$\begin{array} { c | c c c c c c c c }
\mathrm { x } & 10 & 11 & 16 & 9 & 7 & 15 & 16 & 10 \
\hline \mathrm { y } & 96 & 51 & 62 & 58 & 89 & 81 & 46 & 51
\end{array}$
A) r=-0.335 ; no linear relation exists
B) r=0.462 ; linear relation exists
C) r=-0.335 ; linear relation exists
D) r=-0.284 ; no linear relation exists

Question

$\begin{array} { c | c c c c c c c c } 
\mathrm { x } & 10 & 11 & 16 & 9 & 7 & 15 & 16 & 10 \
\hline \mathrm { y } & 96 & 51 & 62 & 58 & 89 & 81 & 46 & 51
\end{array}$
A)  r=-0.335 ; no linear relation exists
B)  r=0.462 ; linear relation exists
C)  r=-0.335 ; linear relation exists
D)  r=-0.284 ; no linear relation exists

Quizplus · Accepted Answer

DThe correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. A value of r close to 1 or -1 indicates a strong linear relationship, while a value close to 0 suggests little to no linear relationship. Both options A and D suggest weak linear relationships (r values close to 0), but without calculating the exact correlation coefficient, it's not possible to determine the precise value or the existence of a linear relationship based solely on the options provided. However, the presence of a correlation coefficient (whether positive or negative) does not necessarily mean there is no linear relation; it indicates the strength and direction of the relation. The interpretation of "no linear relation exists" is incorrect if taken to mean that there is no relationship at all; rather, it should be understood as indicating a weak linear relationship. Therefore, the correct understanding revolves around the strength of the correlation, not the absolute presence or absence of any relationship.

A) R=-0335 ; No Linear Relation Exists B) R=0

A) R=-0335 ; No Linear Relation Exists
B) R=0