A scatter plot displays two related numerical variables as points on a graph, helping reveal whether a relationship (correlation) exists between them. Positive correlation means as one variable increases, so does the other; negative correlation means as one increases, the other decreases. A line of best fit summarises the trend, and can be used to make predictions — though correlation alone doesn't prove one variable causes the other.
Example
A scatter plot of hours studied versus test score, with points generally trending upward, shows positive correlation. A line of best fit through the data could then predict a likely score for a given number of study hours — while still not proving studying directly "causes" every point of improvement.
Key terms
Scatter plot:
A graph displaying two related variables as points.
Correlation:
The relationship or trend between two variables.
Line of best fit:
A line summarising the overall trend of scattered data.
Questions
1. A scatter plot displays:
Two related numerical variables as points
Only one variable
No numerical data at all
Only categories, never numbers
2. Positive correlation means:
As one variable increases, so does the other
As one increases, the other decreases
The variables have no relationship
Both variables stay exactly constant
3. Negative correlation means:
As one variable increases, the other decreases
Both variables increase together
The variables have no relationship
Both variables are always negative numbers
4. A line of best fit:
Summarises the overall trend of scattered data
Connects every single point exactly
Is always perfectly horizontal
Has no relationship to the data
5. No correlation means:
The two variables show no clear relationship
The variables are perfectly related
One variable causes the other
The data is always wrong
6. Hours studied and test scores generally showing an upward trend suggests:
Positive correlation
Negative correlation
No correlation
A causation guarantee
7. A scatter plot with points scattered randomly with no pattern suggests:
Little to no correlation
Strong positive correlation
Strong negative correlation
A perfect line of best fit
8. Ice cream sales and temperature showing an upward trend together suggests:
Positive correlation
Negative correlation
No correlation
They must be identical values
9. Hours spent watching TV and exam scores showing a downward trend suggests:
Negative correlation
Positive correlation
No correlation
A perfect causal relationship
10. A line of best fit can be used to:
Make predictions based on the trend
Guarantee a 100% accurate future value
Replace the need for any real data
Prove causation automatically
11. Why is correlation not the same as causation?
Two variables can be related without one directly causing the other
Correlation always proves one thing causes another
Causation and correlation are identical concepts
Correlation never has any relationship to causation
12. A scatter plot with points closely clustered around a clear upward line shows:
Strong positive correlation
Weak or no correlation
Strong negative correlation
An error in the data
13. Using a line of best fit to estimate a value within the range of existing data is called:
Interpolation
Extrapolation only
Causation
A random guess
14. Using a line of best fit to predict a value far beyond the existing data range is called:
Extrapolation
Interpolation only
Causation
A guaranteed accurate prediction
15. A study finds ice cream sales and shark attacks are positively correlated. The most likely explanation is:
Both increase in summer due to a third factor (warm weather), not because one causes the other
Ice cream directly causes shark attacks
Shark attacks directly cause more ice cream sales
The correlation must be completely fabricated
16. Why is extrapolation (predicting far beyond your data range) considered less reliable than interpolation?
The trend might not continue in the same way outside the range where it was actually observed
Extrapolation is always more accurate than interpolation
Data trends always continue identically forever in every direction
There is no meaningful difference between the two
17. A scatter plot shows a strong correlation, but a closer look reveals one extreme outlier skewing the line of best fit. This shows:
Outliers can distort trend lines and should be considered carefully
Outliers always improve the accuracy of a trend line
Outliers have no effect on a line of best fit
A single outlier should always be ignored automatically without consideration
18. Why might researchers be cautious about claiming a causal relationship from an observational scatter plot alone?
Correlational data alone cannot rule out other explanations or reversed causation
Scatter plots always definitively prove causation
Observational data is always identical to experimental data
Causation can always be assumed once correlation is found
19. A "weak" correlation (points loosely scattered but with a slight trend) suggests:
Some relationship exists, but it does not explain the data very precisely
No relationship exists at all
A perfect, guaranteed predictive relationship
The data must be measured incorrectly
20. Why might two variables show a strong correlation purely by coincidence, especially with a small data set?
Random chance can sometimes produce apparent patterns, especially with limited data
Correlation can never occur by random chance
Small data sets always produce the most reliable correlations
Coincidental correlation is impossible in statistics
21. A scatter plot of ice cream sales versus temperature, and a separate one of sunscreen sales versus temperature, both show positive correlation. This suggests:
Temperature may be a common underlying factor influencing both, not that one causes the other
Ice cream sales must directly cause sunscreen sales
The two scatter plots have no possible connection
Correlation with a third variable is impossible
Answer key (parent copy)
1. Two related numerical variables as points
2. As one variable increases, so does the other
3. As one variable increases, the other decreases
4. Summarises the overall trend of scattered data
5. The two variables show no clear relationship
6. Positive correlation
7. Little to no correlation
8. Positive correlation
9. Negative correlation
10. Make predictions based on the trend
11. Two variables can be related without one directly causing the other
12. Strong positive correlation
13. Interpolation
14. Extrapolation
15. Both increase in summer due to a third factor (warm weather), not because one causes the other
16. The trend might not continue in the same way outside the range where it was actually observed
17. Outliers can distort trend lines and should be considered carefully
18. Correlational data alone cannot rule out other explanations or reversed causation
19. Some relationship exists, but it does not explain the data very precisely
20. Random chance can sometimes produce apparent patterns, especially with limited data
21. Temperature may be a common underlying factor influencing both, not that one causes the other