Correlation and Determination
What does a correlation coefficient of r = 0.98 indicate?
A very strong positive linear relationship.
Q: What is the “form” of a relationship shown in a scatterplot?
A: Whether it is linear or non-linear.
Q: In the regression line y=2.3x + 3, what does the slope represent?
A: The x increases by 2.3
Q: Shoe size and reading level—what type of association?
A: Common response (age).
Q: What is an outlier?
A: A data point that does not follow the pattern.
If r = 0.5, what is R² as a percentage?
R² = 0.25, which is 25%
Q: If the points slope downwards from left to right, what is the direction?
A: Negative.
Q: In the same line y=2.3x + 5, what does the y-intercept represent?
A: Predicted y value of 5 revenue when x = 0
Q: Number of fire trucks and property damage— what type of association?
A: Confounded (big fires cause both).
Q: What effect does an outlier have on r?
A: It weakens the correlation.
What does R² represent?
The percentage of variation explained by the model.
Q: Describe the association between health expenditure and infant mortality.
A: Moderate to strong negative linear relationship.
Q: What is the formula for a residual?
A: Residual = actual y – predicted y.
Q: Ice-cream sales and drowning incidents— what type of association?
A: Common response (hot weather).
Q: In a residual plot, what pattern indicates a poor fit?
A: A curved or systematic pattern.
What value of r indicates NO linear association?
r = 0.
Q: Name one reason it is appropriate to calculate r for the health vs mortality data.
A: The relationship is reasonably linear.
Q: If the slope is negative, what does this mean?
A: As x increases, y decreases.
Q: Pirates vs global temperature— what type of association??
A: Coincidental
Q: If an outlier lies far above the regression line, what is the residual?
A: A large positive residual.
Q: What does the remaining (1 – R²) represent?
A: Variation explained by other factors not in the model.
Q: What type of plot shows whether data points fit the regression line well?
A: A residual plot.
Q: If an outlier is removed, how will the slope and r typically change?
A: Both become stronger (slope steeper, |r| increases).
Q: Explain why correlation does not imply causation.
A: A third variable may be influencing both.
Q: Why should outliers be investigated rather than simply removed?
A: They may indicate errors or meaningful unusual cases.