error and the residual plot.
⏱ ~5 min

Video — "Residual plots" (Khan Academy)
🔗 https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/xfb5d8e68:residuals/v/residual-plots
Why it earns the click: shows the difference that decides whether a line is even appropriate — a random residual plot (line is fine) versus a patterned one like a U-shape (you fit a line to a curve). This is the Segment-6 "stethoscope for the fit" in action.
⏱ ~5 min

③ r² · The Share of Variation Explained

Maps to Lecture Segment 4. r² = the correlation squared, between 0 and 1 — the percent of the variation in y the line explains. Remember: r² is NOT the slope (slope = how much, with units; r² = how well, unitless).

Reading — "Coefficient of Determination (R²) | Calculation & Interpretation" (Scribbr)
🔗 https://www.scribbr.com/statistics/coefficient-of-determination/
Why it's assigned: the clearest plain-language take on r² as the proportion of variance explained by the model (and the leftover 1 − r² that isn't), with pictures of a high-r² tight fit vs. a low-r² loose one. It even notes the spreadsheet =RSQ() we use in Segment 8.
⏱ ~7 min

Video — "Linear Regression, Clearly Explained!!!" (StatQuest with Josh Starmer)
🔗 https://www.youtube.com/watch?v=nk2CQITm_eo
Why it earns the click: the single friendliest tour of fitting a line with least squares and what R² actually measures — watch roughly the first 12 minutes (fitting a line, then R²) for everything this week needs; the later sections go beyond our scope and are optional.
⏱ ~12 min (of a longer video)

④ Inference for the Slope · Is It Really There?

Maps to Lecture Segment 5. H₀: slope = 0 (flat line, no relationship). The output gives a t and a p-value; compare p to α: p < α → reject → the slope is significant (real); p ≥ α → fail to reject → it could be noise.

Reading — "Inference for quantitative data: slopes" (Khan Academy unit)
🔗 https://www.khanacademy.org/math/ap-statistics/inference-slope-linear-regression
Why it's assigned: the unit that frames the exact question from Segment 5 — does the linear relationship we see in a sample hold in the population, or could the true slope be 0? Skim the intro sections; it builds straight on the hypothesis-testing machinery from Weeks 13–14.
⏱ ~6 min for the intro sections

Video — "Introduction to inference about slope in linear regression" (Khan Academy)
🔗 https://www.khanacademy.org/math/ap-statistics/inference-slope-linear-regression/inference-slope/v/intro-inference-slope
Why it earns the click: sets up the slope's t-test in plain terms — a sample slope, a null of "slope = 0," and a p-value you compare to α — exactly the decision rule we used to call study-hours "significant" and height "not significant."
⏱ ~6 min

Optional: the whole idea in one lively video

Video — "Regression: Crash Course Statistics #32"
🔗 https://www.youtube.com/watch?v=WWqE7YHR4Jc
Why it's here: a high-energy overview that ties the week together — fitting a line, predicting, and reading what the model says — in one entertaining pass. Entirely optional; great if you like the big picture before the details.
⏱ ~12 min

Optional one-stop reference (free online text)

If you'd like one optional reference to skim, OpenIntro Statistics keeps its full text and per-section videos free to read online. Chapter 8 ("Introduction to Linear Regression") covers everything in this week — the least-squares line, residuals, r², and inference for the slope — formalized in one place.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to while you study for the final — entirely optional this week.

Pick-one quick path (≈18 min total)

In a hurry? Do exactly these four and you'll be ready for the quiz:
1. Read the "interpret" sections of Simple Linear Regression (group ①).
2. Watch Residual plots (group ②).
3. Read Coefficient of Determination (R²) (group ③).
4. Watch Introduction to inference about slope (group ④).

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