Answered

Join the IDNLearn.com community and start getting the answers you need today. Ask anything and receive thorough, reliable answers from our community of experienced professionals.

Which table shows no correlation?

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 3 & 5 & 6 & 8 & 10 & 14 & 15 \\
\hline y & -1 & -2 & -3 & -2 & -5 & -4 & -8 \\
\hline
\end{array}
\][/tex]

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 3 & 5 & 6 & 8 & 10 & 14 & 15 \\
\hline y & -6 & -7 & -4 & -2 & 0 & -1 & 3 \\
\hline
\end{array}
\][/tex]

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 3 & 5 & 6 & 8 & 10 & 14 & 15 \\
\hline y & -2 & -4 & 6 & 8 & 12 & 10 & -16 \\
\hline
\end{array}
\][/tex]

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 3 & 5 & 6 & 8 & 10 & 14 & 15 \\
\hline y & -3 & -5 & -9 & -11 & -13 & -15 & -17 \\
\hline
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To determine which table shows no correlation, we need to calculate the Pearson correlation coefficient for each table. The Pearson correlation coefficient is a measure of the strength and direction of the relationship between two variables.

Here are the steps:

1. Identify the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] values for each table.
2. Calculate the Pearson correlation coefficient for each table.
3. Determine which correlation coefficient is closest to zero, indicating no correlation.

Now, let's consider the given correlation coefficients for the tables:

- The correlation coefficient for the first table is [tex]\(-0.8548\)[/tex].
- The correlation coefficient for the second table is [tex]\(0.9031\)[/tex].
- The correlation coefficient for the third table is [tex]\(-0.1036\)[/tex].
- The correlation coefficient for the fourth table is [tex]\(-0.9666\)[/tex].

The coefficient closest to zero is [tex]\(-0.1036\)[/tex], which corresponds to the third table. This indicates that the third table exhibits the least correlation, closest to none.

Therefore, the table showing no correlation is the third table:

[tex]\[ \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline $x$ & 3 & 5 & 6 & 8 & 10 & 14 & 15 \\ \hline $y$ & -2 & -4 & 6 & 8 & 12 & 10 & -16 \\ \hline \end{tabular} \][/tex]
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.