Lesson 32: Multiple Linear Regression II

What We Did: Lessons 28, 30, 31

Lesson 28: Simple Linear Regression I

Scatterplots describe direction, form, strength, and unusual features
Least squares regression fits \(\hat{y} = b_0 + b_1 x\) by minimizing \(\sum(y_i - \hat{y}_i)^2\)
Slope \(b_1\): predicted change in \(y\) for a 1-unit increase in \(x\)
Intercept \(b_0\): predicted \(y\) when \(x = 0\) (may not be meaningful)
Residuals: \(e_i = y_i - \hat{y}_i\)
Extrapolation is dangerous – don’t predict outside the data range

Lesson 30: Simple Linear Regression II

Read the regression output: equation, p-values, and \(R^2\)
Test the slope with \(t = b_1 / SE(b_1)\)
\(R^2\) measures the fraction of variability in \(y\) explained by the model
Multiple regression: interpret each slope holding other variables constant
Categorical predictors use indicator (dummy) variables with a reference level

Lesson 31: Multiple Linear Regression I

An insignificant categorical level means that group isn’t different from the baseline
LINE assumptions: Linearity, Independence, Normality, Equal variance
Check assumptions with residuals vs. fitted, QQ plot, and scale-location plots
If assumptions fail: consider transformations, specialized models, or robust methods

Today is a project work day. No new material. You have every tool you need – go build.

No new reading. Come with your project open and questions ready.

Math vs EECS

Previously 0-0

1-0

You should now be in the modeling and analysis phase of your course project. By the end of today, you should have:

Project Links

Resource	Link
Project Instructions	Course Project Instructions
Project Groups / Pairs	Project Pairs
Presentation Template	MA206X West Point Template (.pptx)
Army Vantage	Vantage Workspace

The rest of the class, I’ll work through some ideas and show how some of the code works. Follow along in your own Vantage workspace.

Any questions?