In AP Statistics, the response variable is the outcome being measured, the y-variable whose values you're trying to predict or explain. In regression it's the variable on the vertical axis (ŷ predicts it); in an experiment it's the result you record after applying treatments.
The response variable is the "what happened" variable. It's the outcome you measure, and you're studying it because you think another variable (the explanatory variable) influences it. In Unit 2's two-variable setup, the response variable is always y. The least-squares regression line ŷ = a + bx predicts the response variable from the explanatory variable, and the residual (y - ŷ) measures how far the actual response landed from the predicted one.
A quick gut check works almost every time. Ask yourself which variable depends on the other. Energy consumption depends on temperature, exam scores depend on study time, blood pressure depends on flavonoid intake. The one that depends is your response variable. Getting this assignment right matters because regression is not symmetric. If you swap x and y, you get a completely different line with a different slope, so identifying the response variable correctly is step one of every regression problem.
This term lives in Unit 2 (Exploring Two-Variable Data), specifically Topics 2.7 and 2.8. Learning objective 2.8.A has you estimate the regression line, and the slope formula b = r(s_y/s_x) literally requires you to know which standard deviation belongs to the response variable (s_y) and which to the explanatory variable (s_x). Mix them up and your slope is wrong. Objective 2.8.B has you interpret coefficients, and the CED defines the y-intercept as the predicted value of the response variable when the explanatory variable equals 0. In Topic 2.7, residuals are differences in the response variable, since residual = y - ŷ compares the actual response to the predicted response. The phrase shows up again in r², which is interpreted as the percent of variation in the response variable explained by the linear relationship with the explanatory variable. If you can't name the response variable, you can't write a single one of these interpretations correctly.
Keep studying AP Statistics Unit 2
Explanatory Variable (Unit 2)
These two are a matched pair. The explanatory variable (x) is the suspected cause or predictor, and the response variable (y) is the outcome. Every regression line, residual, and r² interpretation depends on assigning them correctly, because swapping x and y changes the entire model.
Residuals (Unit 2)
A residual is the response variable's prediction error, the actual y minus the predicted ŷ. Residual plots graph these errors against the explanatory variable or the predicted responses to check whether a linear model actually fits.
Coefficient of Determination (Unit 2)
r² is interpreted using the response variable by name. The template is "r² percent of the variation in [response variable] is explained by the linear relationship with [explanatory variable]." If you can't identify the response variable, you can't write this sentence.
Experimental Design (Unit 3)
In experiments, the response variable is what you measure after applying treatments, like blood pressure reduction after a flavonoid diet. Unit 3 FRQs routinely ask you to name the response variable when describing a well-designed experiment.
On multiple choice, the term shows up inside slope, intercept, and r² questions. One classic stem gives you r = -0.8 and tells you the explanatory variable's standard deviation is twice the response variable's, then asks for the slope, which forces you to plug into b = r(s_y/s_x) correctly. Another asks you to interpret a y-intercept like ŷ = 45 - 1.8x, and the right answer phrases it as the predicted value of the response variable (energy consumption) when the explanatory variable (temperature) is 0. On FRQs, the response variable appears constantly in experimental design questions. The 2019 FRQ (fungus concentrations vs. insect control), 2021 FRQ (coupon offers vs. repeat purchases), and 2022 FRQs (flavonoids vs. blood pressure, acne drug on twins) all required identifying what outcome gets measured. The standard move is to name the response variable explicitly in your design description and in every interpretation sentence you write. Vague pronouns like "it goes up" lose points; "predicted energy consumption decreases by 1.8 kWh" earns them.
The explanatory variable is the input (x), the thing you suspect causes or predicts the change. The response variable is the output (y), the thing that responds. In "does midterm score predict final exam score," midterm is explanatory and final exam is response. The mix-up costs real points because the slope formula b = r(s_y/s_x) puts the response variable's standard deviation on top, and regressing y on x gives a different line than regressing x on y.
The response variable is the outcome you measure, and it's always the y-variable in a regression setting.
In the slope formula b = r(s_y/s_x), s_y is the standard deviation of the response variable, so identifying it correctly is required to compute the slope.
The y-intercept of a regression line is the predicted value of the response variable when the explanatory variable equals 0, though that interpretation doesn't always make sense in context.
A residual is the actual response minus the predicted response (y - ŷ), so residuals always describe errors in the response variable.
Interpret r² as the percent of variation in the response variable explained by the linear relationship with the explanatory variable, not the percent of points on the line.
In experiments, the response variable is what you measure after applying treatments, and FRQ design answers should name it explicitly.
It's the outcome variable being measured or predicted, always plotted as y. In ŷ = 25 + 0.7x predicting final exam scores from midterm scores, the final exam score is the response variable.
Yes, they're the same idea. AP Stats prefers "response variable" (paired with "explanatory variable") over "dependent variable," and using the CED's terms makes your FRQ answers cleaner.
The explanatory variable (x) is the predictor or suspected cause; the response variable (y) is the outcome that responds to it. In the 2022 flavonoid FRQ, the diet was explanatory and the reduction in blood pressure was the response.
No. Labeling variables as explanatory and response does not prove causation. Correlation alone can't establish a causal relationship; only a well-designed experiment with random assignment can, since observational data can hide confounding variables.
The response variable's. The slope is b = r(s_y/s_x), so if r = -0.8 and the explanatory variable's standard deviation is twice the response variable's, the slope is -0.8 × (1/2) = -0.4.
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