Bluebook SAT Test Two-Variable Data: Models and Scatterplots 3 — Questions and Answers
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?
- 23 cm (Correct answer)
- 18 cm
- 28 cm
- 15 cm
Correct answer: 23 cm
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?
- There is a strong negative linear relationship (Correct answer)
- There is a weak negative linear relationship
- There is a strong positive linear relationship
- There is no linear relationship
Correct answer: There is a strong negative linear relationship
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?
- Exponential (Correct answer)
- Linear
- Quadratic
- Inverse
Correct answer: Exponential
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?
- 6 (Correct answer)
- −6
- 4
- −4
Correct answer: 6
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)?
- When 0 miles are driven, the predicted fuel cost is $40 (Correct answer)
- Fuel cost increases by $40 per mile
- The maximum fuel cost is $40
- The average miles driven is 40
Correct 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.
Question 6: Two variables x and y have the linear model y = 3x − 7. For what value of x does y = 20?
- 9 (Correct answer)
- 13
- 7
- 27
Correct answer: 9
20 = 3x − 7 → 3x = 27 → x = 9.
Question 7: A scatterplot shows values loosely scattered with no discernible direction. What does this suggest about the correlation?
- The correlation is near zero (Correct answer)
- The correlation is near +1
- The correlation is near −1
- The data follows a quadratic pattern
Correct answer: The correlation is near zero
A random scatter with no direction implies little to no linear correlation, so r ≈ 0.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 3
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?