Two-Variable Data: Models and Scatterplots Flashcards

A model for monthly sales (y) based on marketing spend (x, hundreds of dollars) is y = 12x + 80. How many units are sold when $500 is spent on marketing?

Answer: 140

x = 5 (hundreds): y = 12(5) + 80 = 60 + 80 = 140.

The data points (1, 3), (2, 6), (3, 9), (4, 12) lie exactly on a line. What is the slope of the best-fit line?

Answer: 3

The y value increases by 3 for each unit increase in x, so slope = 3.

A dataset has a line of best fit y = −0.5x + 100. When x = 0, what is y? When x = 100, what is y?

Answer: y = 100 when x = 0; y = 50 when x = 100

At x = 0: y = 100; at x = 100: y = −0.5(100) + 100 = −50 + 100 = 50.

A researcher collects data and finds the second differences of y are approximately constant. What type of model fits best?

Answer: Quadratic

Constant second differences are the hallmark of a quadratic (second-degree polynomial) model.

The correlation coefficient between hours of TV watched and GPA is r = −0.73. What can you conclude?

Answer: Students who watch more TV tend to have lower GPAs, and the relationship is moderately strong

r = −0.73 indicates a moderately strong negative association; correlation doesn't establish causation.

Using the model y = 1.5x² − 3x + 4, what is y when x = 4?

Answer: 16

y = 1.5(16) − 3(4) + 4 = 24 − 12 + 4 = 16.

A line of best fit is drawn through a scatterplot. Most points are very close to the line, and r = 0.98. What does this tell you?

Answer: A linear model explains most of the variation in the data

r = 0.98 means r² = 0.96, so about 96% of variability in y is explained by the linear model.