John sells frozen fruit bars at a stand in a park during the summer months. He records the average weekly temperature and number of frozen fruit bars sold for 6 weeks. A 2-column table with 6 rows. The first column is labeled temperature (degrees Fahrenheit) with entries 67, 71, 76, 76, 82, 87. The second column is labeled fruit bars sold with entries 50, 54, 63, 65, 65, 100. What type of correlation exists between the temperature and the number of fruit bars sold? What is the real-world meaning of the slope of the line of best fit for the given scenario? There are approximately more fruit bars sold for every degree(s) the temperature rises.

Respuesta :

The correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.

What is the correlation coefficient?

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

  • 1 indicates a strong positive relationship.
  • -1 indicates a strong negative relationship.

A result of zero indicates no relationship at all, therefore, independent variable.

We know that the correlation coefficient is given by the formula,

[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

r = correlation coefficient

[tex]x_{i}[/tex] = values of the x-variable in a sample

[tex]\bar{x}[/tex] = mean of the values of the x-variable

[tex]y_{i}[/tex] = values of the y-variable in a sample

[tex]\bar{y}[/tex] = mean of the values of the y-variable

Calculate the value of [tex](x_i-\bar{x})(y_i-\bar{y}),\ (x_i-\bar{x})^2,{ \rm and}\ (y_i-\bar{y})^2[/tex] each separately, and then find the sum of them as shown below, therefore, the formula can be written as,

[tex]r =\dfrac{571.5}{261.5\times 1566.833333}= 0.0014[/tex]

Hence, the correlation that exists between the temperature and the number of fruits sold is positive but is almost negligible.

Learn more about Correlation Coefficients:

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Answer:

1. positive

2. 2.2

3. 1

Step-by-step explanation: