SAT Math · Two-variable data: models and scatterplots · medium
Two stores each fit a linear model relating advertising spending to monthly sales. Store A's model has a slope of 3.5, and Store B's model…
Two stores each fit a linear model relating advertising spending to monthly sales. Store A's model has a slope of 3.5, and Store B's model has a slope of 2.1. What does this comparison suggest?
Answer and explanation
Answer: D: Each additional dollar of advertising is associated with a larger increase in sales for Store A than for Store B.
The slope of a linear model is the predicted change in the output for each one-unit increase in the input. Store A's slope of 3.5 means each additional advertising dollar is associated with $3.50 more in sales, compared with $2.10 for Store B. So an extra dollar is associated with a larger increase in sales at Store A, choice D. Choice A confuses slope with total sales, which depends on the intercepts. Choice B reverses the comparison. Choice C ignores the difference in slopes. Note that the wording "associated with" is appropriate because the model shows correlation, not proof of cause.
More Two-variable data: models and scatterplots questions
- Question 20 · easyThe equation C = 3.5g + 40 models the total cost C, in dollars, of a rental car after driving g…
- Question 241 · mediumA linear model predicts a plant's height, in centimeters, as h(w) = 2.5w + 8, where w is the…
- Question 259 · mediumA linear model predicts that a company will sell 50 units in a given month. The company actually…
- Question 260 · mediumA linear model was used to predict the weight of four different animals based on their length. The…
- Question 261 · easyA line of best fit for a data set is given by y = 2.5x + 30, where x represents years of…
- Question 279 · easyA scatterplot shows that as the number of hours studied increases, exam scores tend to increase as…
Learn the method behind questions like this one
The SAT Math course teaches each tested skill through lessons, step-by-step solutions to sample problems, the complete study guide and full-length practice tests.