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The table shows the number of calories in four meals and the cost of each meal.

Cost of Meal and Number of Calories

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Number of calories \\
in the meal
\end{tabular} & \begin{tabular}{c}
Cost of \\
the meal
\end{tabular} \\
\hline
550 & [tex]$\$[/tex] 12$ \\
\hline
1,250 & [tex]$\$[/tex] 11$ \\
\hline
780 & [tex]$\$[/tex] 13$ \\
\hline
650 & [tex]$\$[/tex] 10$ \\
\hline
\end{tabular}

Which best describes the strength of the model?

A. A weak positive correlation
B. A strong positive correlation
C. A weak negative correlation
D. A strong negative correlation



Answer :

GinnyAnswer
To determine the strength and direction of the correlation between the number of calories and the cost of the meals, we first calculate the correlation coefficient. The correlation coefficient ranges from -1 to 1:
- A value near 1 indicates a strong positive correlation.
- A value near -1 indicates a strong negative correlation.
- A value near 0 indicates no correlation.

Given the calculated correlation coefficient, \(-0.1292396089051281\), we can analyze its strength and direction:

1. Direction:
- The correlation coefficient is negative \(-0.1292396089051281 < 0\), indicating a negative correlation between the number of calories in the meal and the cost of the meal.

2. Strength:
- We determine the strength of correlation with the following thresholds:
- If the absolute value of the correlation coefficient \(|r|\) is between 0.7 and 1.0, the correlation is strong.
- If \(|r|\) is between 0.3 and 0.7, the correlation is moderate.
- If \(|r|\) is between 0 and 0.3, the correlation is weak.

The absolute value of our correlation coefficient is \( | -0.1292396089051281 | \approx 0.129 \). This value falls within the range of [0, 0.3], indicating a weak correlation.

Therefore, the best description based on the correlation coefficient \(-0.1292396089051281\) is a weak negative correlation.

The correct answer is:
- a weak negative correlation

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