Do stock prices of competing companies move together? Below...

Do stock prices of competing companies move together? Below are daily closing prices of two computer services firms (IBM = International Business Machines Corporation, EDS = Electronic Data Systems Corporation). (a) Calculate the sample correlation coefficient (e.g., using Excel or MegaStat). (b) At $\alpha=.01$ can you conclude that the true correlation coefficient is greater than zero? (c) Make a scatter plot of the data. What does it say? $$ \begin{array}{ccc} \hline \begin{array}{l} \text { Daily Closing Price (\$) of Two Stocks in October and November } \mathbf{2 0 0 4} \\ (\boldsymbol{n}=\mathbf{4 2} \text { days) } \end{array} & & \\ \hline \text { Date } & \text { IBM } & \text { EDS } \\ \hline 9 / 1 / 04 & 84.22 & 19.31 \\ 9 / 2 / 04 & 84.57 & 19.63 \\ 9 / 3 / 04 & 84.39 & 19.19 \\ \vdots & \vdots & \vdots \\ 10 / 27 / 04 & 90.00 & 21.26 \\ 10 / 28 / 04 & 89.50 & 21.41 \\ 10 / 29 / 04 & 89.75 & 21.27 \\ \hline \end{array} $$

Do stock prices of competing companies move together? Below are daily closing prices of two computer services firms (IBM = International Business Machines Corporation, EDS = Electronic Data Systems Corporation). (a) Calculate the sample correlation coefficient (e.g., using Excel or MegaStat). (b) At $\alpha=.01$ can you conclude that the true correlation coefficient is greater than zero? (c) Make a scatter plot of the data. What does it say?
$$
\begin{array}{ccc}
\hline \begin{array}{l}
\text { Daily Closing Price (\$) of Two Stocks in October and November } \mathbf{2 0 0 4} \\
(\boldsymbol{n}=\mathbf{4 2} \text { days) }
\end{array} & & \\
\hline \text { Date } & \text { IBM } & \text { EDS } \\
\hline 9 / 1 / 04 & 84.22 & 19.31 \\
9 / 2 / 04 & 84.57 & 19.63 \\
9 / 3 / 04 & 84.39 & 19.19 \\
\vdots & \vdots & \vdots \\
10 / 27 / 04 & 90.00 & 21.26 \\
10 / 28 / 04 & 89.50 & 21.41 \\
10 / 29 / 04 & 89.75 & 21.27 \\
\hline
\end{array}
$$

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Key Concepts

Correlation Coefficient

The correlation coefficient measures the strength and direction of a linear relationship between two quantitative variables. It is computed from sample data to give an estimate of how closely the variables move together, with values ranging from -1 (perfect negative relationship) to 1 (perfect positive relationship).

Sample versus Population Parameters

This concept involves distinguishing between characteristics calculated from sample data and the true parameters in the entire population. In the context of correlation, the sample correlation coefficient is used as an estimate to make inferences about the true population correlation.

Hypothesis Testing for Correlation

Hypothesis testing for correlation assesses whether an observed correlation coefficient is statistically different from a value (often zero) indicating no linear relationship. This involves formulating null and alternative hypotheses, calculating a test statistic, and determining significance based on a chosen alpha level.

Scatter Plot

A scatter plot is a graphical tool used to visualize the relationship between two numerical variables. It displays data points on a coordinate plane, which can help in identifying correlation, trends, clusters, or outliers, thereby offering a quick visual check of the data's linearity or other patterns.

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