Let $x$ be the average number of employees in a group health insurance plan, and let $y$ be the average administrative cost as a percentage of claims. Suppose a random sample of employees gave the following information.
\begin{tabular}{l|lllll}
\hline$x$ & 2 & 8 & 14 & 32 & 73 \\
\hline$y$ & 50 & 45 & 35 & 28 & 16 \\
\hline
\end{tabular}

As $x$ increases, does the value of $r$ imply that $y$ should tend to increase, decrease, or remain the same? Explain.
Since $r$ is negative, as $x$ increases, $y$ remains the same.
Since $r$ is zero, as $x$ increases, $y$ decreases.
Since $r$ is zero, as $x$ increases, $y$ remains the same.
Since $r$ is negative, as $x$ increases, $y$ decreases.
Since $r$ is zero, as $x$ increases, $y$ increases.

Step 1 ：The question is asking about the correlation coefficient, denoted as 'r', between the average number of employees in a group health insurance plan (x) and the average administrative cost as a percentage of claims (y). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative relationship, 1 indicates a strong positive relationship, and 0 indicates no relationship.

Step 2 ：In this case, we need to calculate the correlation coefficient 'r' between x and y to determine the relationship. If 'r' is positive, as x increases, y should also increase. If 'r' is negative, as x increases, y should decrease. If 'r' is zero, there is no linear relationship between x and y, so we cannot predict the behavior of y as x increases.

Step 3 ：Let's calculate 'r' using the given data. The data for x is [2, 8, 14, 32, 73] and for y is [50, 45, 35, 28, 16].

Step 4 ：The correlation coefficient 'r' is calculated to be approximately -0.95, which is close to -1. This indicates a strong negative linear relationship between x and y.

Step 5 ：Therefore, as x increases, y should tend to decrease.

Step 6 ：Final Answer: \(\boxed{\text{As x increases, y should tend to decrease.}}\)