Scatterplot
Describe the association if points rise from left to right and follow a straight pattern.
Answer: Positive linear association
What does correlation measure?
Strength and direction of a linear relationship.
What is the purpose of a regression line?
To predict y using x.
Does correlation prove cause and effect?
No.
A student says r = 1.3. What is wrong?
Correlation must be between –1 and 1.
A scatterplot shows points tightly grouped around a curve. Is linear regression ideal? Why or why not?
No, because the relationship is not linear.
If r = –0.88, describe the relationship.
Strong negative linear association.
Interpret slope = 4.
Predicted y increases by 4 for every 1-unit increase in x.
What are the three things to describe in a scatterplot?
Form, direction, and strength.
A regression line predicts negative human height. What issue is this?
The model may be inappropriate or extrapolated.
What feature suggests an unusual observation needing investigation?
Outlier
Why does r have no units?
Correlation is standardized.
Interpret the y-intercept in context.
Predicted y when x = 0.
Why is association not always causation?
Other variables may influence both variables.
Two variables have r = 0. What statement can we make?
No linear relationship, but there could still be a non-linear relationship.
What does a cluster tell us about the data?
There may be groups with similar characteristics.
A graph shows strong curved association but r = 0.1. Explain.
Correlation only measures linear relationships.
Why should we avoid predicting far outside the data range?
Extrapolation may be unreliable.
Can a strong association exist without causation? Give an example.
Yes. Example: ice cream sales and drowning rates are related because of hot weather.
A scatterplot has strong negative association and one influential point. Predict what may happen if the point is removed.
Correlation and the regression line may change greatly.
Why might two clusters weaken correlation?
Different groups can distort the overall linear relationship.
If an outlier is removed and r changes from 0.45 to 0.91, what does this suggest?
The outlier strongly influenced correlation
Residual = –7. What does this mean?
Actual value is 7 below predicted value.
Why must context matter in statistics?
Numbers alone may mislead without real-world meaning.
A scatterplot shows strong positive association, but a student claims one variable causes the other. What statistical reasoning would you use to respond?
Correlation does not imply causation. Other variables or coincidence may explain the relationship.