Direction in AP Statistics

In AP Statistics, direction describes whether two quantitative variables have a positive association (y tends to increase as x increases), a negative association (y tends to decrease as x increases), or no clear association. It is one of the four features used to describe a scatterplot.

What is Direction?

Direction is the answer to one simple question about a scatterplot. As you move left to right, do the points tend to go up or down?

• Positive association means that as the explanatory variable (x) increases, the response variable (y) tends to increase too. Think height and weight.
• Negative association means that as x increases, y tends to decrease. Think car age and resale value.
• No association means there's no consistent upward or downward trend.

Direction is one of four features you describe for any scatterplot, along with form (linear or curved), strength (how tightly the points follow the pattern), and unusual features (outliers, clusters). The word tend matters. Direction describes the overall trend, not every single point. A positive association can still contain pairs where a larger x has a smaller y.

Why Direction matters in AP® Statistics

Direction lives in Topic 5.1, Graphical Representations Between Two Quantitative Variables, which is the hub guide for scatterplots. It's the first thing you read off a scatterplot, and everything later in two-variable analysis builds on it. The sign of the correlation coefficient r matches the direction, and so does the sign of the slope of a least-squares regression line. If you get the direction wrong, your interpretation of r and of the slope will be wrong too. Describing a relationship "in context" on the AP exam means naming the direction with the actual variables, not just saying "positive."

How Direction connects across the course

Correlation (Topic 5.1)

The sign of r is basically direction turned into a number. A positive r means a positive direction, and a negative r means a negative one. The size of r tells you strength, not direction, so r = -0.92 is just as strong as r = 0.92.

Scatter Plot (Topic 5.1)

You can only judge direction from a graph that shows paired quantitative data, and the scatterplot is that graph. Read it left to right, the same way you'd read a hill. If the points climb, the direction is positive. If they fall, it's negative.

Regression Analysis (Topic 5.1 and later regression topics)

The slope of the least-squares line always has the same sign as r, so the line's tilt matches the scatterplot's direction. When you interpret a slope as "for each additional unit of x, predicted y increases/decreases by...", the word increases or decreases is the direction.

Response Variable (Topic 5.1)

Direction is always stated as what happens to the response variable when the explanatory variable increases. That's why you need to identify which variable is x and which is y first, a skill several practice questions test directly.

Is Direction on the AP® Statistics exam?

Direction shows up in a few predictable ways:

• "Describe the relationship" prompts. You're expected to cover direction, form, strength, and unusual features in context. "There is a strong, positive, linear association between student height and weight" earns credit. "It's positive" alone usually doesn't.
• Explanatory vs. response setups. Practice questions ask you to identify the explanatory and response variables (for example, CO₂ levels and global temperature) or to spot a scenario where that's hard to decide. Direction only makes sense once you know which variable you're tracking as x increases.
• What a graph can and can't show. One practice question gives a tight, positive-slope height/weight scatterplot with r = 0.92 and asks what would NOT be evident from the scatterplot alone. Direction and rough strength are visible on the graph. Things like causation are not.
• Direction that changes. A fertilizer-vs-growth-rate question describes growth rising quickly and then leveling off. That tests whether you can separate direction (still non-decreasing) from form (curved, not linear).

The word "direction" also appears in inference contexts, where it describes which way a difference or effect goes. Released FRQs like 2018 Q6 (systolic blood pressure compared to a reported mean of 122) and 2018 Q4 (ACL surgery recovery) reward you for stating clearly which way an effect points.

Direction vs Strength

Direction tells you which way the trend goes (up or down). Strength tells you how closely the points follow that trend. A common mistake is thinking "negative" means "weak." It doesn't. An r of -0.95 describes a very strong negative association, and an r of 0.20 describes a weak positive one. Direction comes from the sign of r, and strength comes from how close r is to 1 or -1.

Key things to remember about Direction

• Direction describes whether the response variable tends to increase (positive) or decrease (negative) as the explanatory variable increases.

• Direction is one of four features you describe in a scatterplot, along with form, strength, and unusual features.

• The sign of the correlation coefficient r and the sign of the regression slope always match the direction of the scatterplot.

• A negative association can be very strong, because direction and strength are separate features.

• Always state direction in context using the actual variable names, not just the word positive or negative.

• A positive or negative direction never proves that one variable causes the other to change.

Frequently asked questions about Direction

What is direction in AP Statistics?

Direction is whether a scatterplot shows a positive association (y tends to rise as x increases), a negative association (y tends to fall as x increases), or no clear association. It's one of the four features you describe for any two-variable quantitative relationship, covered in Topic 5.1.

Does a negative correlation mean the relationship is weak?

No. Negative only describes direction. An r of -0.92 is just as strong as r = 0.92, and strength depends on how close r is to 1 or -1, not on its sign.

How is direction different from form in a scatterplot?

Direction is whether the trend goes up or down, and form is the shape of the trend, like linear or curved. For example, plant growth rate that rises quickly with fertilizer and then levels off has a positive direction but a curved, nonlinear form.

Does a positive direction mean x causes y?

No. A positive association, even a tight one like height and weight with r = 0.92, only shows that the variables tend to increase together. Showing causation requires a well-designed experiment, not just a scatterplot.

How do I write the direction of a relationship on an AP Stats FRQ?

Name the direction alongside form and strength, using the variables in context. For example, write "There is a strong, positive, linear association between height and weight," not just "It's positive."