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The correlation coefficient, often expressed as r, indicates a measure of the direction and strength of a relationship between two variables. When the r value is closer to +1 or -1, it indicates that there is a stronger linear relationship between the two variables.

A negative correlation can indicate a strong relationship or a weak relationship. A correlation of -1 indicates a near perfect relationship along a straight line, which is the strongest relationship possible. The minus sign simply indicates that the line slopes downwards, and it is a negative relationship.

The correlation coefficient measures the strength of the relationship between two variables. If they had a correlation coefficient of -0.1, it would be considered a weak negative correlation.

A negative correlation is a relationship between two variables in which an increase in one variable is associated with a decrease in the other. An example of negative correlation would be height above sea level and temperature. As you climb the mountain (increase in height) it gets colder (decrease in temperature).

A negative r values indicates that as one variable increases the other variable decreases, and an r of -1 indicates that knowing the value of one variable allows perfect prediction of the other. A correlation coefficient of 0 indicates no relationship between the variables (random scatter of the points).

Limitations to Correlation and Regression

- We are only considering LINEAR relationships.
- r and least squares regression are NOT resistant to outliers.
- There may be variables other than x which are not studied, yet do influence the response variable.
- A strong correlation does NOT imply cause and effect relationship.
- Extrapolation is dangerous.