Name: Advanced Linear Regression
Uploaded: 2019-10-15T00:00:00.000Z
Description: In part two of a three-part series, we meet Least-Squares Regression Lines. We learn how to use them to make predictions, how to interpret the slope/intercept of the equation, and the meaning and dangers of "extrapolation." Then, we define "residuals" and discuss how to calculate and interpret them in context.

AP Statistics

Unit 1 – Exploring One–Variable Data

Unit 2 – Exploring Two–Variable Data

Unit 3 – Collecting Data

Unit 4 – Probability, Random Variables, and Probability Distributions

Unit 5 – Sampling Distributions

Unit 6 – Proportions

Unit 7 – Means

Unit 8 – Chi–Squares

Unit 9 – Slopes

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Previous Exam Prep

AP Cram Sessions 2021

Live Cram Sessions 2020

January

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Study Tools

Exam Skills

In part two of a three-part series, we meet Least-Squares Regression Lines. We learn how to use them to make predictions, how to interpret the slope/intercept of the equation, and the meaning and dangers of "extrapolation." Then, we define "residuals" and discuss how to calculate and interpret them in context.

What is Statistics?

What's the Point of Statistics?

Context of Data

Describing Data

Unit 1 Overview: Exploring One-Variable Data

Statistics & Data, Data, Data

Going Deeper into Data and the "W"s

Introducing Statistics: What Can We Learn from Data?

Intro to Z-Scores

Normal Model: More than Just a Hump

The Empirical (68–95–99.7) Rule

Practice Problems

The Normal Distribution

Types of Variables

Going Deeper: Categorical vs. Quantitative Variables

Example Question

The Language of Variation: Variables

Frequency Tables

Extension: Relative Frequency Tables

Representing a Categorical Variable with Tables

Bar Graphs

Pie Charts

Contingency Table (Two-Way Table)

Real-Life Applications: To Trust or Not To Trust a Bar/Pie Chart?

Representing a Categorical Variable with Graphs

Representing a Quantitative Variable with Graphs

Describing the Distribution of a Quantitative Variable

Statistics of Center

Statistics of Spread

A Note About Outliers

Summary Statistics for a Quantitative Variable

Five Number Summaries

Box Plots

Practice Questions

Graphical Representations of Summary Statistics

Comparing Groups with Stem-and-Leaf Plots: Warm Up

Comparing Groups with Histograms: Practice AP-Style Problem

Comparing Groups with Box Plots: Practice AP-Style Problem

Comparing Distributions of a Quantitative Variable

Unit 1 – Exploring One-Variable Data

Exam Weighting

Bivariate Data 🧠

Computer Outputs 🖥️

Mathematical Practices 🧮

Main Ideas for this Unit

Unit 2 Overview: Exploring Two-Variable Data

Types of Data 

How Can I Use This Data?

Introducing Statistics: Are Variables Related?

Various Tables and Diagrams

Determining Associations from Graphical Representations

Representing Two Categorical Variables

Additional Relative Frequencies

Determining Associations from a Two-Way Table

Vocabulary Practice from 2.1 to 2.3 Material

Statistics for Two Categorical Variables

What is a Scatterplot? ❓

Describing Scatterplots 🗒️

Example

Representing the Relationship Between Two Quantitative Variables

Calculating the Correlation Coefficient

Correlation

What is a LSRL?

Extrapolation

Practice Problem

Linear Regression Models

Residual Plots

Good or Bad? 🧐

Calculating Residuals

Residuals

LSRL—Slope

LSRL—y-intercept

LSRL—Coefficient of Determination

LSRL—Standard Deviation of the Residuals

Reading a Computer Printout

Least Squares Regression

Influential Points

Transforming Data and Nonlinear Regression

Analyzing Departures from Linearity

Unit 2 – Exploring Two-Variable Data

How Do We Approach Data Collection?

Unit 3 Overview: Collecting Data

📊 Data: Truth-Revealing or Deceiving?

Introducing Statistics: Do the Data We Collected Tell the Truth?

Introduction to Planning a Study

Types of Non-Biased Sampling Methods 

Random Sampling and Data Collection

Bias in Sampling 

Why does this matter, then? 

Potential Problems with Sampling

🗃 Components of an Experiment

🖋 Elements of a Well-Designed Experiment

🗄 Types of Experiments

Introduction to Experimental Design

Essential Knowledge

Selecting an Experimental Design

Inferences for Studies/Samples

Inferences for Experiments

Inference and Experiments

Probability: What are the Odds?

Probability Rules

Probability Distributions

Unit 4 Overview:  Probability, Random Variables, and Probability Distributions

🌐 Daily Experiences 

📊 Statistical Significance

🤔 Examples, Examples, Examples: Random vs. Non-Random Patterns

Introducing Statistics: Random and Non-Random Patterns?

Binomial Basics

Introduction to the Binomial Distribution

Parameters for a Binomial Distribution

Binomial vs. Geometric: Spot the Difference!

Calculating Probabilities

Shape, Center, and Variability

The Geometric Distribution

Simulation Time!

Estimating Probabilities Using Simulation

📝 Basic Probability Rules 

Probabilities and Context

Introduction to Probability

Intersections and Mutually Exclusive Events

Practice Problem #1

Practice Problem #2

Mutually Exclusive Events

Representations of Probability 

Conditional Probability

Independent Events and Unions of Events

❓ Types of Random Variables

🫂 Probability Distributions = Best Friend!

🧠 Example

Introduction to Random Variables and Probability Distributions

Mean and Standard Deviation of Random Variables

Linear Transformations of a Random Variable

Combining Random Variables

Unit 4 – Probability, Random Variables, & Probability Distributions

What is a Sampling Distribution?

Sampling Distribution for Proportions

Sampling Distribution for Means

Sampling Distributions for the Differences in Means and Proportions

Unit 5 Overview: Sampling Distributions

Sampling Distributions... Defined

Parameters vs. Statistics

Introducing Statistics: Why Is My Sample Not Like Yours?

Empirical Rule Review

The Normal Distribution, Revisited

Definition

The Central Limit Theorem

How to Tell if a Sample is Unbiased

Bias and Variability

Biased and Unbiased Point Estimates

Formulas

Large Counts Condition

Sampling Distributions for Sample Proportions

Differences (Non-Distribution) Recap

Proportion Differences

Sampling Distributions for Differences in Sample Proportions

Normal Condition: Central Limit Theorem

Sampling Distributions for Sample Means 

Sampling Distributions for Differences in Sample Means

Inference Who?

Confidence Intervals

Significance Tests

Inference with Two Proportions

Unit 6 Overview: Inference for Categorical Data: Proportions

What does it mean to be normal?

Why is it important?

How do we know if it is normal?

Introducing Statistics: Why Be Normal?

Hypotheses and Parameters

Conditions

Setting Up a Test for the Difference of Two Population Proportions

Calculating Values

Concluding the Test

Continued Example

Carrying Out a Test for the Difference of Two Population Proportions

Checking Conditions

One Sample z-interval for Proportions

Calculating the Interval

Constructing a Confidence Interval for a Population Proportion

Concluding a Confidence Interval

The Big Three

Testing a Claim Using Intervals

Sample Size, Confidence Interval Width, Confidence Level, and Margin of Error

Justifying a Claim Based on a Confidence Interval for a Population Proportion

Advanced Linear Regression

Advanced Linear Regression

AP Statistics 📊

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