Relationship Between Variables (Linear, Non-linear and Unrelated Relationship) | RESEARCH I

Summary

This tutorial covers the relationships between variables, exploring linear (both positive and negative), non-linear, and unrelated relationships. It explains how variables can move in tandem (positive), in opposite directions (negative), or show no correlation (unrelated). Key examples, such as interest rates, gas consumption, and airline stock prices, help illustrate these concepts. The non-linear relationship is defined by curves on graphs, such as quadratic or exponential growth. By understanding these relationships, users can draw accurate conclusions and analyze data patterns effectively, with a focus on real-world phenomena.

Takeaways

• 😀 Understanding the relationship between variables is crucial for drawing correct conclusions in research and science.
• 😀 A **linear relationship** between variables is represented by a straight line on a graph, where one variable’s change corresponds to a proportional change in another.
• 😀 **Positive linear relationships** occur when both variables increase or decrease together, such as more work hours leading to a higher paycheck.
• 😀 **Negative linear relationships** occur when one variable increases while the other decreases, such as crude oil prices affecting airline stock prices.
• 😀 **Non-linear relationships** are represented by curves on a graph and include quadratic and exponential relationships where changes are not proportional.
• 😀 In a **non-linear relationship**, the increase in one variable does not directly correlate with the other, like the area of a square increasing quadratically as the side length doubles.
• 😀 **Unrelated relationships** show no correlation between the variables, meaning changes in one do not affect the other, such as milk prices and pen prices.
• 😀 **Linear relationships** are the easiest to understand and model, making them common in various scientific methodologies and research.
• 😀 The key difference between **positive and negative linear relationships** is the direction of the change: positive relationships increase together, while negative ones move in opposite directions.
• 😀 A clear distinction is made between correlation (the relationship between two variables) and causation (one variable causing the other), with a focus on avoiding confusion between the two.

Q & A

What is the first step before drawing a conclusion between two variables?

The first step is to understand how one variable changes with the other, and to establish how they are related—whether the relationship is linear, quadratic, inverse, logarithmic, or something else.

What are the three types of relationships between variables mentioned in the script?

The three types of relationships between variables are linear relationships, unrelated relationships, and non-linear relationships.

What defines a linear relationship between variables?

A linear relationship is one where increasing or decreasing one variable causes a corresponding increase or decrease in another variable. It can be represented by a straight line on a scatter plot.

What is the difference between a positive and a negative linear relationship?

In a positive linear relationship, both variables move in the same direction (as one increases, the other increases). In a negative linear relationship, the variables move in opposite directions (as one increases, the other decreases).

Can you provide an example of a positive linear relationship?

A simple example is when an employee works more hours, their paycheck increases proportionately, showing a positive relationship between hours worked and paycheck.

What is a negative linear relationship, and can you provide an example?

A negative linear relationship is when one variable increases as the other decreases. An example is the negative correlation between crude oil prices and airline stock prices, where a rise in oil prices negatively affects airlines' profitability.

What does a non-linear relationship mean?

A non-linear relationship refers to any relationship between two quantities that doesn't form a straight line on a graph. The relationship may involve curves, such as quadratic or exponential patterns.

How can non-linear relationships be identified on a graph?

Non-linear relationships can be identified by a curved line on a graph, unlike linear relationships that are represented by a straight line.

What is an example of a non-linear relationship mentioned in the script?

An example is the area of a square in relation to its side. Doubling the side of the square results in the area increasing four times, which is a quadratic relationship.

What does an unrelated relationship indicate?

An unrelated relationship indicates that there is no relationship between the changes in the two variables. The variables do not follow any pattern of change together.