Read the notes, then try the practice. It adapts as you go.When you're ready.
Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
11
Scatterplots are one of the most frequently tested representations on the Digital SAT. Students must interpret slope and y-intercept in real-world context, use the line of best fit to make predictions, analyze residual plots to judge model quality, and decide whether a linear or exponential model better fits a data pattern. This topic covers every scatterplot-and-modeling skill that appears on the SAT Math section.
Beyond reading graphs, the SAT asks students to reason about what a model means: what happens to the predicted value when the input changes by one unit, how much of the variation in y the model explains, and whether a pattern in the residuals signals that a different model type would be more appropriate. Mastering these questions requires fluency with the equation $\hat{y} = a + bx$, the residual formula $e = y - \hat{y}$, and the distinction between correlation and causation.
This module includes 15 SAT-style word problems that cover line of best fit, interpreting slope and intercept, residual analysis, $R^2$, correlation coefficient, linear vs. exponential growth comparisons, interpolation vs. extrapolation, and outlier effects. Each question features detailed step-by-step solutions, targeted misconception interventions, and adaptive follow-ups to build lasting statistical-reasoning skills.
One step at a time.
The straight line $\hat{y} = a + bx$ that minimizes the sum of squared residuals for a scatterplot. It summarizes the overall trend in the data.
Example: If a scatterplot of study hours vs. test score yields $\hat{y} = 52 + 4.3x$, then 0 hours predicts a score of 52, and each additional hour predicts 4.3 more points.
The slope $b$ in a regression equation $\hat{y} = a + bx$ represents the predicted change in the response variable $y$ for each 1-unit increase in the explanatory variable $x$. The SAT always asks you to interpret slope using the units of both variables.
Example: If $\hat{y} = 200 + 15x$ models cost (dollars) vs. number of guests, the slope means 'each additional guest increases the predicted cost by $\$15$.'
The constant $a$ in $\hat{y} = a + bx$ is the predicted value of $y$ when $x = 0$. On the SAT, you must state its meaning in the scenario and note whether $x = 0$ makes practical sense.
Example: In $\hat{y} = 200 + 15x$ for party cost vs. guests, the y-intercept 200 represents a fixed base cost when there are 0 guests (e.g., a venue rental fee).
The difference between an observed value and its predicted value: $e = y - \hat{y}$. A positive residual means the actual value is above the line; a negative residual means the actual value is below.
Example: If the model predicts $\hat{y} = 80$ but the actual score is 73, the residual is $73 - 80 = -7$, meaning the student scored 7 points below the prediction.
A graph of residuals vs. the explanatory variable $x$. If residuals scatter randomly around 0, a linear model is appropriate. A curved pattern suggests a nonlinear model would fit better.
Example: A U-shaped residual plot for a linear model of population growth suggests that an exponential or quadratic model would capture the curvature the line misses.
A number from $-1$ to $1$ that measures the strength and direction of a linear relationship. Values near $\pm 1$ indicate strong linear association; values near 0 indicate weak or no linear association.
Example: $r = 0.92$ indicates a strong positive linear relationship; $r = -0.15$ indicates a weak negative one.
$R^2$ is the proportion (0 to 1) of the variance in $y$ that is explained by the linear model. It equals the square of $r$.
Example: If $r = 0.9$, then $R^2 = 0.81$, meaning 81% of the variation in $y$ is explained by the model.
A linear model has constant additive change: $y = a + bx$. An exponential model has constant multiplicative (percent) change: $y = a \cdot b^x$ with $b > 0, b \neq 1$. For large $x$ with $b > 1$, exponential growth always overtakes linear growth.
Example: A savings account earning 3% annually is exponential ($y = 1000 \cdot 1.03^t$), while adding a flat $\$30$/month is linear ($y = 1000 + 30t$).
More terms are available in the glossary.
Choose a different way to engage with this topic — no grading, just richer thinking.
Explore your way — choose one:
See how the key ideas connect. Nodes color in as you practice.
Walk through a solved problem step-by-step. Try predicting each step before revealing it.
This is guided practice, not just a quiz. Hints and pacing adjust in real time.
Small steps add up.
What you get while practicing:
The best way to know if you understand something: explain it in your own words.
More ways to strengthen what you just learned.