Problem 5 What is meant when the relations... [FREE SOLUTION]

Chapter 10: Problem 5

What is meant when the relationship between the two variables is called positive? Negative?

Short Answer

Expert verified

A positive relationship means both variables increase together, while a negative relationship means one increases as the other decreases.

Step by step solution

Define Positive Relationship

In a positive relationship between two variables, as one variable increases, the other variable also increases. For instance, if we have variables \(x\) and \(y\), and \(x\) increases, \(y\) will also increase. The same is true in reverse; as \(x\) decreases, \(y\) will also decrease. A typical example of a positive relationship is the correlation between hours studied and exam scores, where more studying typically leads to higher scores.

Define Negative Relationship

In a negative relationship between two variables, as one variable increases, the other variable decreases. In other words, if variable \(x\) increases, variable \(y\) will decrease, and vice versa. An example of a negative relationship can be the amount of exercise and body weight, where more exercise may lead to a decrease in body weight.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Positive Relationships

In the realm of statistics, a positive relationship between two variables signifies a direct association where both variables move in the same direction. This means that when one variable increases, the other tends to increase as well, and conversely, when one decreases, the other also tends to decrease. This pattern can be intuitively understood by considering real-world examples.

Think about the relationship between daily hours spent studying and academic performance. Typically, as one dedicates more hours to studying, exam scores improve, illustrating a positive relationship.
Similarly, consider the relationship between temperature and ice cream sales. As the temperature rises, so do ice cream sales, showing a direct, positive link.

This type of relationship can be depicted as an upward-sloping line on a graph, visually confirming that the two variables move in tandem. Recognizing a positive relationship allows predictions to be made about one variable based on knowledge of the other.

Exploring Negative Relationships

A negative relationship describes an inverse association where one variable's increase corresponds with the other's decrease. This type of relationship is equally common and vital in understanding how different variables interact.

An everyday example involves exercise and body weight. Increasing exercise levels often result in decreased body weight, indicating a negative relationship.
Another example is the correlation between the amount of gas in a car and the distance it can travel. As more gas is used, the remaining distance the car can travel decreases.

Graphically, this relationship is typically represented by a downward-sloping line, signaling that as one factor rises, the other falls. Grasping this concept aids in predicting how changes in one variable might inversely affect another.

Decoding Correlation

Correlation is a statistical measurement that describes the strength and direction of a relationship between two variables. It is a key concept for understanding how variables are interlinked.

Correlation helps ascertain if an increase or decrease in one variable will coincide with a similar change in another variable, either positively or negatively.
The range of the correlation coefficient is from -1 to 1. A coefficient close to 1 indicates a strong positive relationship, while a coefficient close to -1 signifies a strong negative relationship.
A correlation near 0 suggests little to no linear relationship between variables.

Importantly, correlation does not imply causation, which means that while two variables may have a correlated relationship, it doesn't automatically indicate that one causes the other to change. Understanding correlation is crucial in the analysis of data and in making informed decisions based on statistical evidence.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

What is meant when the relationship between the two variables is called positive? Negative?

Short Answer

Step by step solution

Define Positive Relationship

Define Negative Relationship

Key Concepts

Understanding Positive Relationships

Exploring Negative Relationships

Decoding Correlation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.