Week 15 — Linear Regression & Inference for the Slope

Welcome to your Week 15 Start Here page.

Why this matters

A hospital dietitian estimating a healthy weight range from height and a small-business owner forecasting sales from advertising both use a line, and both need to know how far to trust it.

In plain language

This week you learn to draw the one straight line that best fits a cloud of points and to use it to predict (make an informed guess about) one measurement from another. You will read what the line's tilt and starting point mean in real units, measure how far the line usually misses, and say how much of the story the line tells. Then you will ask whether the tilt is real or a fluke of one sample, using the same test-and-interval thinking you built in Weeks 11 to 14. You will also learn where a line stops being trustworthy, and why one odd point can drag it around. It is the last new idea of the course, and it pulls almost every earlier idea together.

• Already covered: Weeks 1 to 14 built description, correlation, probability, intervals, and tests.
• This week: the least-squares line, residuals, r squared, and the test and interval for the slope.
• How they connect: the line turns Week 4's pattern into predictions, and Week 14's t test checks its slope.
• Where we're going next: finals week, with no new lessons.

Focus

Can you predict one variable from another with a line, and how far should you trust it?

By the end of this module, you should be able to:

• [ ] interpret a slope and an intercept in context
• [ ] predict, and tell interpolation from extrapolation
• [ ] compute a residual and read r squared
• [ ] test a slope and interpret its interval

To-do

Plan your week

1. Read Chapter 15 (about 55 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Data Lab (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: predict a penguin's body mass from a 200 mm flipper and say whether the prediction is interpolation.

You've got this

Say every slope as a sentence with its units, and ask your instructor early if a step snags.

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