LECTURE HUB
Lecture 12 - Fitting a line
🚦 Status🟣 Formatted
🧠 Mastery🐥 Apprentice
📅 Last Review6 Dec 2025
🎯KEY TAKEAWAYS
- The 📐 Least-squares line is the one line that makes the squared misses as small as possible. That is all best fit means.
- The slope is the average change in y for one more unit of x, across these cases. It is not what happens if you turn the dial.
- Look at the residuals. A line through a curve has a slope and an r² and is still wrong.
- Never read the line outside the range of the data that made it.
⚡QUICK JOTS
- quiz first, ten minutes on regression to the mean. felt fine
- forty batches, oven temperature against breakage
- line: −9.0 + 0.08 × temp
- least squares = smallest total of SQUARED misses. squaring punishes the big ones
- one wild batch out → slope drops by a third. so look at the dots before the line
- intercept −9 % at zero degrees. nonsense. do not read the line where there is no data
- slope ≠ what happens if I turn the dial. hot batches might be the rushed ones
- residuals: plot them. a curve hides in there
- assignment 3: one x, one y, one chart
☑️HOMEWORK
- Write 📐 Least-squares line: slope, intercept, and what the slope does not mean
- Choose a dataset for 📌 Statistics II - Assignment 3 - A regression you can explain
- Start 📌 Statistics II - Reading response - What a p-value is not
- Check the residual chart before believing any line again