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The table shows the time a patient spends at the dentist and the amount of the bill.

Bill Amount for Time Spent at the Dentist

\begin{tabular}{|c|c|}
\hline \begin{tabular}{c}
Time spent at the \\
dentist (in hours)
\end{tabular} & \begin{tabular}{c}
Bill \\
amount
\end{tabular} \\
\hline 1.4 & [tex]$\$[/tex] 235[tex]$ \\
\hline 2.7 & $[/tex]\[tex]$ 867$[/tex] \\
\hline 0.75 & [tex]$\$[/tex] 156[tex]$ \\
\hline 1.6 & $[/tex]\[tex]$ 215$[/tex] \\
\hline
\end{tabular}

What is the correlation coefficient for the data in the table?

A. [tex]$-0.93$[/tex]
B. [tex]$-0.27$[/tex]
C. 0.27
D. 0.93



Answer :

GinnyAnswer
To determine the correlation coefficient for the data provided, follow these steps:

1. Identify the data points:
- Time spent at the dentist (in hours): [tex]\([1.4, 2.7, 0.75, 1.6]\)[/tex]
- Bill amount (in dollars): [tex]\([235, 867, 156, 215]\)[/tex]

2. Define the correlation coefficient:
The correlation coefficient, often denoted by [tex]\( r \)[/tex], measures the strength and direction of a linear relationship between two variables. Its value ranges between [tex]\(-1\)[/tex] and [tex]\(1\)[/tex], where:
- [tex]\( r = 1 \)[/tex] implies a perfect positive linear relationship,
- [tex]\( r = -1 \)[/tex] implies a perfect negative linear relationship,
- [tex]\( r = 0 \)[/tex] implies no linear relationship.

3. Calculate the correlation coefficient:
In this case, the correlation coefficient is calculated specifically for the given data points. The result of this calculation is [tex]\( 0.929720561266332 \)[/tex].

4. Interpret the correlation coefficient:
- The correlation coefficient is close to [tex]\(0.93\)[/tex].
- A value of [tex]\(0.93\)[/tex] indicates a strong positive linear relationship between the time spent at the dentist and the bill amount. This means that as the time spent at the dentist increases, the bill amount also tends to increase.

5. Choose the closest value from the given options:
- Given options are [tex]\( -0.93, -0.27, 0.27, 0.93 \)[/tex].
- The calculated correlation coefficient [tex]\(0.929720561266332\)[/tex] is closest to [tex]\(0.93\)[/tex].

Therefore, the correlation coefficient for the data in the table is [tex]\( \boxed{0.93} \)[/tex].

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