Question

In an effort to determine whether any correlation exists between the price of stocks of airlines, an analyst sampled six days of activity of the stock market. Using the following prices of Delta stock and Southwest stock, compute the coefficient of correlation. Stock prices have been rounded off to the nearest tenth for ease of computation.

Delta Southwest
47.6 15.1
47.0 15.4
50.6 15.9
52.6 15.6
52.4 16.4
53.1 17.9
Round your answer to 4 decimal places, the tolerance is +/-0.0005.
r =
In an effort to determine whether any correlation exists between the price of stocks of airlines, an analyst sampled six days of activity of the stock market. Using the following prices of Delta stock and Southwest stock, compute the coefficient of correlation. Stock prices have been rounded off to the nearest tenth for ease of computation.
Round your answer to 4 decimal places, the tolerance is +/-0.0005.
r = ?

Answer 1

The coefficient of correlation is 0.7098.

Explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The formula to compute the correlation coefficient is:

`r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^(2)-(\sum X)^(2)][n\cdot\sum Y^(2)-(\sum Y)^(2)]}}`

The required values are computed in the Excel sheet attached below.

Compute the value of r as follows:

`r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^(2)-(\sum X)^(2)][n\cdot\sum Y^(2)-(\sum Y)^(2)]}}`

`=\frac{(6\cdot 4877.5)-(303.3\cdot 96.3)}{\sqrt{[(6\cdot15367.3)-(303.3)^(2)][(6\cdot1550.7)-(96.3)^(2)]}}\\\\=(57.21)/(80.597)\\\\=0.70983\\\\\approx 0.7098`

Thus, the coefficient of correlation is 0.7098.