No Correlation Graph: Examples & How to Identify One

Introduction

Have you ever looked at a scatter plot and wondered why the points seem completely random?

A no correlation graph shows data points without a clear linear relationship between two variables. Unlike positive or negative correlation, the points do not follow an obvious upward or downward pattern.

Understanding this pattern is important when learning statistics, especially when reading scatter plots in class. It can help you recognize whether changes in one variable are connected to changes in another.

For beginners, identifying a graph with no correlation can feel confusing at first. The points may spread across the graph without forming a neat pattern.

In this guide, you will learn what a no correlation scatter graph looks like and how to identify one. You will also see simple examples that make the concept easier to understand.

By the end, you will know how to distinguish zero correlation from positive and negative correlation with confidence.

What Is a No Correlation Graph?

A no correlation graph shows two variables with no clear linear relationship. In a scatter plot, the points appear spread out rather than following a recognizable direction.

You won’t see a consistent upward pattern from left to right. You also won’t see a consistent downward pattern. Instead, the points may appear scattered across different parts of the graph.

Example of a No Correlation Graph

Illustrative scatter plot showing points without a clear linear pattern.0369036912

The key idea is simple: one variable does not reliably predict the other. Knowing the value of one variable gives you little useful information about the other.

For example, as Variable 1 increases, Variable 2 does not consistently increase or decrease. This lack of direction suggests no correlation in statistics.

A no correlation scatter graph does not mean the variables can never relate in any way. It means the data does not show a clear linear relationship.

What Is a No Correlation Graph?

A no correlation graph shows two variables with no clear linear relationship. In a scatter plot, the points appear spread out rather than following a recognizable direction.

You won’t see a consistent upward pattern from left to right. You also won’t see a consistent downward pattern. Instead, the points may appear scattered across different parts of the graph.

Example of a No Correlation Graph

Illustrative scatter plot showing points without a clear linear pattern.0369036912

X	Y
1	7
2	3
3	8
4	4
5	6
6	2
7	7
8	4
9	8
10	3
11	6
12	5

The key idea is simple: one variable does not reliably predict the other. Knowing the value of one variable gives you little useful information about the other.

For example, as Variable 1 increases, Variable 2 does not consistently increase or decrease. This lack of direction suggests no correlation in statistics.

A no correlation scatter graph does not mean the variables can never relate in any way. It means the data does not show a clear linear relationship.

What Does a No Correlation Graph Look Like?

A no correlation graph usually looks like a cloud of points without a clear direction. The points can appear random, making it difficult to draw a straight line through them.

When you inspect the graph from left to right, the points do not steadily rise or fall. Instead, they remain spread across the graph without forming a clear linear pattern.

Visual Characteristics

A no correlation scatter plot has several easy-to-recognize features:

• Random-looking point pattern: The data points appear scattered rather than grouped around a clear line.
• No obvious slope: The points do not clearly move upward or downward.
• No linear trend: Increasing X values do not consistently produce higher or lower Y values.
• Points spread across the graph: The observations can appear at different heights across the entire X-axis.
• Approximately flat trendline: A fitted trendline may appear nearly horizontal when the correlation is close to zero.

No Correlation Scatter Plot

Original illustrative example with scattered data points and no clear linear trend.0369036912

X	Y
1	8
2	4
3	7
4	3
5	6
6	2
7	8
8	5
9	3
10	7
11	4
12	6

Example of a No Correlation Graph

Consider the scatter plot above. The X-axis represents one variable, while the Y-axis represents another variable. Each dot represents one observation from the dataset.

Notice how the data points move in different directions. Some points are high, while others are low. There is no consistent pattern as X increases.

An optional trendline would sit approximately flat through the data. It would not show a strong upward or downward slope.

This is what makes the graph a scatter plot with no correlation. The visual pattern does not provide a reliable way to predict Y from X.

What Is a No Correlation Scatter Graph?

A scatter plot, also called a scatter graph, displays the relationship between two quantitative variables. Each point represents one pair of measured values.

A no correlation scatter graph shows little or no clear linear relationship between those variables. The points do not consistently rise or fall as one variable changes.

For example, a teacher might compare students’ study hours with another quantitative measurement. If the plotted points show no consistent linear direction, the graph may indicate no linear correlation.

The important feature is the overall pattern, not the position of every individual point. A few points can move upward or downward without creating a meaningful trend.

No Correlation vs. Random Scatter

A graph that looks scattered does not automatically prove zero correlation. You should look for the overall direction and strength of the relationship.

Some datasets contain a weak correlation even when their points appear widely spread. Other datasets can show a curved relationship that a basic linear correlation does not capture well.

Expert tip: Don’t decide from one or two points. Examine the entire scatter plot and consider the correlation coefficient when available.

How Do You Know if a Graph Has No Correlation?

Students can use a simple four-step process to identify possible no correlation.

Step 1: Look for an Upward Pattern

First, examine the points from left to right. Ask whether the points generally move upward as X increases.

If the points tend to rise, the graph may show positive correlation. If no upward pattern appears, continue to the next step.

Step 2: Look for a Downward Pattern

Next, check whether the points generally move downward as X increases.

A clear downward pattern suggests negative correlation. If the points don’t consistently fall, continue your analysis.

Step 3: Look for a Clear Linear Pattern

Now examine the entire point cloud. Ask whether the points follow any noticeable straight-line direction.

If they don’t, the graph may show no linear correlation. Avoid judging the graph from how random individual points appear.

Step 4: Check the Correlation Coefficient

When available, check the correlation coefficient, represented by r. It measures the direction and strength of a linear relationship.

A value of r close to zero indicates little or no linear correlation. Values closer to +1 or −1 indicate stronger positive or negative linear relationships.

Pro Tip: Use the graph and r together. The visual pattern helps you understand the data, while r gives a numerical measure of linear correlation.

What Does No Correlation Mean in Statistics?

In statistics, no correlation means two variables do not show a clear linear association. Changes in one variable do not consistently match changes in the other variable.

For example, suppose you compare students' study time with their quiz scores. If the data points show no consistent upward or downward pattern, the variables may have little or no linear correlation.

Correlation describes the relationship between two quantitative variables. It helps show whether the variables tend to move together in a predictable linear direction.

The correlation coefficient, written as r, measures the direction and strength of this linear association. Its value ranges from −1 to +1.

• A value near +1 shows a strong positive linear association.
• A value near −1 shows a strong negative linear association.
• A value near 0 shows little or no linear association.

When correlation is close to zero, knowing one variable gives little information for making a linear prediction about the other variable.

However, correlation does not prove that one variable causes another. Even a strong correlation only shows an association between the variables. Other factors may explain the pattern, or the relationship may occur without direct causation.

Does No Correlation Mean No Relationship?

No. No linear correlation does not necessarily mean there is absolutely no relationship between two variables.

This is an important concept in AP Statistics. Pearson's correlation coefficient measures linear association, so it may miss relationships that follow a curved or nonlinear pattern.

For example, imagine that one variable increases as another variable moves toward a certain point. After reaching that point, the second variable begins to decrease. The data can form a curved pattern even though the linear correlation is close to zero.

Therefore, a correlation coefficient near zero should not be interpreted as proof that two variables are completely unrelated.

When examining data, look at the scatter plot and the correlation coefficient together. A graph can reveal a nonlinear pattern that the correlation coefficient does not describe well.

The key distinction is simple: zero correlation means no linear association, not necessarily no relationship at all.

Examples of No Correlation Graphs

Different scatter plots can look similar at first, but their patterns may have important differences. Looking at the overall direction of the points helps you identify the type of association.

Example 1 — Clearly No Correlation

A clearly no correlation graph has points spread across the graph without a consistent direction. As the x-variable increases, the y-variable does not regularly increase or decrease.

The points may look random, with some observations high and others low. No straight-line pattern stands out from the overall data.

For example, a dataset could compare two variables that do not have a meaningful linear association. The scatter plot would show a broad cloud of points rather than an upward or downward trend.

The main clue is the absence of a consistent linear pattern.

Example 2 — Weak Correlation

A weak correlation can look somewhat random, but it still has a slight overall direction. This makes it different from true no correlation.

For example, the points might generally move upward from left to right. However, they are widely scattered around that direction.

This pattern suggests a weak positive correlation rather than zero correlation. A weak negative correlation would show a similar spread while moving slightly downward.

The key difference is the overall trend. With no correlation, there is no consistent linear direction. With weak correlation, a small linear direction may still be present.

When a correlation coefficient is available, it can help describe the strength of the linear association.

Example 3 — Nonlinear Relationship

A nonlinear relationship occurs when variables are related, but their pattern does not follow a straight line.

For example, the points might form a U-shaped or curved pattern. As x increases, y could first decrease and then increase.

A Pearson correlation coefficient may be close to zero in this situation. That does not mean the variables are unrelated.

Instead, the near-zero value can occur because the curved pattern does not have a strong overall linear direction.

This is different from simply having no relationship. A nonlinear pattern can provide useful information about how the variables are connected.

For AP Statistics, remember this distinction: r measures linear association, so always inspect the overall shape of the data before concluding that no relationship exists.

No Correlation vs. Positive vs. Negative Correlation

Scatter plots can show three basic patterns when describing linear association. The main difference is the direction of the points as x increases.

Type	Pattern
Positive Correlation	Points generally rise from left to right
Negative Correlation	Points generally fall from left to right
No Correlation	No clear linear pattern

A positive correlation means larger x-values tend to be associated with larger y-values. The points generally move upward from left to right.

A negative correlation means larger x-values tend to be associated with smaller y-values. The points generally move downward from left to right.

With no correlation, the points do not show a clear linear direction. They may appear scattered across the graph without forming a consistent upward or downward pattern.

The important word is linear. A graph can have no linear correlation while still showing a curved relationship.

When comparing scatter plots, focus on the overall pattern rather than individual points. A few points can move against the general direction without changing the association.

No Correlation and the Correlation Coefficient

The correlation coefficient, represented by r, measures the direction and strength of a linear relationship between two quantitative variables.

The value of r ranges from −1 to +1. The sign shows the direction, while the size of the value shows the strength of the linear association.

Positive r

A positive value of r indicates a positive linear relationship. As one variable increases, the other variable tends to increase as well.

Values closer to +1 represent stronger positive linear relationships. For example, an r value of 0.85 indicates a stronger positive association than an r value of 0.25.

Negative r

A negative value of r indicates a negative linear relationship. As one variable increases, the other variable tends to decrease.

Values closer to −1 represent stronger negative linear relationships. For example, an r value of −0.80 indicates a stronger negative association than an r value of −0.20.

r Near 0

When r is near 0, the data shows little or no linear relationship between the variables.

The points may not follow a consistent upward or downward pattern. However, you should not use r alone to decide whether the variables have any relationship.

Important AP Statistics Note

A correlation coefficient close to zero does not rule out a nonlinear relationship.

A dataset can have a strong curved pattern while its linear correlation is near zero. This happens because r measures the strength of a linear association.

For this reason, AP Statistics questions often require you to examine both the scatter plot and the value of r. The graph can reveal patterns that the correlation coefficient does not capture.

Which Graph Shows No Correlation?

A common statistics question asks you to identify which scatter plot shows no correlation. The best approach is to examine the overall direction of the points.

AP Statistics-Style Question

Question: Which graph shows no correlation between the two quantitative variables?

Graph A: The points generally rise from left to right and cluster around an upward trend.

Graph B: The points generally fall from left to right and cluster around a downward trend.

Graph C: The points are widely scattered with no consistent upward or downward pattern.

Graph D: The points closely follow a strong upward linear pattern.

Answer: Graph C

Explanation: Graph C shows no clear linear correlation because its points do not consistently rise or fall as the x-variable increases.

Graph A shows a positive correlation because the points generally move upward. Graph B shows a negative correlation because the points generally move downward.

Graph D also shows a positive correlation, but its points follow the upward pattern more closely. This indicates a stronger positive linear association.

The key is to look at the overall pattern, not individual points. A few scattered observations do not automatically mean a graph has no correlation.

How to Identify No Correlation on a Scatter Plot

Identifying no correlation becomes easier when you follow the same checklist each time. Focus on the overall pattern rather than individual data points.

Quick Student Checklist

Look For:

• No upward trend: The points do not generally rise as x increases.
• No downward trend: The points do not generally fall as x increases.
• No obvious straight-line pattern: The points do not follow a clear linear direction.
• Random-looking distribution: The points appear spread out without a consistent linear pattern.
• Correlation coefficient close to zero: When r is available, a value near zero suggests little or no linear association.

Do Not Assume:

• Every scattered graph has exactly zero correlation.
• Zero correlation means the variables cannot have any possible relationship.
• Correlation proves that one variable causes another.

A graph can look scattered while still having a weak positive or negative correlation. Also, a curved relationship can exist even when r is close to zero.

For the most accurate interpretation, consider the shape of the scatter plot and the correlation coefficient together.

No Correlation vs. Weak Correlation

No correlation and weak correlation can be easy to confuse because both may contain widely scattered points. The key difference is whether the points show a consistent overall direction.

Pattern	What the Scatter Plot Shows
No Correlation	No meaningful linear pattern
Weak Positive Correlation	A slight upward tendency
Weak Negative Correlation	A slight downward tendency

No Correlation

With no correlation, the points do not show a meaningful linear direction. As x increases, the y-values can move both upward and downward without a consistent pattern.

The correlation coefficient is typically close to zero when there is little linear association.

Weak Positive Correlation

A weak positive correlation has a slight upward tendency. The points may be widely scattered, but the overall pattern moves upward from left to right.

The correlation coefficient is positive but relatively close to zero.

Weak Negative Correlation

A weak negative correlation has a slight downward tendency. The points can still appear scattered, but the overall direction moves downward as x increases.

The correlation coefficient is negative but relatively close to zero.

Visual Comparison

Think of the three patterns from left to right:

No Correlation:
• • • •
• • •
• • •

Weak Positive Correlation:
• •
• • •
• • •

Weak Negative Correlation:
• •
• •
• • •

These simple patterns are only visual guides. In a real scatter plot, the points will not form perfectly neat arrangements.

The main question is: Do the points have a slight overall direction? If yes, the relationship may be weakly positive or negative. If not, the graph may show no linear correlation.

Can a Graph Have No Correlation but Still Have a Relationship?

Yes. A graph can have little or no linear correlation while still showing a clear relationship between two variables.

This usually happens when the relationship is nonlinear. Instead of following a straight-line pattern, the data follows a curve.

For example, imagine a scatter plot where y decreases as x increases at first. After reaching a low point, y begins increasing as x continues to increase. The points form a U-shaped pattern.

This is a real relationship because changes in x are connected to changes in y. However, the relationship does not follow one straight direction.

Linear vs. Nonlinear Relationships

A linear relationship can be reasonably described with a straight line. As x changes, y tends to change at a fairly consistent rate.

A nonlinear relationship follows a curve or another changing pattern. The direction or rate of change can vary across the graph.

The correlation coefficient r measures linear association. Therefore, it may be close to zero when the data follows a strong curved pattern.

For this reason, students should not conclude that two variables have no relationship simply because r is near zero.

Example of a Nonlinear Pattern

Consider a U-shaped scatter plot. The points decrease at first and then increase, creating a curved pattern.

This pattern shows that the variables are related, even though there may be little overall linear association.

The important lesson is simple: zero or near-zero linear correlation does not prove that no relationship exists.

Common Mistakes When Identifying No Correlation

Students often confuse no correlation with weak correlation or no relationship at all. These mistakes can lead to incorrect interpretations of scatter plots.

Mistake 1: Looking Only at Individual Points

One or two points do not determine the type of correlation. Always examine the overall pattern.

A few points can move against the general direction without eliminating a relationship.

Mistake 2: Assuming Random Means Exactly r = 0

A graph that looks random does not necessarily have a correlation coefficient of exactly zero.

A scattered dataset can still have a small positive or negative correlation. Exact values should be determined from the data rather than visual appearance alone.

Mistake 3: Ignoring Nonlinear Patterns

A curved pattern can represent a meaningful relationship even when r is close to zero.

Always check whether the points form a curve, U-shape, or another recognizable pattern.

Mistake 4: Confusing Weak Correlation With No Correlation

Weak correlation means the points show a slight linear tendency. No correlation means there is no meaningful linear direction.

The difference can be subtle, so consider the entire scatter plot and r when available.

Mistake 5: Thinking No Correlation Means No Possible Relationship

No linear correlation does not mean the variables are completely unrelated.

A nonlinear relationship may still exist. This distinction is especially important when interpreting scatter plots in AP Statistics.

Mistake 6: Confusing Correlation With Causation

Correlation describes an association between variables. It does not prove that changes in one variable cause changes in the other.

Even a strong correlation cannot establish causation by itself. Other variables, study design, or outside factors may affect the observed association.

No Correlation Graph Examples for AP Statistics

Understanding no correlation is important when interpreting scatter plots on AP Statistics questions. You need to recognize the pattern, interpret r, and avoid confusing weak or nonlinear relationships with no correlation.

The following practice questions focus on the types of situations you may encounter when analyzing relationships between two quantitative variables.

Practice Question 1 — Identify the Graph

Question: A scatter plot has points spread randomly across the graph. There is no clear upward or downward trend. Which description best matches the graph?

A. Strong positive correlation
B. Strong negative correlation
C. No linear correlation
D. Perfect positive correlation

Answer: C. No linear correlation

Explanation: The points do not show a consistent upward or downward direction. Therefore, the graph shows little or no linear association.

Practice Question 2 — Interpret r

Question: A study reports a correlation coefficient of r = 0.04 between two quantitative variables. What does this value suggest?

A. Strong positive correlation
B. Strong negative correlation
C. Little or no linear correlation
D. A strong nonlinear relationship

Answer: C. Little or no linear correlation

Explanation: An r value close to zero indicates little or no linear association. However, r alone cannot rule out a nonlinear relationship.

Practice Question 3 — Identify Weak vs. No Correlation

Question: Two scatter plots are shown. Plot A has points with a slight upward tendency. Plot B has points scattered without any consistent direction. Which statement is correct?

A. Both plots show no correlation.
B. Plot A may show weak positive correlation, while Plot B may show no linear correlation.
C. Plot A shows negative correlation, while Plot B shows positive correlation.
D. Both plots show strong positive correlation.

Answer: B. Plot A may show weak positive correlation, while Plot B may show no linear correlation.

Explanation: A slight upward tendency suggests weak positive correlation. A plot without a consistent direction suggests little or no linear correlation.

Practice Question 4 — Recognize a Nonlinear Relationship

Question: A scatter plot forms a clear U-shaped pattern. The correlation coefficient is r = 0.02. What is the best interpretation?

A. The variables have no relationship.
B. The variables have a strong positive linear relationship.
C. The variables have a nonlinear relationship with little linear association.
D. The correlation coefficient proves the variables are unrelated.

Answer: C. The variables have a nonlinear relationship with little linear association.

Explanation: The U-shaped pattern shows a clear relationship. However, the relationship is curved rather than linear, so r can be close to zero.

Practice Question 5 — Interpret a Scatter Plot

Question: A scatter plot shows points generally moving downward as x increases. The points are somewhat spread out, but the overall direction is clear. What type of association is most appropriate?

A. Weak or moderate negative linear association
B. No possible relationship
C. Positive linear association
D. Perfect correlation

Answer: A. Weak or moderate negative linear association

Explanation: The downward direction indicates a negative association. The amount of scatter determines how strong that relationship is.

Quick Reference: No Correlation Graph

NO CORRELATION

Pattern: No clear linear pattern

Points: Broadly scattered without a consistent direction

Correlation coefficient: r is close to 0

Prediction: One variable does not provide a useful linear prediction of the other

Important: A nonlinear relationship may still exist.

AP Statistics reminder: A correlation near zero does not automatically mean the variables are completely unrelated.

The safest approach is to examine the scatter plot and r together. Look for the overall shape before deciding whether the data has no linear correlation.

Conclusion

A no correlation graph shows little or no clear linear association between two quantitative variables. We covered how to identify it, interpret r, and distinguish it from weak or nonlinear relationships.

Remember that scattered points do not always mean exactly zero correlation. A curved pattern can still show a meaningful relationship, even when r is near zero. Checking the overall scatter plot is essential before drawing conclusions.

With practice, recognizing a graph with no correlation becomes much easier. Focus on the direction, strength, and shape of the data.

If this guide helped you understand no correlation in statistics, share it with a classmate. You can also explore more statistics guides and calculators to strengthen your skills.