Sure! Let's analyze the given tables to see which one shows a negative correlation.
### Correlation Values:
1. First table: [tex]\( r \approx 0.953 \)[/tex]
2. Second table: [tex]\( r = 0 \)[/tex]
3. Third table: [tex]\( r \approx 0.050 \)[/tex]
4. Fourth table: [tex]\( r \approx -0.966 \)[/tex]
### Interpretation:
- Positive Correlation (r > 0): As [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] tends to increase.
- No Correlation (r = 0): [tex]\( x \)[/tex] and [tex]\( y \)[/tex] do not show any linear relationship.
- Negative Correlation (r < 0): As [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] tends to decrease.
#### Step-by-Step Analysis:
1. Table 1:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 2 & 5 & 6 & 7 & 10 & 12 \\
\hline
y & -8 & -5 & -6 & -3 & -2 & -1 \\
\hline
\end{array}
\][/tex]
- Correlation coefficient [tex]\( r \approx 0.953 \)[/tex]
- This is a strong positive correlation.
2. Table 2:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 2 & 5 & 6 & 7 & 10 & 12 \\
\hline
y & -5 & -5 & -5 & -5 & -5 & -5 \\
\hline
\end{array}
\][/tex]
- Correlation coefficient [tex]\( r = 0 \)[/tex]
- No correlation.
3. Table 3:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 2 & 5 & 6 & 7 & 10 & 12 \\
\hline
y & 6 & 3 & 1 & 1 & 3 & 6 \\
\hline
\end{array}
\][/tex]
- Correlation coefficient [tex]\( r \approx 0.050 \)[/tex]
- Very weak positive correlation.
4. Table 4:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 2 & 5 & 6 & 7 & 10 & 12 \\
\hline
y & 4 & 2 & -4 & -3 & -11 & -12 \\
\hline
\end{array}
\][/tex]
- Correlation coefficient [tex]\( r \approx -0.966 \)[/tex]
- This is a strong negative correlation.
### Conclusion:
Among the given tables, the fourth table shows a strong negative correlation with a correlation coefficient of approximately [tex]\( -0.966 \)[/tex].
