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Bivariate data and relationships (scatterplots, correlation) — ACT practice questions

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• 45 questions on the paper
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Practice 44 Bivariate data and relationships (scatterplots, correlation) questions in the app

What this topic is

Bivariate data and relationships (scatterplots, correlation) on the ACT Mathematics test covers how two quantitative variables move together, including scatterplots, the direction and strength of association, and simple linear models.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

A coach recorded the number of hours athletes practiced each week ($x$) and the number of push-ups they could complete ($y$). The line of best fit for the data is $y = 2.5x + 8$. What does the value 2.5 represent in this context?

AAn athlete who practices 0 hours per week can do 2.5 push-ups.✗ Not this oneBThe average athlete practices 2.5 hours per week.✗ Not this oneCFor each additional hour of practice per week, the number of push-ups an athlete can do increases by about 2.5.✓ CorrectDFor each additional push-up an athlete can do, the weekly practice time increases by 2.5 hours.✗ Not this one

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Answer: C — For each additional hour of practice per week, the number of push-ups an athlete can do increases by about 2.5.

In a line of best fit $y = mx + b$, the slope $m$ gives the change in $y$ per unit increase in $x$. Here $x$ is practice hours and $y$ is push-ups, so 2.5 means push-ups increase by about 2.5 for each additional hour of weekly practice.

Question 2Easier

A fitted model for a sensor’s response $R$, in units, at temperature $t$ degrees Celsius is $R = 2.4t + 18$. Which of the following is the best interpretation of the slope and the intercept of this model?

AThe response increases by 18 units per degree, and the predicted response at $0^\circ$C is 2.4 units.✗ Not this oneBThe temperature increases by $2.4^\circ$C per response unit, and the predicted temperature at a response of 0 is $18^\circ$C.✗ Not this oneCThe response increases by 2.4 units per degree, and the predicted response at $18^\circ$C is 0 units.✗ Not this oneDThe response increases by 2.4 units per degree, and the predicted response at $0^\circ$C is 18 units.✓ Correct

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Answer: D — The response increases by 2.4 units per degree, and the predicted response at $0^\circ$C is 18 units.

The coefficient of t is the predicted change in response for each $1^\circ$C increase, so the slope is 2.4 response units per degree. The constant 18 is the model’s predicted response when t = $0^\circ$C.

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