Questions: A correlation coefficient between average temperature and coat sales is most likely to be between 0 and -1 between -1 and -2 between 1 and 2 between 0 and 1

A correlation coefficient between average temperature and coat sales is most likely to be between 0 and -1 between -1 and -2 between 1 and 2 between 0 and 1
Transcript text: A correlation coefficient between average temperature and coat sales is most likely to be $\qquad$ between 0 and -1 between -1 and -2 between 1 and 2 between 0 and 1
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Solution

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Solution Steps

Step 1: Calculate Covariance

The covariance between average temperature \( X \) and coat sales \( Y \) is calculated as follows:

\[ \text{Cov}(X,Y) = -116.67 \]

Step 2: Calculate Standard Deviations

The standard deviations of the two variables are given by:

\[ \sigma_X = 10.8 \] \[ \sigma_Y = 10.8 \]

Step 3: Calculate Correlation Coefficient

The correlation coefficient \( r \) is calculated using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values we have:

\[ r = \frac{-116.67}{10.8 \times 10.8} = -1.0 \]

Final Answer

The correlation coefficient between average temperature and coat sales is \( r = -1.0 \), indicating a perfect negative correlation. Therefore, the correlation coefficient is most likely to be between \( 0 \) and \( -1 \).

\[ \boxed{r \text{ is between } 0 \text{ and } -1} \]

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