Find the value of the linear correlation coefficient r.
-$\begin{array}{r|rrrrr}
x & 1 & 3 & 5 & 7 & 9 \
\hline y & 143 & 116 & 100 & 98 & 90
\end{array}$
A) $\hat { y } = - 150.7 + 6.8 x$
B) $\hat { y } = 140.4 - 6.2 x$
C) $\hat { y } = - 140.4 + 6.2 x$
D) $\hat { y } = 150.7 - 6.8 x$

Question

Find the value of the linear correlation coefficient r.
-$\begin{array}{r|rrrrr}
x & 1 & 3 & 5 & 7 & 9 \
\hline y & 143 & 116 & 100 & 98 & 90
\end{array}$
A) $\hat { y }  = - 150.7 + 6.8 x$
B) $\hat { y } = 140.4 - 6.2 x$
C) $\hat { y } = - 140.4 + 6.2 x$
D) $\hat { y } = 150.7 - 6.8 x$

Quizplus · Accepted Answer

The linear correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. To find the value of $r$, we don't directly calculate $r$ from the options given but rather identify the correct linear regression equation that fits the data points. The correct equation should have a negative slope since the $y$ values decrease as the $x$ values increase, indicating a negative correlation. Among the options, only option B, $\hat { y } = 140.4 - 6.2 x$, correctly represents a decreasing trend. Therefore, without calculating $r$ directly, we infer that the equation that best fits the data points is the one that shows a negative correlation, which is option B.

Find the Value of the Linear Correlation Coefficient R x13579y1431161009890\begin{array}{r|rrrrr}x & 1 & 3 & 5 & 7 & 9 \\\hline y & 143 & 116 & 100 & 98 & 90\end{array}xy​1143​3116​5100​798​990​​

Find the Value of the Linear Correlation Coefficient R $\begin{array}{r|rrrrr}x & 1 & 3 & 5 & 7 & 9 \\\hline y & 143 & 116 & 100 & 98 & 90\end{array}$