Unit 9 · Bivariate Data
A scatter plot shows bivariate numerical data. A line of best fit models the trend. Slope and intercept must be interpreted in context.
Positive, negative, or none. Linear or nonlinear. Strong or weak. Outliers sit apart from the cloud. Correlation is not causation — Algebra I will make that explicit.
If ŷ = 2.4x + 31 models minutes of practice (x) and quiz score (y), the slope 2.4 means each additional minute of practice is associated with about 2.4 more points. The intercept 31 is the model’s predicted score with 0 minutes of practice — which may or may not make sense in the real world.
A line that comes close to the data points and models the linear trend.
Example: A line through the middle of a positively associated cloud.
A data point that is unusually far from the overall pattern.
Example: A student who studied 5 minutes and scored 100 may be an outlier.
Try the prompt first. The steps stay folded until you ask to see them.
A model ŷ = 0.8t + 12 relates weeks of practice t to free-throw percentage. What does 0.8 mean?
Watch for
Saying the intercept always makes sense
x = 0 may be outside the data or physically impossible.
Fix: Ask whether the intercept is an interpolation or an extrapolation.
Submit each answer to check it. The key is not shown until you do.
The scatter plot of an alligator’s weight (pounds) versus growth time (weeks) is modeled by a line of best fit. Which statement best describes what the slope of that line represents?
Nathan models sunflower height y (cm) against fertilizer x (grams) with the line of best fit y = 0.35x + 2. Based on the model, what does the slope of the line represent?
The scatter plot of an alligator’s weight (pounds) versus growth time (weeks) is modeled by a line of best fit. Which statement best describes what the slope of that line represents?
Sort association cards: positive/negative/none paired with sample plots.
Algebra I: discuss residual sign (above/below the line) without requiring computation by hand.
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