Scatterplots and Line of Best Fit

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Scatterplots and Line of Best Fit is part of the SAT Prep course on Study Mondo, specifically in the Problem-Solving and Data Analysis section. You can explore the full course for more related topics and practice resources.

Q: Are there practice problems for Scatterplots and Line of Best Fit?

Yes, this page includes 10 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Analyze scatterplots, determine lines of best fit, interpret slope and intercepts in context, and make predictions using linear and nonlinear models.

Written and reviewed by the Study Mondo Education TeamLast updated April 18, 2026

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Scatterplots and Line of Best Fit on the SAT

What Is a Scatterplot?

A scatterplot displays the relationship between two quantitative variables as points on a coordinate plane.

$x$ -axis: independent (explanatory) variable
$y$ -axis: dependent (response) variable

Types of Association

Pattern	Description	Example
Positive	As $x$ increases, $y$ increases	Height vs. weight
Negative	As $x$ increases, $y$ decreases	Temperature vs. hot chocolate sales
None	No clear pattern	Shoe size vs. GPA

Strength of Association

Strong: Points cluster tightly around a line/curve
Weak: Points are widely scattered
Nonlinear: Points follow a curve, not a line

Line of Best Fit (Regression Line)

The line of best fit is the straight line that best approximates the data.

$y = mx + b$

$m$ (slope): The predicted change in $y$ for each 1-unit increase in $x$
$b$ ( $y$ -intercept): The predicted value of $y$ when $x = 0$

Interpreting Slope in Context

"For each additional [unit of $x$ ], [the $y$ variable] is predicted to [increase/decrease] by [slope] [units of $y$ ]."

Example: If $y = 2.5x + 10$ models the relationship between hours studied ( $x$ ) and test score ( $y$ ): "For each additional hour of study, the test score is predicted to increase by 2.5 points."

Interpreting the $y$ -Intercept

"When [ $x$ variable] is 0, the predicted [ $y$ variable] is [ $b$ ]."

Note: The $y$ -intercept may not always make practical sense (e.g., "0 hours of study" may be unrealistic).

Residuals

$\text{Residual} = \text{Actual value} - \text{Predicted value}$

Positive residual: Actual > Predicted (point is ABOVE the line)
Negative residual: Actual < Predicted (point is BELOW the line)
Zero residual: Point is exactly ON the line

Residual Plots

A good model has residuals that are randomly scattered around zero. A pattern in residuals suggests the model is not a good fit.

Correlation Coefficient ( $r$ )

$r$ value	Meaning
$r = 1$	Perfect positive linear relationship
$r = -1$	Perfect negative linear relationship
$r = 0$	No linear relationship
$	r
$	r

Remember:

$r$ only measures LINEAR relationships
$r$ does NOT indicate causation
Outliers can significantly affect $r$

Making Predictions

Interpolation vs. Extrapolation

Interpolation: Predicting within the range of data → generally reliable
Extrapolation: Predicting beyond the data range → less reliable (may be inaccurate)

SAT Question Types

Type 1: Describe the Association

"Which best describes the relationship?" → positive/negative, strong/weak, linear/nonlinear

Type 2: Interpret Slope or $y$ -Intercept

"In context, what does the slope represent?" → rate of change per unit

Type 3: Find a Residual

Given a point and the line equation, calculate residual = actual − predicted.

Type 4: Make a Prediction

Use the line equation to predict $y$ for a given $x$ value.

Type 5: Identify an Outlier

The point farthest from the line of best fit (largest residual).

Common SAT Mistakes

Claiming causation from a scatterplot — scatterplots show ASSOCIATION, not causation
Extrapolating too far beyond the data range
Misinterpreting slope — it's per unit change, not total change
Confusing positive and negative residuals — positive = above the line
Ignoring the context — always interpret slope and intercept in terms of the actual variables

📚 Practice Problems

1Problem 1easy

❓ Question:

A scatterplot shows the relationship between hours of sleep ( $x$ ) and alertness score ( $y$ ). The points trend upward from left to right and cluster closely around a line. How would you describe this association?

💡 Show Solution

Direction: Points trend upward → positive association

Strength: Points cluster closely → strong association

Form: Follows a line → linear association

Answer: Strong, positive, linear association.

In context: As hours of sleep increase, alertness scores tend to increase.

2Problem 2easy

❓ Question:

💡 Show Solution

Direction: Points trend upward → positive association

Strength: Points cluster closely → strong association

Form: Follows a line → linear association

Answer: Strong, positive, linear association.

In context: As hours of sleep increase, alertness scores tend to increase.

3Problem 3medium

❓ Question:

The line of best fit for a scatterplot relating years of experience ( $x$ ) to salary in thousands ( $y$ ) is $y = 3.2x + 32$ . Interpret the slope in context.

💡 Show Solution

The slope is 3.2.

Interpretation: For each additional year of experience, the predicted salary increases by $3,200 (3.2 thousand dollars).

Template: "For each 1-unit increase in [x-variable], the [y-variable] is predicted to [increase/decrease] by [slope] [units]."

Note: The $y$ -intercept of 32 means a person with 0 years of experience has a predicted salary of $32,000.

4Problem 4medium

❓ Question:

The line of best fit for a scatterplot relating years of experience ( $x$ ) to salary in thousands ( $y$ ) is $y = 3.2x + 32$ . Interpret the slope in context.

💡 Show Solution

The slope is 3.2.

Interpretation: For each additional year of experience, the predicted salary increases by $3,200 (3.2 thousand dollars).

Template: "For each 1-unit increase in [x-variable], the [y-variable] is predicted to [increase/decrease] by [slope] [units]."

Note: The $y$ -intercept of 32 means a person with 0 years of experience has a predicted salary of $32,000.

5Problem 5medium

❓ Question:

The line of best fit is $y = -0.5x + 100$ . A data point has coordinates $(30, 88)$ . What is the residual for this point?

💡 Show Solution

Step 1: Find the predicted value at $x = 30$ : $\hat{y} = -0.5(30) + 100 = -15 + 100 = 85$

Step 2: Calculate the residual: $\text{Residual} = \text{Actual} - \text{Predicted} = 88 - 85 = 3$

Answer: The residual is $+3$ .

Interpretation: The actual value (88) is 3 units ABOVE the predicted value (85), so this point lies above the line of best fit.

6Problem 6medium

❓ Question:

The line of best fit is $y = -0.5x + 100$ . A data point has coordinates $(30, 88)$ . What is the residual for this point?

💡 Show Solution

Step 1: Find the predicted value at $x = 30$ : $\hat{y} = -0.5(30) + 100 = -15 + 100 = 85$

Step 2: Calculate the residual: $\text{Residual} = \text{Actual} - \text{Predicted} = 88 - 85 = 3$

Answer: The residual is $+3$ .

Interpretation: The actual value (88) is 3 units ABOVE the predicted value (85), so this point lies above the line of best fit.

7Problem 7hard

❓ Question:

A researcher collects data and finds a correlation coefficient of $r = 0.85$ between ice cream sales and drowning incidents. Can the researcher conclude that eating ice cream causes drowning?

💡 Show Solution

Answer: No!

Explanation: A strong correlation ( $r = 0.85$ ) shows that ice cream sales and drowning incidents are associated — they tend to increase together. However, correlation does NOT prove causation.

What's really happening: There is a confounding variable — hot weather. When it's hot:

More people buy ice cream
More people go swimming → more drownings

The heat is the common cause. Ice cream doesn't cause drowning.

SAT Rule: Only a randomized controlled experiment can establish causation. Observational studies can only show association.

8Problem 8hard

❓ Question:

A researcher collects data and finds a correlation coefficient of $r = 0.85$ between ice cream sales and drowning incidents. Can the researcher conclude that eating ice cream causes drowning?

💡 Show Solution

Answer: No!

What's really happening: There is a confounding variable — hot weather. When it's hot:

More people buy ice cream
More people go swimming → more drownings

The heat is the common cause. Ice cream doesn't cause drowning.

SAT Rule: Only a randomized controlled experiment can establish causation. Observational studies can only show association.

9Problem 9expert

❓ Question:

A line of best fit is $y = 1.8x + 22$ for data where $x$ ranges from $5$ to $50$ . Which of the following predictions is most reliable?

A) Predicting $y$ when $x = 30$ B) Predicting $y$ when $x = 80$ C) Predicting $y$ when $x = 100$ D) Predicting $y$ when $x = -5$

💡 Show Solution

Key concept: Interpolation vs. Extrapolation

The data ranges from $x = 5$ to $x = 50$ .

A) $x = 30$ : This is WITHIN the data range → interpolation → most reliable ✓ B) $x = 80$ : Beyond the range → extrapolation → less reliable ✗ C) $x = 100$ : Far beyond the range → extrapolation → unreliable ✗ D) $x = -5$ : Below the range → extrapolation → unreliable ✗

Answer: A

SAT Tip: Predictions within the data range (interpolation) are more trustworthy than predictions outside it (extrapolation). The farther outside the range, the less reliable the prediction.

10Problem 10expert

❓ Question:

A line of best fit is $y = 1.8x + 22$ for data where $x$ ranges from $5$ to $50$ . Which of the following predictions is most reliable?

A) Predicting $y$ when $x = 30$ B) Predicting $y$ when $x = 80$ C) Predicting $y$ when $x = 100$ D) Predicting $y$ when $x = -5$

💡 Show Solution

Key concept: Interpolation vs. Extrapolation

The data ranges from $x = 5$ to $x = 50$ .

Answer: A

SAT Tip: Predictions within the data range (interpolation) are more trustworthy than predictions outside it (extrapolation). The farther outside the range, the less reliable the prediction.

Explain using:

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❓ Frequently Asked Questions

What is Scatterplots and Line of Best Fit?▾

Analyze scatterplots, determine lines of best fit, interpret slope and intercepts in context, and make predictions using linear and nonlinear models.

How can I study Scatterplots and Line of Best Fit effectively?▾

Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 10 problems provided, checking solutions as you go. Regular review and active practice are key to retention.

Is this Scatterplots and Line of Best Fit study guide free?▾

Yes — all study notes, flashcards, and practice problems for Scatterplots and Line of Best Fit on Study Mondo are free to access. No account is needed.

What course covers Scatterplots and Line of Best Fit?▾

Scatterplots and Line of Best Fit is part of the SAT Prep course on Study Mondo, specifically in the Problem-Solving and Data Analysis section. You can explore the full course for more related topics and practice resources.

Are there practice problems for Scatterplots and Line of Best Fit?▾

Yes, this page includes 10 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.

Scatterplots and Line of Best Fit

Try the Interactive Version!

Scatterplots and Line of Best Fit on the SAT

What Is a Scatterplot?

Types of Association

Strength of Association

Line of Best Fit (Regression Line)

Interpreting Slope in Context

Interpreting the yyy-Intercept

Residuals

Residual Plots

Correlation Coefficient (rrr)

Making Predictions

Interpolation vs. Extrapolation

SAT Question Types

Type 1: Describe the Association

Type 2: Interpret Slope or yyy-Intercept

Type 3: Find a Residual

Type 4: Make a Prediction

Type 5: Identify an Outlier

Common SAT Mistakes

📚 Practice Problems

1Problem 1easy

❓ Question:

2Problem 2easy

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3Problem 3medium

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4Problem 4medium

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5Problem 5medium

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6Problem 6medium

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7Problem 7hard

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8Problem 8hard

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9Problem 9expert

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10Problem 10expert

❓ Question:

Practice Lab

Practice with Flashcards

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📌 Related Topics in Problem-Solving and Data Analysis

❓ Frequently Asked Questions

Interpreting the $y$ -Intercept

Correlation Coefficient ( $r$ )

Type 2: Interpret Slope or $y$ -Intercept