Questions: If the stock prices of Ford Motors and General Motors both fell during the recession, what type of covariance did they exhibit? Positive Covariance Negative Covariance No Covariance

If the stock prices of Ford Motors and General Motors both fell during the recession, what type of covariance did they exhibit? Positive Covariance Negative Covariance No Covariance
Transcript text: If the stock prices of Ford Motors and General Motors both fell during the recession, what type of covariance did they exhibit? Positive Covariance Negative Covariance No Covariance
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Solution

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Solution Steps

Step 1: Calculate Covariance

The covariance between the stock prices of Ford Motors and General Motors during the recession is calculated as follows:

\[ \text{Cov}(X,Y) = 6.65 \]

Step 2: Calculate Standard Deviations

The standard deviations of the stock prices for Ford Motors and General Motors are given by:

\[ \sigma_X = 2.41 \] \[ \sigma_Y = 2.77 \]

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:

\[ r = \frac{6.65}{2.41 \times 2.77} = 1.0 \]

Final Answer

The covariance between Ford Motors and General Motors stock prices is \( \text{Cov}(X,Y) = 6.65 \) and the correlation coefficient is \( r = 1.0 \).

Thus, the answer is:

\[ \boxed{6.65} \] for covariance and \(\boxed{1.0}\) for correlation coefficient.

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