Bluebook SAT Test Two-Variable Data: Models and Scatterplots 2 — Questions and Answers
Question 1: The line of best fit for data relating study time (x, hours) to GPA (y) is y = 0.3x + 2.1. A student studies 5 hours. What GPA does the model predict?
- 3.6 (Correct answer)
- 3.3
- 3.9
- 2.6
Correct answer: 3.6
y = 0.3(5) + 2.1 = 1.5 + 2.1 = 3.6.
Question 2: A scatterplot shows data points tightly clustered around a line sloping upward from left to right. What can be concluded?
- There is a strong positive linear correlation (Correct answer)
- There is a weak positive linear correlation
- There is a strong negative linear correlation
- There is no correlation
Correct answer: There is a strong positive linear correlation
Points tightly clustered around an upward-sloping line indicate a strong positive linear correlation.
Question 3: The linear model y = 6x + 15 predicts the cost (y, dollars) of renting x hours of equipment. By how much does cost increase for each additional hour of rental?
- $6 (Correct answer)
- $15
- $21
- $9
Correct answer: $6
The slope is 6, meaning each additional hour increases cost by $6.
Question 4: Which scatterplot characteristic suggests an exponential model is more appropriate than a linear model?
- The data curves upward with increasing steepness (Correct answer)
- The data forms a straight line
- The data curves upward then downward symmetrically
- The residuals are randomly scattered
Correct answer: The data curves upward with increasing steepness
Exponential growth produces a curve that steepens continuously, unlike the U-shape of quadratic or the straight line of linear models.
Question 5: In a scatterplot, an outlier is a point that lies far from the line of best fit. If a point is an outlier, what happens to the residual for that point?
- The residual has a large absolute value (Correct answer)
- The residual equals zero
- The residual is always negative
- The residual is always positive
Correct answer: The residual has a large absolute value
A residual = actual − predicted; a point far from the line has a large difference, so the residual's absolute value is large.
Question 6: A line of best fit passes through the points (2, 10) and (6, 18). What is the slope of this line?
- 2 (Correct answer)
- 4
- 0.5
- 8
Correct answer: 2
Slope = (18 − 10)/(6 − 2) = 8/4 = 2.
Question 7: A quadratic model y = x² − 4x + 7 is fitted to data. What is the predicted value when x = 3?
- 4 (Correct answer)
- 10
- 7
- 2
Correct answer: 4
y = (3)² − 4(3) + 7 = 9 − 12 + 7 = 4.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 2
The line of best fit for data relating study time (x, hours) to GPA (y) is y = 0.3x + 2.1.
A student studies 5 hours.
What GPA does the model predict?