Question

OPEN-ENDED Give two real-life quantities that have (a) a positive correlation, (b) a negative correlation, and (c) approximately no correlation. Explain.

Short answer

(a) Positive Correlation: The size of a house and its price - usually, larger houses tend to cost more. (b) Negative Correlation: The remaining amount of a product in a store and its demand - as the product becomes rarer, its demand increases. (c) No Correlation: The color of a car and its speed - changing a car's color doesn't impact its speed.

Step-by-step solution

Identifying the Positive Correlation

Think of a situation in life where an increase in one quantity results in the rise of the other. One classical example is the relationship between house size and price. Generally speaking, as the size of a house (measured in square feet) increases, its price also increases. This is considered a positive correlation because both quantities move in the same direction.

Identifying the Negative Correlation

Now consider a real-life example where when one quantity increases, the other decreases. A common example is the relationship between the remaining amount of a product in a store and its demand. As the product's quantity decreases (because of increased sales), its demand increases because it becomes rarer. This is a negative correlation.

Identifying No Correlation

Lastly, ponder an instance where a change in one quantity doesn't affect the other. For instance, the relationship between the color of a car and its speed. Changing the color of a car doesn't affect its speed. Thus, there is no correlation.

Key concepts

Positive Correlation

In our daily lives, we often encounter relationships where two quantities increase together. This phenomenon is known as a **positive correlation**. A good example of this is the relationship between house size and price. As the size of a house increases, its price typically rises as well. This relationship makes sense because larger houses often offer more features, which adds to their value.

• Both variables move in the same direction
• Examples include more hours studied leading to better exam scores, or higher temperature leading to increased ice cream sales.

Recognizing positive correlations helps in making predictions. For instance, if a larger house implies higher price, a property developer can predict the market value based on the size.

Negative Correlation

A **negative correlation** occurs when one quantity goes up while the other goes down. This concept is evident when considering the relationship between the amount of a product available in a store and its demand. As the amount of product decreases, often due to sales, its demand tends to increase because fewer units are available, possibly creating urgency among customers.

• The variables move in opposite directions
• Examples include the relationship between the speed of a car and the time taken to travel a set distance, where faster speeds result in less time required.

Understanding negative correlations can be useful in inventory management and sales strategies, helping businesses anticipate product shortage scenarios.

No Correlation

Sometimes, two quantities have no obvious connection to each other, resulting in **no correlation**. This situation can be seen in the relationship between the color of a car and its speed. Changing the color does not affect how fast the car moves, implying there's no direct link between these two factors.

• Changes in one variable do not affect the other
• Examples include the relationship between a person's age and the color of their favorite shirt.

Recognizing instances of no correlation is crucial for avoiding erroneous conclusions, ensuring that we don't assume a link where none exists.