Project 5: Simple Linear Regression

Build a linear regression analysis and interpret coefficients.

Project Overview

Attribute Value
Difficulty Level 2: Intermediate
Time Estimate Weekend
Main Language R
Alternative Languages Python, Julia
Knowledge Area Regression
Tools ggplot2
Main Book “OpenIntro Statistics” by Diez et al.

What you’ll build: A regression model with diagnostic plots and clear interpretation.

Why it teaches stats: Regression is the most common statistical modeling tool.

Core challenges you’ll face:

  • Fitting the model correctly
  • Interpreting slope and intercept
  • Checking model assumptions

Real World Outcome

You will fit a line, report coefficients, and produce diagnostic plots.

Example Output:

Slope: -5.3
Intercept: 37.2
R-squared: 0.75

Verification steps:

  • Compare predicted vs observed values
  • Inspect residuals for patterns

The Core Question You’re Answering

“How does one variable predict another, and how strong is that relationship?”

This is the core of statistical modeling.

Concepts You Must Understand First

Stop and research these before coding:

  1. Least squares fit
    • Why do we minimize squared residuals?
    • Book Reference: “OpenIntro Statistics”, Ch. 7
  2. Interpretation of coefficients
    • What does the slope mean in context?
    • Book Reference: “OpenIntro Statistics”, Ch. 7
  3. Residual analysis
    • What patterns indicate model issues?
    • Book Reference: “OpenIntro Statistics”, Ch. 7

Questions to Guide Your Design

  1. Model choice
    • Which variable will be the predictor, and why?
    • How will you justify linearity?
  2. Diagnostics
    • Will you include residual plots and QQ plots?
    • How will you report outliers?

Thinking Exercise

Slope Meaning

If slope = -5, what does that mean for a 1-unit increase in x?

Questions while working:

  • Is the relationship plausible in context?
  • What if slope is near zero?

The Interview Questions They’ll Ask

Prepare to answer these:

  1. “What does the slope represent?”
  2. “What is R-squared?”
  3. “How do you check regression assumptions?”
  4. “What do residuals tell you?”
  5. “When is linear regression inappropriate?”

Hints in Layers

Hint 1: Starting Point Plot the data with a fitted line.

Hint 2: Next Level Compute and interpret coefficients.

Hint 3: Technical Details Inspect residuals for patterns and heteroscedasticity.

Hint 4: Tools/Debugging Try a transformation if residuals show curvature.

Books That Will Help

Topic Book Chapter
Least squares “OpenIntro Statistics” Ch. 7
Coefficient interpretation “OpenIntro Statistics” Ch. 7
Residuals “OpenIntro Statistics” Ch. 7

Implementation Hints

  • Use summary() to inspect model output.
  • Plot residuals vs fitted values.
  • Explain results in plain language.

Learning Milestones

  1. First milestone: You can fit a linear model in R.
  2. Second milestone: You can interpret coefficients and R-squared.
  3. Final milestone: You can diagnose model issues.