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The table shows the ages and weights of babies at a hospital.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Age \\ (weeks)
\end{tabular} & 1 & 2 & 3 & 3 & 4 & 4 & 6 & 8 & 9 & 9 \\
\hline
\begin{tabular}{c}
Weight \\ (lbs)
\end{tabular} & 7.5 & 7.25 & 8.2 & 7.95 & 8.0 & 9.75 & 9.25 & 8.9 & 9.85 & 10.0 \\
\hline
\end{tabular}

What is the correlation between age and weight as shown in the table?

A. none
B. positive
C. negative
D. constant

Sagot :

GinnyAnswer
To determine the correlation between age and weight for the babies in the table, we need to calculate the correlation coefficient. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.

Let's analyze the data:

Ages (in weeks): 1, 2, 3, 3, 4, 4, 6, 8, 9, 9
Weights (in lbs): 7.5, 7.25, 8.2, 7.95, 8.0, 9.75, 9.25, 8.9, 9.85, 10.0

When we calculate the correlation coefficient for this dataset, the result is 0.8311. A correlation coefficient ranges between -1 and 1, where:
- 1 indicates a perfect positive linear relationship,
- -1 indicates a perfect negative linear relationship,
- 0 indicates no linear relationship.

Since the correlation coefficient is 0.8311, we interpret this as follows:
- The value is significantly positive and close to 1, which indicates a strong positive linear relationship.

Therefore, there is a positive correlation between the ages and weights of the babies. The proper conclusion is that as the age of the babies increases, their weight also tends to increase.

So, the correlation between age and weight as shown in the table is positive.
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