What is Negative Linear Correlation?

S3-SA3-0314

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

Negative linear correlation describes a relationship between two quantities where if one quantity increases, the other quantity tends to decrease. When plotted on a graph, the points generally form a straight line sloping downwards from left to right.

Simple Example

Quick Example

Imagine you have a certain amount of mobile data for the month. As you watch more videos (increase data usage), the amount of data remaining tends to decrease. This is a negative correlation: more videos watched means less data left.

Worked Example

Step-by-Step

Let's look at the relationship between the price of petrol and the number of people using public transport.

Step 1: Collect data for petrol price and public transport users over a few months.
---Monthly Data---
Month 1: Petrol Price = Rs 100, Public Transport Users = 5000
Month 2: Petrol Price = Rs 105, Public Transport Users = 4800
Month 3: Petrol Price = Rs 110, Public Transport Users = 4500
Month 4: Petrol Price = Rs 115, Public Transport Users = 4200

Step 2: Observe the trend. As the petrol price increases from Rs 100 to Rs 115, the number of public transport users decreases from 5000 to 4200.

Step 3: If you were to plot these points on a graph (petrol price on x-axis, users on y-axis), you would see the points generally going downwards.

Answer: This shows a negative linear correlation because as the petrol price goes up, the number of public transport users tends to go down.

Why It Matters

Understanding negative correlation helps scientists, economists, and data analysts predict trends. For example, economists use it to understand how price changes affect demand, and data scientists use it in AI to find relationships in data, helping to build smarter apps.

Common Mistakes

MISTAKE: Thinking that 'negative' means a bad relationship. | CORRECTION: In correlation, 'negative' simply means one quantity goes down as the other goes up, not that the relationship itself is bad or undesirable.

MISTAKE: Confusing negative correlation with no correlation. | CORRECTION: Negative correlation shows a clear downward trend. No correlation means the points are scattered randomly with no clear pattern.

MISTAKE: Assuming negative correlation always means one thing CAUSES the other. | CORRECTION: Correlation shows a relationship, but it doesn't always mean one variable causes the change in the other. There might be other factors involved.

Practice Questions

Try It Yourself

QUESTION: If the number of hours a student spends studying for a test increases, what kind of correlation would you expect with their test scores? | ANSWER: Positive correlation (more study, higher scores)

QUESTION: A shop owner notices that as the temperature outside increases, the sales of woollen sweaters decrease. Is this a positive or negative correlation? | ANSWER: Negative correlation

QUESTION: Imagine a street food vendor selling pakoras. If the price of pakoras increases, what would likely happen to the number of pakoras sold? Explain the correlation. | ANSWER: The number of pakoras sold would likely decrease. This is a negative correlation because as the price goes up, the demand (and thus sales) tends to go down.

MCQ

Quick Quiz

Which of these scenarios best represents a negative linear correlation?

As you eat more ladoos, your happiness increases.

As the number of hours of daylight increases, the number of hours of darkness decreases.

The amount of rainfall has no clear effect on the price of gold.

As a plant gets more sunlight, it grows taller.

The Correct Answer Is:

Option B shows that as one quantity (daylight hours) increases, the other quantity (darkness hours) decreases, which is the definition of negative correlation. The other options show positive or no correlation.

Real World Connection

In the Real World

In cricket analytics, data scientists might find a negative correlation between the number of dot balls bowled by a bowler and the runs scored by the opposing team in that over. More dot balls (no runs) means fewer runs for the opposition, helping teams plan strategies.

Key Vocabulary

Key Terms

CORRELATION: A relationship between two or more quantities | LINEAR: Forming a straight line pattern on a graph | QUANTITY: An amount or number that can be measured | TREND: A general direction in which something is developing or changing | VARIABLE: A quantity that can change or vary

What's Next

What to Learn Next

Next, you can learn about 'Positive Linear Correlation' to understand when two quantities move in the same direction. After that, explore 'No Correlation' to see when there's no clear relationship at all!