Algebra 1 Practice Test: Scatter Plots, Correlation and Lines of Best Fit
- Scatter Plots and Lines of Fit
- 10 questions
- 13 minutes
These 10 questions cover reading the direction and strength of a correlation, using a line of fit to predict and interpreting slope and intercept in context. Tip: correlation alone never proves that one thing causes the other.
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Question 1
In a class, students who studied more hours tended to get higher test scores. What kind of correlation is this?
Correct answer: B
When both quantities tend to increase together, the correlation is positive. A negative correlation would mean scores fall as study time rises.
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Question 2
A data set has a correlation coefficient of r = −0.92. Which description fits best?
Correct answer: D
The sign shows the direction (negative), and a value close to −1 shows a strong linear relationship. Strength depends on the distance from 0, not on the sign.
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Question 3
A shop models daily lemonade sales with y = 3.2x + 15, where x is the high temperature above 60°F and y is the number of cups sold.
How many cups does the model predict when x = 20?
Correct answer: C
y = 3.2(20) + 15 = 64 + 15 = 79. The answer 64 forgets to add the intercept 15.
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Question 4
A club models its membership with y = 45x + 120, where x is the number of years since 2015.
What does the slope 45 mean?
Correct answer: B
Slope is the change in y for each 1-unit increase in x: about 45 more members each year. The number 120 is the intercept, the starting membership.
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Question 5
Use the same model, y = 45x + 120, where x is the number of years since 2015.
What does the number 120 represent?
Correct answer: A
The y-intercept is the value of y when x = 0, and x = 0 stands for the year 2015.
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Question 6
A line of best fit predicts that a student will score 52.5 points. The student actually scores 58 points.
What is the residual for this student?
Correct answer: C
Residual = actual − predicted = 58 − 52.5 = 5.5. A positive residual means the point lies above the line; −5.5 subtracts in the wrong order.
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Question 7
In one city, daily ice cream sales and the number of sunburn cases have a strong positive correlation.
Which conclusion is best supported?
Correct answer: C
Correlation does not show causation. Hot, sunny days raise both ice cream sales and time spent in the sun, so a lurking variable explains the pattern.
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Question 8
Which correlation coefficient shows the strongest linear relationship?
Correct answer: D
Strength is measured by how close |r| is to 1. |−0.95| = 0.95 is larger than 0.81, even though the relationship is negative.
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Question 9
A line of fit was found using data on children aged 2 to 10. It relates age to height.
Why is it unreliable to use this line to predict the height of a 40-year-old?
Correct answer: B
Predicting far outside the data (extrapolation) assumes the trend continues, but people stop growing. A positive slope is not the problem.
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Question 10
A line of fit passes through the points (2, 50) and (6, 70). What is its equation?
Correct answer: D
Slope = (70 − 50) ÷ (6 − 2) = 5. Then 50 = 5(2) + b, so b = 40. The slope 0.2 comes from dividing run by rise.
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