Pregunta
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
.
Choose the correct answer below.
A. The value of
B. The value of
C. The value of
D. The value of
Ask by Deleon Willis. in the United States
Mar 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The value of
and
always have the same sign.
Solución
-
The linear correlation coefficient,
, measures the strength and direction of a linear relationship between two variables. -
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. -
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
.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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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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