Card 1 of 20
EasyStudy card 1
Prompt
What does a scatter plot display?
Each point is one pair \((x,y)\).
Answer
Paired numerical observations for two variables.
Example
Study hours and practice score.
MathChapter 8: Statistics
Flashcards
Scatter Plots Flashcards
Twenty concise cards on association, regression, slope, prediction, residuals, extrapolation, outliers, and nonlinear form.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is a positive association?
The point cloud rises overall.
Answer
Larger \(x\)-values tend to occur with larger \(y\)-values.
Example
More study time tends to accompany higher scores.
Card 3 of 20
EasyStudy card 3
Prompt
What is a negative association?
The point cloud falls overall.
Answer
Larger \(x\)-values tend to occur with smaller \(y\)-values.
Example
As speed rises, travel time may fall.
Card 4 of 20
EasyStudy card 4
Prompt
What is no clear association?
The points form an unstructured cloud.
Answer
No consistent upward or downward pattern is visible.
Example
Input gives little linear predictive information.
Card 5 of 20
EasyStudy card 5
Prompt
What describes association form?
Look for a straight band or curve.
Answer
Whether the pattern is linear or nonlinear.
Example
An upward bend is nonlinear.
Card 6 of 20
EasyStudy card 6
Prompt
What describes association strength?
Less scatter around the form means stronger association.
Answer
How tightly points follow the overall pattern.
Example
A narrow band is stronger than a diffuse cloud.
Card 7 of 20
EasyStudy card 7
Prompt
Does association prove causation?
Study design and context are required.
Answer
No.
Example
A lurking variable may explain both measurements.
Card 8 of 20
MediumStudy card 8
Prompt
What is a line of best fit?
It need not pass through every point.
Answer
A line summarizing the center of a linear association for prediction.
Example
\(\hat{y}=6x+48\).
Card 9 of 20
MediumStudy card 9
Prompt
What does \(\hat{y}\) mean?
The hat distinguishes model output from observation.
Answer
The response predicted by a model.
Example
At \(x=5\), the model may give \(\hat{y}=78\).
Card 10 of 20
MediumStudy card 10
Prompt
How is regression slope interpreted?
Include response units per input unit.
Answer
Predicted response change for each one-unit increase in the explanatory variable.
Example
\(6\) score points per study hour.
Card 11 of 20
MediumStudy card 11
Prompt
What does the intercept represent?
Check whether zero is meaningful.
Answer
The predicted response when input equals \(0\).
Example
In \(\hat{y}=6x+48\), the intercept is \(48\).
Card 12 of 20
MediumStudy card 12
Prompt
What is a residual?
Keep the subtraction order.
Answer
Observed minus predicted: \(y-\hat{y}\).
Example
Observed \(81\), predicted \(84\): residual \(-3\).
Card 13 of 20
MediumStudy card 13
Prompt
What does a positive residual mean?
Observed exceeds predicted.
Answer
The observed point lies above the model line.
Example
Residual \(4\) means the model underpredicted by \(4\).
Card 14 of 20
MediumStudy card 14
Prompt
What does a negative residual mean?
Observed is less than predicted.
Answer
The observed point lies below the model line.
Example
Residual \(-2\) means the model overpredicted by \(2\).
Card 15 of 20
MediumStudy card 15
Prompt
What is interpolation?
It stays among known inputs.
Answer
Prediction within the observed input range.
Example
Observed \(x\) from \(1\) to \(7\); predict at \(5\).
Card 16 of 20
MediumStudy card 16
Prompt
What is extrapolation?
The pattern may change outside the data.
Answer
Prediction beyond the observed input range.
Example
Observed through \(x=7\); predict at \(x=20\).
Card 17 of 20
HardStudy card 17
Prompt
Why is extrapolation risky?
Models are not guarantees.
Answer
The observed relationship may not continue beyond the data range.
Example
A linear trend may flatten later.
Card 18 of 20
HardStudy card 18
Prompt
What is an outlier on a scatter plot?
Inspect it rather than automatically deleting it.
Answer
A point unusually far from the overall pattern.
Example
It may be an error or a meaningful unusual case.
Card 19 of 20
HardStudy card 19
Prompt
What visual feature suggests a nonlinear model?
Residuals from a line may also curve.
Answer
A systematic curve in the point cloud.
Example
Quadratic or exponential form may be more appropriate.
Card 20 of 20
HardStudy card 20
Prompt
What is a reliable regression strategy?
Label the quantities.
Answer
Separate observed \(y\), predicted \(\hat{y}\), slope units, and residual before calculating.
Example
Compute prediction first, then residual.
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