To determine which best describes the strength of the model, we need to calculate the Pearson correlation coefficient between the number of calories in the meal and the cost of the meal. The steps to do this are as follows:
1. List the data points:
- Number of calories: 550, 1250, 780, 650
- Cost of the meal: \[tex]$12, \$[/tex]11, \[tex]$13, \$[/tex]10
2. Calculate the Pearson correlation coefficient:
The Pearson correlation coefficient [tex]\(r\)[/tex] measures the linear correlation between two variables. This coefficient ranges from -1 to 1, where:
- [tex]\(r = 1\)[/tex] indicates a perfect positive linear relationship,
- [tex]\(r = -1\)[/tex] indicates a perfect negative linear relationship,
- [tex]\(r = 0\)[/tex] indicates no linear relationship.
For this data, the Pearson correlation coefficient between the calories and the cost of the meal is approximately [tex]\(-0.129\)[/tex].
3. Determine the strength and direction of the correlation:
- A coefficient of [tex]\(-0.129\)[/tex] indicates a very weak negative correlation since it is close to 0.
- If [tex]\(-0.7 \leq r < -0.3\)[/tex], it indicates a weak negative correlation.
- If [tex]\(r < -0.7\)[/tex], it indicates a strong negative correlation.
- If [tex]\(0.3 \leq r < 0.7\)[/tex], it indicates a weak positive correlation.
- If [tex]\(r \geq 0.7\)[/tex], it indicates a strong positive correlation.
- If [tex]\(-0.3 \leq r < 0.3\)[/tex], it indicates no correlation.
In this case, since [tex]\(-0.129\)[/tex] falls between [tex]\(-0.3\)[/tex] and [tex]\(0.3\)[/tex], it indicates "no correlation."
Therefore, the answer to the given question is that there is "no correlation" between the number of calories in the meals and the cost of the meals.
