Two-Variable Data: Models and Scatterplots Flashcards

A linear model predicts plant height (y, cm) from days of growth (x): y = 1.8x + 5. What is the predicted height at day 10?

Answer: 23 cm

y = 1.8(10) + 5 = 18 + 5 = 23 cm.

The correlation coefficient for two variables is r = −0.95. Which statement is true?

Answer: There is a strong negative linear relationship

r = −0.95 is close to −1, indicating a strong negative linear relationship.

A model for population growth is y = 500(1.04)^x, where x is years. What type of model is this?

Answer: Exponential

The base 1.04 raised to the power x makes this an exponential growth model.

A scatterplot of x vs. y has the best-fit line y = −2x + 50. A data point has x = 12, actual y = 30. What is the residual for this point?

Answer: 6

Predicted y = −2(12) + 50 = 26; residual = actual − predicted = 30 − 26 = 6.

Which of the following is a correct interpretation of a y-intercept of 40 in a model relating miles driven (x) to fuel cost (y)?

Answer: When 0 miles are driven, the predicted fuel cost is $40

The y-intercept is the model's output when x = 0, representing cost before driving any miles.

Two variables x and y have the linear model y = 3x − 7. For what value of x does y = 20?

Answer: 9

20 = 3x − 7 → 3x = 27 → x = 9.

A scatterplot shows values loosely scattered with no discernible direction. What does this suggest about the correlation?

Answer: The correlation is near zero

A random scatter with no direction implies little to no linear correlation, so r ≈ 0.