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The table shows the heights and weights of a few students in a class.

\begin{tabular}{|c|c|}
\hline Height (inches) & Weight (pounds) \\
\hline 58 & 122 \\
\hline 59 & 128 \\
\hline 60 & 126 \\
\hline 62 & 133 \\
\hline 63 & 145 \\
\hline 64 & 136 \\
\hline 66 & 144 \\
\hline 68 & 150 \\
\hline 70 & 152 \\
\hline
\end{tabular}

Complete the following sentences based on your observations.

The data seems to have a correlation coefficient close to [tex]$\square$[/tex].
This indicates that the weight of a student [tex]$\square$[/tex] as the height of the student increases.

Sagot :

GinnyAnswer
Let's analyze the provided data step-by-step and complete the sentences based on the observations:

1. Identify the data: We have a list of heights (in inches) and corresponding weights (in pounds) for a group of students.

- Heights: 58, 59, 60, 62, 63, 64, 66, 68, 70
- Weights: 122, 128, 126, 133, 145, 136, 144, 150, 152

2. Calculate the correlation coefficient: The correlation coefficient measures the strength and direction of the linear relationship between the heights and weights. From the given result, we know that the correlation coefficient for this data is approximately 0.9445.

3. Interpret the correlation coefficient value:

- A correlation coefficient close to 1 indicates a very strong positive relationship.
- Here, the value 0.9445 is quite close to 1, suggesting a strong positive correlation between height and weight.

4. Describe the relationship: Given the correlation coefficient is positive, it means that as one variable increases, the other variable also tends to increase. Hence, in this context, as the height of the student increases, the weight of the student also tends to increase.

Given these steps, we can now complete the sentences accurately:

- The data seems to have a correlation coefficient close to 1.
- This indicates that the weight of a student increases as the height of the student increases.
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