Correlation is a statistical relationship between two variables where changes in one are associated with changes in the other. Positive correlation means both increase together; negative correlation means one increases as the other decreases; no correlation means no consistent pattern.
When one thing goes up and another tends to go up with it (like study time and test scores), that's positive correlation. When one goes up and the other goes down (like TV time and exercise), that's negative correlation. They 'move together' in some pattern.
Showing a random 20 of 50 problems.
Example 1
medium
If y is constant for all x, what is r?
Example 2
easy
A car's age vs. its resale value. What sign of r would you expect?
Example 3
easy
As outdoor temperature rises, hot-chocolate sales fall. What type of correlation is this?
Example 4
easy
Outdoor temperature vs. heating bill in winter usually shows what kind of correlation?
Example 5
medium
Data points: as x goes 1,2,3,4, y goes 2,4,6,8. Describe the correlation and its strength.x: 1, 2, 3, 4 → y: 2, 4, 6, 8
Example 6
easy
Which correlation is stronger: r=0.6 or r=−0.8?
Example 7
medium
Is r affected if both x and y are multiplied by 10?
Example 8
medium
Variable x is in meters and y in kilograms with r=0.7. If x is reconverted to centimeters (multiply by 100), what happens to r?
Example 9
easy
What is the range of possible values for the correlation coefficient r?
Example 10
medium
A study finds a strong positive correlation between the number of firefighters at a fire and the damage caused. Does this mean sending more firefighters causes more damage? Explain.
Example 11
medium
A scatter plot shows that as hours of study increase, test scores tend to increase. Describe the correlation and state whether it implies causation.
Example 12
medium
Two variables have r=0.6. A single new outlier is added that is far from the trend. Will ∣r∣ tend to increase or decrease?
Example 13
medium
Two variables have r=0.5. What fraction of the variation in y is explained by the linear relationship?
Example 14
medium
Does correlation depend on which variable is called x and which is called y?
Example 15
hard
A study finds r=0.10 between coffee and longevity. The author claims coffee strongly affects longevity. Critique.
Example 16
medium
If r=0 between two variables, can we conclude they are unrelated?
Example 17
medium
A scatter plot of weight vs. price for diamonds shows tight upward trend except for one $10,000 diamond weighing 0.1 carat. Should this outlier raise concern?Diamond weight (carats) vs. price ($) — should the outlier at 0.1 carat, $10,000 raise concern?
Example 18
challenge
Suppose z=x+y where x and y are unrelated. Why would z be positively correlated with x even though x and y are not correlated?
Example 19
medium
Two studies report r=0.3 and r=0.85 for the same kind of relationship. Which study's data shows points clustering more tightly around a line?
Example 20
medium
Data: (1,2),(2,3),(3,4),(4,5),(5,6). What is r?Data: (1,2), (2,3), (3,4), (4,5), (5,6)