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According to the data shown in the table, which of the following statements is true?

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Hours Spent \\
Driving
\end{tabular} & 2 & 5 & 1 & 4 & 3 & 7 & 9 & 11 & 8 \\
\hline
\begin{tabular}{c}
Distance \\
Traveled \\
(miles)
\end{tabular} & 130 & 325 & 65 & 260 & 195 & 455 & 585 & 715 & 520 \\
\hline
\end{tabular}

A. There is a positive non-linear relationship between the hours spent driving and the distance traveled.

B. There is a positive linear relationship between the hours spent driving and the distance traveled.

C. There is a negative non-linear relationship between the hours spent driving and the distance traveled.

D. There is a negative linear relationship between the hours spent driving and the distance traveled.

Sagot :

GinnyAnswer
To determine the relationship between the hours spent driving and the distance traveled, we can examine the correlation coefficient. This value measures the strength and direction of a linear relationship between two variables.

1. Calculate the Correlation Coefficient:
- The correlation coefficient between the hours spent driving and the distance traveled is [tex]\( \rho = 1.0 \)[/tex].

2. Interpret the Correlation Coefficient:
- The range of the correlation coefficient is from -1 to 1.
- When the correlation coefficient is close to 1, it indicates a strong positive linear relationship.
- When the correlation coefficient is close to -1, it indicates a strong negative linear relationship.
- When the correlation coefficient is close to 0, it indicates no linear relationship; however, there still might be a non-linear relationship.

3. Determine the Relationship Type:
- Since the correlation coefficient is [tex]\( 1.0 \)[/tex], which is both positive and exactly 1, it suggests a perfect positive linear relationship between the hours spent driving and the distance traveled.

Based on this understanding, the correct statement from the options provided is:

B. There is a positive linear relationship between the hours spent driving and the distance traveled.
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