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. A student has to read a scatterplot or an equation of a fitted line, describe the association, and interpret the slope and intercept in context, including what each coefficient means for a change in the input and for the value when the input is zero. Questions often present a linear model and ask which statement best interprets the slope and intercept, with choices that swap the two coefficients, reverse the variables, drop the units, or treat correlation as causation.
Question 1
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∘C is 2.4 units.
- BThe temperature increases by 2.4∘C per response unit, and the predicted temperature at a response of 0 is 18∘C.
- CThe response increases by 2.4 units per degree, and the predicted response at 18∘C is 0 units.
- DThe response increases by 2.4 units per degree, and the predicted response at 0∘C is 18 units.
Show answer
Answer: D — The response increases by 2.4 units per degree, and the predicted response at 0∘C is 18 units.
The coefficient of t is the predicted change in response for each 1∘C increase, so the slope is 2.4 response units per degree. The constant 18 is the model's predicted response when t = 0∘C.
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