AP Statistics Unit 5: Regression Analysis Notes

Introduction

Regression describes paired quantitative data through scatterplots, correlation, prediction, residuals, and the least-squares line; the revised course does not include inference for slope.

Preserve each ordered pair and name explanatory and response variables before calculating. Direction, form, strength, and unusual features determine whether a linear summary is useful.

A fitted line predicts rather than explains cause. Residuals expose what the line misses, while correlation and $r^2$ summarize only the linear relationship visible in the data.

Paired measurements

scatterplot

Linear form

correlation and prediction

Observed minus predicted

residual diagnosis

Squared residuals

least-squares fit

Current exam guidance: Aligned to the effective Fall 2026 AP Statistics framework, including its current calculator and inference expectations.

5.1

Graphical Representations Between Two Quantitative Variables

How should paired quantitative measurements be displayed and described?

Short answer

Plot one point per observational unit, place the explanatory variable on x, and describe direction, form, strength, and unusual features in context.

Know firstQuantitative variables · Ordered pairs · Distribution description

Keep each pair intact

A scatterplot preserves which x and y measurements belong to the same machine run. For the eight authored pairs, output generally rises with setting, so the direction is positive and the main form is roughly linear. Strength concerns how closely points follow that form; it is not the steepness of the pattern.

The point at $x=11$ is far from the other x-values and has high leverage: it can strongly affect a fitted line even if its vertical residual is modest. A vertically unusual point is an outlier in y for its x. These roles are different. Axes need variable names and units, and connecting dots is inappropriate unless sequence or time matters. Association—however strong—does not establish causation.

Paired observations: 8
Main direction: positive

Machine setting and outputDisplay paired data and distinguish a high-leverage x position from vertical departure. $(x_i,y_i)\text{ stays paired for each unit}$

Seven points from x equals one through seven form a broadly positive, roughly linear pattern. The eighth point at x equals eleven lies far to the right and is high leverage.

x	y	Note
		main pattern
		main pattern
		main pattern
		main pattern
		main pattern
		main pattern
		main pattern
		high leverage

Read a scatterplot in order

Name the observational unit and paired variables.
Assign explanatory x and response y.
Describe direction and form.
Judge strength relative to that form.
Identify unusual points by leverage or vertical departure.
Limit conclusions to association unless design supports more.

Keep these three ideas

Preserve pairing.
Describe direction, form, strength, and unusual features.
Association is not causation.

Keep reading Unit 5: Regression Analysis

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5.1 Graphical Representations Between Two Quantitative VariablesRead

5.2 Correlation

5.3 Linear Regression Models

5.4 Residuals

5.5 Least-Squares Regression

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