Scatterplot Mastery Reference Chart
Scatterplot Mastery Reference Chart
9th Grade Algebra I • Interpreting Bivariate Data, Patterns, & Linear Models
Name:
Period:
1. Bivariate Data Anatomy
\(x\)-Axis: Explanatory / Independent
The input variable thought to explain or predict changes (e.g., hours studied, daily temperature).
\(y\)-Axis: Response / Dependent
The outcome measured to see if it responds to \(x\) (e.g., test score, ice cream sales).
Point \((x, y)\): Paired Observation
A single dot showing two numeric measurements from the exact same person, item, or event.
2. Association • Direction, Form, & Strength
Describe all 3: Direction + Form + Strength
Positive Association
As \(x\) increases, \(y\) tends to increase.
Positive slope (\(m > 0\))
Negative Association
As \(x\) increases, \(y\) tends to decrease.
Negative slope (\(m < 0\))
No Association
Points are scattered randomly.
No predictable relationship.
Form: Linear (forms a straight path) vs. Non-Linear (curves, arches, or changes direction).
Strength: Strong (points hug trend closely) vs. Moderate / Weak (points spread loosely around trend).
3. Reading Data Features • Clusters, Gaps, & Outliers
Cluster A GAP Cluster B Outlier
Cluster (Grouping): A concentrated subgroup of data points bunching together. Often reveals distinct categories or subpopulations.
Gap (Empty Interval): A noticeable interval along the \(x\)-axis where no data values appear. Indicates missing ranges or boundaries.
Outlier (Anomalous Point): A point that falls far outside the overall pattern. Always inspect outliers to see if they are measurement errors or special cases.
4. Line of Best Fit (Trend Line) & Predictions
\(y = mx + b\)
\(y\)-int \((b)\) Interpolate (Safe) Extrapolate
Slope \(m = \frac{\Delta y}{\Delta x}\) Rate of change: for each \(+1\) unit in \(x\), \(y\) changes by \(m\) units on average.
\(y\)-Intercept \((0, b)\) Initial value: the predicted value of \(y\) when explanatory variable \(x = 0\).
Rules for a Line of Best Fit: • Follows overall slope • Roughly equal points above and below • Passes close to the mean point \((\bar{x}, \bar{y})\).
Interpolation Predicting inside range of data. Accurate & reliable.
Extrapolation Predicting beyond range of data. Unreliable / risky!
Golden Rule: Correlation Does NOT Equal Causation!
A strong statistical relationship between \(x\) and \(y\) does not prove that \(x\) causes \(y\). A lurking third variable could influence both (e.g., hot weather increases both swimming pool visits and sunburns!).
ALGEBRA I CORE
