To determine the type of correlation for the given data set, we need to analyze the relationship between the variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex]. One way to do this is by calculating the correlation coefficient, which quantifies the degree to which two variables are linearly related.
The given data is:
[tex]\[
\begin{array}{c|ccccc}
x & 0 & 1 & 2 & 3 & 4 \\
\hline
y & 24 & 9 & 8 & 12 & 6 \\
\end{array}
\][/tex]
After performing the necessary calculations, the correlation coefficient for the data set is found to be approximately [tex]\(-0.7292\)[/tex].
The correlation coefficient, often denoted as [tex]\( r \)[/tex], ranges from [tex]\(-1\)[/tex] to [tex]\(1\)[/tex]:
- If [tex]\( r \)[/tex] > 0, there is a positive correlation, meaning as [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] tends to increase.
- If [tex]\( r \)[/tex] < 0, there is a negative correlation, meaning as [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] tends to decrease.
- If [tex]\( r = 0 \)[/tex], there is no correlation, indicating no linear relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
Given the correlation coefficient of approximately [tex]\(-0.7292\)[/tex]:
- Since [tex]\(-0.7292\)[/tex] is less than [tex]\(0\)[/tex], it indicates a negative correlation.
Thus, the type of correlation for the given data set is Negative.
