In AP Statistics, direction describes whether two quantitative variables tend to increase together (positive association) or move in opposite ways (negative association) in a scatterplot, and it matches the sign of the correlation coefficient r and the slope of the regression line.
Direction is one of the four things you describe when you look at a scatterplot of two quantitative variables, along with form, strength, and unusual features (many teachers call this DUFS). A positive direction means that as one variable increases, the other tends to increase too. Think height and shoe size. A negative direction means that as one variable increases, the other tends to decrease, like a car's age and its resale value. If the points show no consistent upward or downward pattern, you'd say there is no clear association.
Direction isn't just an eyeball judgment. It shows up in the numbers. The correlation coefficient r is positive for a positive direction and negative for a negative direction, and the slope of the least-squares regression line carries the same sign. So if r = -0.84, you already know the scatterplot trends downward without ever seeing it.
Direction lives in Unit 2 (Exploring Two-Variable Data), where the CED expects you to describe an association between two quantitative variables using direction, form, strength, and unusual features, all in context. It's usually the very first word in a full-credit scatterplot description, something like "There is a strong, positive, linear association between hours studied and exam score." Miss the direction and you've left an easy point on the table. The idea also stretches forward. When you interpret a slope in regression, the sign of that slope is the direction. And in Units 6 and 7, the alternative hypothesis in a one-sided test is literally a claim about direction (is the true mean greater than, or less than, some value?). Learning to read and state direction precisely in Unit 2 pays off all the way through inference.
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Correlation (Unit 2)
The sign of r IS the direction. A positive r means positive association, a negative r means negative association. The magnitude of r measures strength, which is a separate idea. Direction and strength are two different dials, and r reports both at once.
Scatter Plot (Unit 2)
Direction is the first thing you read off a scatterplot. Does the cloud of points drift up to the right (positive) or down to the right (negative)? You can't describe direction for categorical variables, only for two quantitative ones plotted this way.
Regression Analysis (Unit 2)
The slope of the least-squares regression line always shares its sign with r. When you interpret a slope ("for each additional X, predicted Y decreases by..."), the word 'increases' or 'decreases' in that sentence is the direction showing up in your interpretation.
Alternative Hypothesis (Units 6-7)
Direction comes back in inference. A one-sided alternative hypothesis (Ha: μ > 122 or Ha: μ < 122) claims a specific direction of difference, while a two-sided test doesn't. Choosing the wrong direction for Ha can tank an entire hypothesis-test FRQ.
On multiple choice, direction shows up in questions that ask you to match a scatterplot to a correlation value, or to pick the correct description of an association. If the points trend downward, every answer choice with a positive r is instantly gone. On the FRQ side, any question that hands you a scatterplot and says "describe the association" wants direction, form, strength, and unusual features, in context. Saying "strong linear" without "positive" or "negative" costs you. Direction also matters in inference FRQs, like the 2018 question on mean systolic blood pressure, where you have to decide whether the hypothesis is about a directional claim (greater than 122) and write Ha accordingly. The skill being graded is precision. "As gestation period increases, life expectancy tends to increase" earns credit; "the variables are related" does not.
Direction tells you which way the relationship goes (positive or negative). Strength tells you how tightly the points cluster around that pattern. They're independent. You can have a strong negative association (r = -0.95) or a weak positive one (r = 0.2). A common trap is reading r = -0.9 as 'weaker' than r = 0.5 because it's negative. The negative sign is direction only; in absolute value, -0.9 is much stronger.
Direction describes whether two quantitative variables tend to increase together (positive) or move in opposite directions (negative).
The sign of the correlation coefficient r and the sign of the regression slope both tell you the direction of the association.
A full scatterplot description on the AP exam includes direction, form, strength, and unusual features, stated in the context of the variables.
Direction and strength are separate ideas, so r = -0.9 is a stronger relationship than r = 0.5 even though it's negative.
Direction reappears in inference, where a one-sided alternative hypothesis is a claim that a parameter differs from a value in a specific direction.
Direction never proves causation; a positive association can be driven entirely by a confounding variable.
Direction describes whether two quantitative variables in a scatterplot tend to increase together (positive association) or move in opposite ways (negative association). It's one of the four features you describe for any scatterplot, along with form, strength, and unusual features.
No. Negative just means the variables move in opposite directions, not that the relationship is weak. An r of -0.95 describes a very strong negative association, far stronger than an r of 0.3, which is positive but weak.
Direction is one piece of information that the correlation coefficient carries. The sign of r gives you the direction, while the size of r (how close to 1 or -1) gives you the strength. Correlation also assumes a linear form, which direction alone doesn't.
Use the variable names and say which way they move together, for example, "As the number of hours studied increases, exam scores tend to increase, so there is a positive association." The word "tend" matters because the pattern is a trend, not a rule for every point.
No. Direction only describes the pattern in the data, not why it exists. A positive association can come from a confounding variable, so you can only claim causation from a well-designed randomized experiment.