Scatterplots

Learn scatterplot coordinates, local point comparisons.

Lesson 1 of 32 parts Practice Flashcards

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Scatterplot Coordinates

Objective: Explain scatterplot coordinates, apply the stated method, and check its conditions.

A scatterplot displays paired numerical observations. Each point retains the pairing for one observational unit. Vertical differences compare outputs for selected points, but pattern assessment requires the full set, including form, direction, strength, and possible unusual points. Two selected points do not characterize the full dataset.

Formulas

Point=(x measurement, y measurement) for the same unit

Worked examples

Try itA synthetic scatterplot has points (7,7) and (13,49). Find the change in y between these points.Show answer

Step 1: Compare vertical coordinates, retaining the data units. Step 2: Compute (49)−7. Step 3: The y change is 42; two points alone do not characterize a full association.

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Scatterplot Coordinates

Objective: Explain scatterplot coordinates, apply the stated method, and check its conditions.

Formulas

Point=(x measurement, y measurement) for the same unit

Worked examples

Try itA synthetic scatterplot has points (7,7) and (13,49). Find the change in y between these points.Show answer

Step 1: Compare vertical coordinates, retaining the data units. Step 2: Compute (49)−7. Step 3: The y change is 42; two points alone do not characterize a full association.

Local Point Comparisons

Objective: Explain local point comparisons, apply the stated method, and check its conditions.

A line joining two scatterplot points has slope Δy/Δx when their x-values differ. This two-point slope is not necessarily a fitted regression coefficient. Whole-dataset modeling uses all observations and should consider nonlinear structure, leverage, and context. Do not substitute a chosen two-point slope for a fitted regression coefficient.

Formulas

Two-point slope=(y₂−y₁)/(x₂−x₁)

Worked examples

Try itA synthetic scatterplot has points (7,7) and (13,49). Find the slope joining them.Show answer

Step 1: Slope compares y change with x change. Step 2: The changes are 42 and 6. Step 3: The slope is 7.

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