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Positive Direction

Positive Direction

A way of describing the scatterplot of positively associated data.

 

 

See also

Negative direction

Example

Problem: A teacher records the number of hours studied and test scores for 6 students: (1, 55), (2, 60), (3, 68), (4, 75), (5, 82), (6, 90). Determine whether the scatterplot shows a positive direction, negative direction, or no direction.
Step 1: Plot the data points on a coordinate plane with hours studied on the x-axis and test score on the y-axis.
Step 2: Observe the overall pattern. When x increases from 1 to 6, the y-values increase from 55 to 90.
Step 3: Since the points generally rise from left to right, both variables increase together. This means the data shows a positive association.
Answer: The scatterplot has a positive direction because as hours studied increases, test scores also increase — the points trend upward from left to right.

Another Example

Problem: A store tracks the daily high temperature (°F) and the number of ice cream cones sold for 5 days: (70, 40), (75, 55), (80, 63), (85, 78), (90, 95). Does the scatterplot show a positive direction?
Step 1: Identify the variables. Temperature is on the x-axis, and cones sold is on the y-axis.
Step 2: Check the trend: as temperature rises from 70°F to 90°F, cones sold rises from 40 to 95.
Step 3: The points climb from the lower left toward the upper right of the graph.
Answer: Yes, the scatterplot shows a positive direction. Higher temperatures are associated with more ice cream sales.

Frequently Asked Questions

How can you tell if a scatterplot has a positive direction?
Look at the overall trend of the data points from left to right. If the points generally rise — moving from the lower-left area toward the upper-right area — the scatterplot has a positive direction. You don't need every single point to be higher than the last; the general pattern just needs to trend upward.
Is positive direction the same as positive correlation?
They are closely related. Positive direction describes the visual upward trend you see in a scatterplot. Positive correlation is a more precise statistical measurement (using a correlation coefficient r > 0) that quantifies how strongly two variables increase together. A scatterplot with a positive direction will have a positive correlation.

Positive Direction vs. Negative Direction

A scatterplot with a positive direction trends upward from left to right — as one variable increases, the other increases too. A scatterplot with a negative direction trends downward from left to right — as one variable increases, the other decreases. For example, study hours vs. test score typically shows positive direction, while hours of TV watched vs. test score might show negative direction.

Why It Matters

Identifying the direction of a scatterplot is one of the first steps in understanding the relationship between two variables. Recognizing a positive direction tells you that the variables tend to increase together, which helps in making predictions and deciding whether a line of best fit should have a positive slope. This skill is foundational for later work with correlation and linear regression.

Common Mistakes

Mistake: Thinking every point must be higher than the previous one for the direction to be positive.
Correction: Positive direction refers to the overall trend, not a strict point-by-point increase. Real data is scattered, so individual points may dip below the general trend while the overall pattern still moves upward.
Mistake: Confusing the direction of the scatterplot with the strength of the association.
Correction: Direction (positive or negative) and strength (strong or weak) are separate characteristics. A scatterplot can have a positive direction but a weak association if the points are widely spread around the upward trend.

Related Terms