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

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Practice 45 Bivariate data and relationships (scatterplots, correlation) questions in the app

What this topic is

Two variables measured on the same subjects make a scatterplot, and Bivariate data and relationships (scatterplots, correlation) asks what the pattern means.

A line of best fit summarizes the trend; its slope is the predicted change in y for each one-unit increase in x, and its intercept is the predicted y when x is zero. ACT questions often give the equation in context and ask which sentence correctly interprets one of its numbers.

Correlation describes direction and strength, but a strong correlation does not prove that one variable causes the other. Wrong choices typically swap slope and intercept, or describe a predicted value as a guaranteed one.

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 $y = 2.5 x + 8$ . What does the value 2.5 represent in this context?

An athlete who practices 0 hours per week can do 2.5 push-ups.✗ Not this oneThe average athlete practices 2.5 hours per week.✗ Not this oneFor each additional hour of practice per week, the number of push-ups an athlete can do increases by about 2.5.✓ CorrectFor 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 $y = m x + b$ , 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 $R = 2.4 t + 18$ . Which of the following is the best interpretation of the slope and the intercept of this model?

The response increases by 18 units per degree, and the predicted response at

0^{\circ}

C is 2.4 units.✗ Not this oneThe temperature increases by

2. 4^{\circ}

C per response unit, and the predicted temperature at a response of 0 is

1 8^{\circ}

C.✗ Not this oneThe response increases by 2.4 units per degree, and the predicted response at

1 8^{\circ}

C is 0 units.✗ Not this oneThe 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.

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 45 Bivariate data and relationships (scatterplots, correlation) questions in the app

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

What this topic is

Sample questions

More ACT topics

Mathematics