Question

# In an effort to determine whether any correlation exists between the price of stocks of airlines,...

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 46.8 45.41 47.93 15.7 51.78 49.58 52.17 44.34 47.36 18.1 (Round the intermediate values to 2 decimal places. Round your answer to 3 decimal places.) r =

 Delta south 45.96 38.76 47.1 45.41 47.93 16.1 51.78 49.58 52.17 44.34 47.36 18.1

Solution

Back-up Theory

Correlation coefficient, r = Sxy/sqrt(Sxx. Syy), where

Mean X = Xbar = (1/n) Σ(i = 1 to n)xi Mean Y = Ybar = (1/n) Σ(i = 1 to n)yi Sxx = Σ(i = 1 to n)(xi – Xbar)2 Syy = Σ(i = 1 to n)(yi – Ybar)2 Sxy = Σ(i = 1 to n){(xi – Xbar)(yi – Ybar)}

Now to work out the solution,

Let x = Delta stock price and y = Southwest stock price. Then, by the above formula,

the coefficient of correlation between the prices of the two stocks, r = 0.460 Answer

Details of calculations

 n 6 Xbar 48.72 ybar 35.38 Sxx 33.98 Syy 1064.26 Sxy 87.52 r 0.4602

DONE

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