Bluebook SAT Test Two-Variable Data: Models and Scatterplots 10 — Questions and Answers
Question 1: Using the model y = −4x + 100, for what value of x does y = 0?
- 25 (Correct answer)
- 100
- 4
- −25
Correct answer: 25
Set 0 = −4x+100 → 4x=100 → x=25.
Question 2: A scatterplot shows data points that curve upward steeply, consistent with y growing faster than any linear model. Which model is most appropriate?
- Exponential (Correct answer)
- Linear
- Constant
- Absolute value
Correct answer: Exponential
Data that curves upward and accelerates beyond linear growth is best described by an exponential model.
Question 3: A dataset has the best-fit line y = 1.5x + 4. A point at x = 6 has y_actual = 11. What is the residual?
- -2 (Correct answer)
- 2
- 11
- −0.5
Correct answer: -2
Predicted: y = 1.5(6)+4 = 9+4 = 13; residual = actual − predicted = 11−13 = −2.
Question 4: The scatterplot of temperature (x, °C) vs. snowfall (y, cm) shows a strong negative correlation. If x increases by 5°C, and the slope is −3, by how much does y change?
- −15 cm (Correct answer)
- 15 cm
- −5 cm
- 3 cm
Correct answer: −15 cm
Change in y = slope × change in x = −3 × 5 = −15 cm.
Question 5: A linear model y = 0.6x + 12 describes the relationship between monthly rainfall (x, inches) and mushroom count (y). What does 12 represent?
- The predicted mushroom count when rainfall is 0 inches (Correct answer)
- The rate of mushroom growth per inch of rain
- The maximum number of mushrooms
- The minimum rainfall needed for mushrooms to appear
Correct answer: The predicted mushroom count when rainfall is 0 inches
The y-intercept (12) is the predicted value of y when x = 0, meaning 12 mushrooms are expected even with no rainfall.
Question 6: A researcher calculates r² = 0.81 for a linear model. What percentage of the variation in y is explained by the model?
- 81% (Correct answer)
- 9%
- 90%
- 19%
Correct answer: 81%
r² = 0.81 means 81% of the variation in y is explained by the linear relationship with x.
Question 7: A model y = x² − 6x + 10 is fit to data. What is the minimum value of y according to this model?
- 1 (Correct answer)
- 6
- 10
- −6
Correct answer: 1
Complete the square: y = (x−3)²+1; minimum is 1 at x = 3.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 10
Using the model y = −4x + 100, for what value of x does y = 0?