What does "related" or "correlated" mean?
When two data sets are correlated, they move in the same direction: when one rises, the other rises; when one falls, the other falls. When two data sets are inversely correlated, they move in opposite directions: when one rises, the other falls, and vice versa.
Please note that correlation does not imply causation! Two data sets could be highly correlated for completely non-causal reasons. For example, middle-school students' body height is highly correlated with their reading proficiency. It does not mean that being taller makes you a better reader, or that good readers tend to grow taller. But in middle school, taller people tend to be older, thus have had more years in school, thus are better readers. More information on correlation.
When two data sets are correlated, the points on a scatterplot are tightly clustered around a trendline (left).
When there is no correlation, the points are scattered (right).
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| Correlated plot |
Non-correlated plot |
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Method
To compute the correlation between two quantities, we load the data available for the 30 largest cities in your selected state and compute the Pearson correlation coefficient between these two data sets (r). If the absolute value of r is greater than the critical r value for a two-tailed test with 95% confidence and n-2 degrees of freedom, then there is a correlation between the two data sets.
In this case, the Pearson coefficient r = , the r2 value is , and the critical r for degrees of freedom is .
It is very important to note that even a strong correlation does not imply anything about a causal relationship between the two data sets. For example, middle-school students' body height is highly correlated with their reading proficiency. It does not mean that being taller makes you a better reader, or that good readers tend to grow taller. But in middle school, taller people tend to be older, thus have had more years in school, thus are better readers.
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