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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 spread out over 4 months. 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 45.96 38.76 46.7 45.41 47.93 16.0 51.78 49.58 52.17 44.34 47.26 18.2

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Answer:

Check the explanation

Step-by-step explanation:

Following table shows the calculations:

Delta, X      Southwest , Y            X^2              Y^2                      XY

45.96               38.76               2112.3216     1502.3376          1781.4096

46.8                 45.41                2190.24         2062.0681        2125.188

47.93                15.7                 2297.2849      246.49            752.501

51.78                49.58              2681.1684      2458.1764        2567.2524

52.17                44.34              2721.7089      1966.0356        2313.2178

47.36                18                   2242.9696            324               852.48

Total 292       211.79               14245.6934      8559.1077      10392.0488

Sample size: n =6

Now

[tex]S_{yy}=\sum y^{2}-\frac{\left (\sum y \right )^{2}}{n}=1083.27[/tex]

[tex]S_{xx}=\sum x^{2}-\frac{\left (\sum x \right )^{2}}{n}=35.03[/tex]

[tex]S_{xy}=\sum xy-\frac{\left (\sum x \right )\left (\sum y \right )}{n}=84.94[/tex]

The coefficient of correlation is :

[tex]r=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.436[/tex]

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