Scatterplots and Lines of Best Fit
Key vocabulary and PSAT strategies for reading scatterplots and using trend lines to predict values.
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Questions Covered in This Set
10 cards to master
What is a scatterplot?
A graph with one dot per data point, independent variable on the x-axis and dependent variable on the y-axis.
What is the line of best fit?
The straight line that passes as close as possible to all the data points (also called a trend line or least-squares regression line). You never compute it by hand on the PSAT — you just use it.
How do you interpret the slope of a line of best fit?
As the predicted change in y for each 1-unit increase in x — always with units. Example: slope −1900 in P = 25000 − 1900a means the price drops about $1,900 per additional year of age.
What is a residual, and how do you compute it?
Residual = actual value − predicted value (dot minus line). Positive residual = dot above the line; negative = dot below the line.
"According to the line of best fit" vs. "according to the data" — what's the difference?
"Line of best fit" means read the y-value on the line; "the data" or "actual value" means read the dot. This wording trap is the most-tested idea.
Positive, negative, and no association — how do you tell them apart?
Dots trending upward = positive association; trending downward = negative; a shapeless cloud = no association. A curved pattern means the relationship is nonlinear.
When estimating slope from a drawn best-fit line, which points should you use?
Two points where the LINE crosses gridline intersections — not two data dots — then apply m = (y₂ − y₁)/(x₂ − x₁).
Interpolation vs. extrapolation
Interpolation predicts inside the data range and is reliable; extrapolation predicts far outside the range and is risky (e.g., predicting −$13,000 for a 20-year-old car).
How do you interpret the y-intercept of a best-fit line?
It's the predicted y-value when x = 0. In P = 25000 − 1900a, $25,000 is the predicted price of a brand-new (0-year-old) car.
Does a strong association prove causation?
No. Only a randomized controlled experiment supports a cause-and-effect conclusion, and results generalize only to the population that was randomly sampled.
