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Chapter 13: Problem 59

What does a linear correlation coefficient tell about the relationship between two variables? Within what range can a correlation coefficient assume a value?

Short Answer

Expert verified
The Linear Correlation Coefficient measures the strength and direction of the linear relationship between two variables. It can assume a value between -1 and 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and values near zero suggest no correlation.

Step by step solution

01

Understand the concept of a correlation coefficient

The linear correlation coefficient, also known as Pearson's correlation coefficient, measures the strength and direction of association between two continuous variables. If the correlation coefficient is close to +1, it means there's a strong positive linear relationship, meaning as one variable increases, the other also increases. If it鈥檚 close to -1, there's a strong negative linear relationship, which means as one variable increases, the other decreases. A value close to zero suggests there's no linear correlation between the variables.
02

Understand the range of values a correlation coefficient can assume

The correlation coefficient is always between -1 and 1, inclusive. This means the lowest possible value it can assume is -1 (indicating a perfect negative correlation), the highest possible value is 1 (indicating a perfect positive correlation) and it could be anywhere between these values.

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