Bluebook SAT Test Two-Variable Data: Models and Scatterplots 8 — Questions and Answers
Question 1: A scatterplot displays data with the line y = 7x − 3. A point at x = 5 has actual y = 38. Is the actual y above or below the line, and what is the residual?
- Above the line; residual = +6 (Correct answer)
- Below the line; residual = −6
- Above the line; residual = +3
- Below the line; residual = −3
Correct answer: Above the line; residual = +6
Predicted y = 7(5) − 3 = 32; actual = 38; residual = 38 − 32 = +6, so the point lies above the line.
Question 2: If a linear model for x and y has slope 0 (a horizontal line), what does this imply about the correlation?
- The correlation is 0; y does not change as x changes (Correct answer)
- The correlation is 1
- The correlation is −1
- The correlation is undefined
Correct answer: The correlation is 0; y does not change as x changes
A slope of 0 means y is constant regardless of x, implying no linear relationship, i.e., r = 0.
Question 3: Data on the amount of fertilizer used (x) and crop yield (y) shows the model y = −0.1x² + 5x + 20. For what value of x is the yield maximized?
- 25 (Correct answer)
- 50
- 20
- 5
Correct answer: 25
Vertex at x = −b/(2a) = −5/(2·(−0.1)) = −5/(−0.2) = 25.
Question 4: A company's revenue is modeled by y = 300(1.08)^x, where x is years since founding. What does 1.08 represent?
- Revenue grows by 8% per year (Correct answer)
- Revenue grows by 108% per year
- Revenue decreases by 8% per year
- Revenue started at $1.08
Correct answer: Revenue grows by 8% per year
A base of 1.08 means each year revenue is multiplied by 1.08, an 8% growth rate.
Question 5: Two variables have a negative correlation. As x increases by 1, y changes by −4. The line of best fit has y-intercept 60. What is the equation?
- y = −4x + 60 (Correct answer)
- y = 4x + 60
- y = −4x − 60
- y = 60x − 4
Correct answer: y = −4x + 60
Slope = −4 and y-intercept = 60 gives y = −4x + 60.
Question 6: A table shows x: 0, 1, 2, 3 and y: 5, 15, 45, 135. What is the growth factor of this exponential model?
- 3 (Correct answer)
- 5
- 10
- 15
Correct answer: 3
Each y is multiplied by 3 (15/5 = 3, 45/15 = 3, 135/45 = 3), so the growth factor is 3.
Question 7: A line of best fit for a dataset has the equation y = 2.2x + 1.5. Which of the following is closest to the predicted y when x = 7.5?
- 18 (Correct answer)
- 16.5
- 14
- 20
Correct answer: 18
y = 2.2(7.5) + 1.5 = 16.5 + 1.5 = 18.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 8
A scatterplot displays data with the line y = 7x − 3.
A point at x = 5 has actual y = 38.
Is the actual y above or below the line, and what is the residual?