Bluebook SAT Test Two-Variable Data: Models and Scatterplots 3

Question 1

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?

Accepted Answer

23 cm

Answer

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

Question 2

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

Accepted Answer

There is a strong negative linear relationship

Answer

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

Question 3

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

Accepted Answer

Exponential

Answer

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

Question 4

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?

Accepted Answer

6

Answer

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

Question 5

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)?

Accepted Answer

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

Answer

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

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