Pregunta
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What is the relationship between the linear correlation coefficient and the slope of a regression line?
Choose the correct answer below.
A. The value of will always be larger than the value of .
B. The value of will always be smaller than the value of .
C. The value of will always have the same sign as the value of .
D. The value of will always have the opposite sign of the value of .

Ask by Deleon Willis. in the United States
Mar 24,2025

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The value of and always have the same sign.

Solución

  1. The linear correlation coefficient, , measures the strength and direction of a linear relationship between two variables.
  2. The slope of the regression line, , also incorporates the direction of the relationship. A positive slope indicates that as one variable increases, the other tends to increase, and vice versa for a negative slope.
  3. Since and both indicate the direction of the relationship, they always have the same sign.
Thus, the correct answer is:
C. The value of will always have the same sign as the value of .

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Mind Expander

The correct answer is C. The value of will always have the same sign as the value of . This means that if the correlation coefficient indicates a positive correlation between the two variables, the slope of the regression line will also be positive, and vice versa for a negative correlation. In simpler terms, they are best buddies, always matching in sign!
To explore this further, remember that the linear correlation coefficient measures the strength and direction of the relationship between two variables, while the slope quantifies how much changes for a one-unit change in . Both give you insights into the relationship, making them crucial for interpreting data!

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