Two-Variable Data: Models and Scatterplots Flashcards

A line of best fit is described by y = 4x + 8. Which data point lies BELOW the line?

Answer: (3, 18)

At x=3, predicted y = 4(3)+8 = 20; actual y=18 < 20, so this point is below the line.

Data on price (x, dollars) and quantity demanded (y, units) gives the line y = −50x + 1000. What quantity is demanded when price is $12?

Answer: 400 units

y = −50(12)+1000 = −600+1000 = 400 units.

A researcher collects data and finds that first differences of y are NOT constant, but second differences ARE constant. What type of model best fits?

Answer: Quadratic

Constant second differences indicate a quadratic relationship between x and y.

A model for the height of a ball (y, meters) over time (x, seconds) is y = −5x² + 20x. When is the ball at its maximum height?

Answer: x = 2 seconds

x-coordinate of vertex: x = −b/(2a) = −20/(2·(−5)) = 20/10 = 2 seconds.

The slope of a best-fit line for the data is calculated as 2. A second analyst calculates the slope as −2 using the same data. Which is more likely true?

Answer: One analyst likely made a calculation error, since a dataset has only one best-fit slope.

A given dataset has one unique least-squares best-fit line with a single slope; one analyst made an error.

A scatterplot shows a strong positive association between x and y, with r = 0.92. A student concludes: 'Increasing x will increase y.' Is this reasoning correct?

Answer: No; correlation does not imply causation.

Correlation measures the strength of a linear relationship but cannot establish causation.

An exponential model y = 100(1.05)^x predicts savings (y, dollars) after x years. By what percentage does y grow each year?

Answer: 5%

The base 1.05 means y grows by a factor of 1.05 each year — a 5% annual increase.