The Linear Correlation Coefficient: Key Takeaways | Saylor Academy

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Read this discussion on linear correlation. You will learn what the linear correlation coefficient is, how to compute it, and what it tells us about the relationship between two variables x and y.

Key Takeaways

The linear correlation coefficient measures the strength and direction of the linear relationship between two variables $x$ and $y$ .
The sign of the linear correlation coefficient indicates the direction of the linear relationship between $x$ and $y$ .
When $r$ is near 1 or −1 the linear relationship is strong; when it is near 0 the linear relationship is weak.

COURSE INTRODUCTION

Course Syllabus

Unit 1: Statistics and Data

1.1.1: What is Statistics?

What are Statistics?

1.1.2: Descriptive and Inferential Statistics

Descriptive and Inferential Statistics

Basic Definitions and Concepts

1.1.3: Types of Data and Their Collection

Variables and Data Collection

Presenting Data

1.2.1: Graphical Methods for Describing Quantitative Data

Graphing

Three Popular Data Displays

1.2.2: Numerical Measures of Central Tendency and Variability

Numerical Measures of Central Tendency and Variability

Measures of Central Location

Mean, Median, Mode, and Variance

1.2.3: Methods for Describing Relative Standing

Percentiles

1.2.4: Methods for Describing Bivariate Relationships

Scatterplots and Bivariate Data

Pearson's r

Unit 1 Assessment

Unit 1 Assessment

Unit 2: Elements of Probability and Random Variables

2.1.1: Events, Sample Spaces, and Probability

Introduction to Probability

Basic Concepts of Probability

2.1.2: Counting Rules

Permutations and Combinations

The Addition Rule for Probability with a Venn Diagram Example

2.2.1: Common Discrete Random Variables

Random Variables and Probability Distributions

Binomial Distributions

Binomial, Poisson, and Multinomial Distributions

2.2.2: Normal Distribution

The Standard Normal Distribution

More on Normal Distributions

Introduction to the Normal Distribution

Unit 2 Assessment

Unit 2 Assessment

Unit 3: Sampling Distributions

3.1.1: Continuous Random Variables

Continuous Random Variables

3.1.2: Definition and Interpretation

Introduction to Sampling Distributions

3.1.3: Sampling Distributions Properties

Wolfram Demonstrations Project

3.2.1: The Sampling Distribution of Sample Mean

The Sampling Distribution of a Sample Mean

The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean

Sampling Distribution

3.2.2: The Sampling Distribution of Pearson's r

Sampling Distribution of r

3.2.3: The Sampling Distribution of the Sample Proportion

Sampling Distribution of p

Standard Deviation

Unit 3 Assessment

Unit 3 Assessment

Unit 4: Estimation with Confidence Intervals

4.1.1: Sample Statistics and Parameters

Basic Sample Statistics and Parameters

4.1.2: Bias and Sampling Variability

Characteristics of Estimators

4.2.1: Confidence Intervals for Mean

Confidence Intervals for the Mean

Demonstration: Confidence Intervals for a Mean

t Distribution Demonstration

Comparing Normal and Student's t-Distributions

4.2.2: Confidence Intervals for Correlation and Proportion

Confidence Intervals for Correlation and Proportion

Confidence Intervals

Unit 4 Assessment

Unit 4 Assessment

Unit 5: Hypothesis Test

5.1.1: Setting up Hypotheses

Setting Up Hypotheses

5.1.2: Interpreting Hypotheses Testing Results

The Observed Significance of a Test