Solve the problem.
-For the data below, determine the value of the linear correlation coefficient r between y and x2. $$\begin{array} { c | c c c c c }
\mathrm { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline \mathrm { y } & 1.6 & 4.7 & 9.9 & 24.5 & 39.0
\end{array}$$
A)0.913
B)0.990
C)0.985
D)0.873

Question

Solve the problem.
-For the data below, determine the value of the linear correlation coefficient r between y and x2. $$\begin{array} { c | c c c c c } 
\mathrm { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \
\hline \mathrm { y } & 1.6 & 4.7 & 9.9 & 24.5 & 39.0
\end{array}$$
A)0.913
B)0.990
C)0.985
D)0.873

Quizplus · Accepted Answer

The linear correlation coefficient $r$ between $y$ and $x^2$ can be calculated using the formula for Pearson's correlation coefficient. Given the data, when $x$ is squared, the relationship between $x^2$ and $y$ becomes more linear, suggesting a strong positive correlation. The exact calculation involves summing the products of the deviations of $x^2$ and $y$ from their means, dividing by the product of their standard deviations, and then averaging. This process yields a correlation coefficient very close to 1, indicating a nearly perfect linear relationship. Among the provided options, 0.990 is the closest to this description, suggesting a very strong linear relationship between $x^2$ and $y$.

Solve the Problem x1.22.74.46.69.5y1.64.79.924.539.0\begin{array} { c | c c c c c } \mathrm { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm { y } & 1.6 & 4.7 & 9.9 & 24.5 & 39.0\end{array}xy​1.21.6​2.74.7​4.49.9​6.624.5​9.539.0​​

Solve the Problem $\begin{array} { c | c c c c c } \mathrm { x } & 1.2 & 2.7 & 4.4 & 6.6 & 9.5 \\\hline \mathrm { y } & 1.6 & 4.7 & 9.9 & 24.5 & 39.0\end{array}$