Bluebook SAT Test Two-Variable Data: Models and Scatterplots 1 — Questions and Answers
Question 1: A scatterplot shows the relationship between hours studied (x) and test score (y). The line of best fit is y = 4.2x + 52. What does the slope 4.2 represent?
- For each additional hour studied, the predicted test score increases by 4.2 points (Correct answer)
- A student who studies 0 hours is predicted to score 4.2 points
- The average test score is 4.2 points
- For each additional test point, hours studied increase by 4.2
Correct answer: For each additional hour studied, the predicted test score increases by 4.2 points
The slope represents the rate of change: each 1-unit increase in x produces a 4.2-unit increase in predicted y.
Question 2: The line of best fit for a dataset is y = −3x + 90. Which of the following best describes the relationship between x and y?
- As x increases, y decreases (Correct answer)
- As x increases, y increases
- x and y have no relationship
- As x increases, y stays constant
Correct answer: As x increases, y decreases
A negative slope means y decreases as x increases.
Question 3: A scatterplot has the line of best fit y = 2.5x + 10. Using the model, what is the predicted value of y when x = 8?
- 30 (Correct answer)
- 28
- 32
- 20
Correct answer: 30
Substitute x = 8: y = 2.5(8) + 10 = 20 + 10 = 30.
Question 4: A data set about advertising spending (x, in thousands) and sales (y, in thousands) has the line of best fit y = 5x + 20. What does the y-intercept 20 represent in context?
- Predicted sales when advertising spending is $0 (Correct answer)
- The increase in sales for every $1,000 increase in advertising
- The maximum sales achievable
- The average advertising spending
Correct answer: Predicted sales when advertising spending is $0
The y-intercept is the predicted value of y when x = 0, i.e., sales with no advertising.
Question 5: A scatterplot of temperature (x, °F) and ice cream sales (y, dollars) shows a strong positive correlation. Which value of r is most consistent with this description?
- 0.87 (Correct answer)
- −0.87
- 0.05
- −0.05
Correct answer: 0.87
A strong positive correlation corresponds to r close to +1, so 0.87 is correct.
Question 6: The table shows values of x and y. Which type of model best fits the data: x: 1, 2, 3, 4; y: 3, 9, 27, 81?
- Exponential (Correct answer)
- Linear
- Quadratic
- Constant
Correct answer: Exponential
The y values are multiplying by 3 each step (ratio is constant), which is characteristic of an exponential model.
Question 7: A researcher plots data and finds the residuals are randomly scattered around zero with no pattern. What does this indicate?
- The chosen model is a good fit for the data (Correct answer)
- The data has a strong negative correlation
- The model is systematically overestimating y
- A quadratic model would fit better
Correct answer: The chosen model is a good fit for the data
Randomly scattered residuals around zero indicate that the model captures the underlying trend well without systematic error.
Bluebook SAT Test Two-Variable Data: Models and Scatterplots 1
A scatterplot shows the relationship between hours studied (x) and test score (y).
The line of best fit is y = 4.2x + 52.
What does the slope 4.2 represent?