Bluebook SAT Test Two-Variable Data: Models and Scatterplots 5 — Questions and Answers
Question 1: The model y = 200(0.85)^x represents the number of bacteria (y) after x hours. What type of model is this and what is happening to the population?
- Exponential decay; the population is decreasing (Correct answer)
- Exponential growth; the population is increasing
- Linear decay; the population is decreasing at a constant rate
- Quadratic; the population decreases then increases
Correct answer: Exponential decay; the population is decreasing
The base 0.85 is between 0 and 1, making this exponential decay — the population decreases by 15% each hour.
Question 2: A data point at (4, 30) lies above the line of best fit y = 5x + 6. What is the residual?
- 4 (Correct answer)
- −4
- 2
- −2
Correct answer: 4
Predicted y = 5(4) + 6 = 26; residual = 30 − 26 = 4.
Question 3: A line of best fit for the data x: 1, 2, 3, 4, 5 and y: 7, 9, 11, 13, 15 is y = mx + b. What is m?
- 2 (Correct answer)
- 5
- 7
- 1
Correct answer: 2
The y values increase by 2 for every unit increase in x, so the slope m = 2.
Question 4: Which correlation coefficient indicates the weakest linear relationship?
- r = −0.02 (Correct answer)
- r = −0.85
- r = 0.72
- r = 0.91
Correct answer: r = −0.02
The value closest to 0 (r = −0.02) indicates the weakest linear relationship.
Question 5: Using a line of best fit to predict y for an x value far outside the range of the data is called extrapolation. Why is this risky?
- The model may not accurately represent the relationship outside the observed range (Correct answer)
- The slope may be negative
- The y-intercept may be positive
- Extrapolation always overestimates the true value
Correct answer: The model may not accurately represent the relationship outside the observed range
Extrapolation is unreliable because the pattern established in the data range may not continue outside it.
Question 6: Data shows years of experience (x) and salary (y, thousands). The line of best fit is y = 3.5x + 42. Predict the salary for someone with 10 years of experience.
- $77,000 (Correct answer)
- $74,500
- $80,000
- $42,000
Correct answer: $77,000
y = 3.5(10) + 42 = 35 + 42 = 77, so $77,000.
Question 7: A scatterplot shows a strong positive correlation between x and y. A student concludes that x causes y. Is this conclusion valid?
- No; correlation does not imply causation (Correct answer)
- Yes; a strong correlation proves causation
- Only if the correlation coefficient is above 0.9
- Yes, if the data comes from an experiment
Correct answer: No; correlation does not imply causation
Correlation only shows association — a third variable or coincidence may explain the pattern.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 5
The model y = 200(0.85)^x represents the number of bacteria (y) after x hours.
What type of model is this and what is happening to the population?