12. Regression#
This chapter introduces prediction with relationships between numeric variables. You will study correlation, regression lines, least squares, and residual diagnostics.
Chapter Video
Video credit: CrashCourse. (2018, October 3). Regression: Crash Course Statistics #32. YouTube. Watch on YouTube.
This embedded video is provided for educational reference only. All rights are retained by the respective copyright holder.
Learning Objectives
By the end of this chapter, you will be able to:
Describe linear association with scatter plots and correlation.
Use a regression line to make numeric predictions.
Explain least squares as a method for choosing a fitted line.
Use residual plots to diagnose patterns that a line misses.
Communicate prediction limits and uncertainty in applied settings.
Chapter Flow
Glossary
# |
Term |
Explanation |
|---|---|---|
1 |
Regression |
A method for modeling or predicting an outcome from one or more features. |
2 |
Prediction |
An estimate of an outcome for a new or existing case. |
3 |
Feature |
An input variable used to predict an outcome. |
4 |
Target |
The outcome variable being predicted. |
5 |
Scatter plot |
A plot showing paired numeric values. |
6 |
Association |
A relationship or pattern between variables. |
7 |
Correlation |
A standardized measure of linear association. |
8 |
Regression line |
A straight line used to predict an outcome from a feature. |
9 |
Slope |
The predicted change in the outcome for a one-unit change in the feature. |
10 |
Intercept |
The predicted outcome when the feature is zero. |
11 |
Fitted value |
The model prediction for an observed case. |
12 |
Residual |
The observed value minus the fitted value. |
13 |
Least squares |
A method that chooses the line with the smallest sum of squared residuals. |
14 |
Residual plot |
A plot of residuals used to check model patterns. |
15 |
Standard units |
Values expressed in standard deviations from the mean. |
16 |
Root mean squared error |
A typical prediction error measured in outcome units. |
17 |
Linearity |
The assumption that a straight line captures the main trend. |
18 |
Extrapolation |
Prediction outside the range of observed data. |
19 |
Influential point |
An observation that strongly affects a fitted model. |
20 |
Diagnostics |
Checks used to evaluate how well a model fits. |
21 |
Overfitting |
Fitting noise instead of a durable pattern. |