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QUAN 2010 Notes: Introduction to Business Statistics

Omar Ortega

Section 3.5 Measures of Association Between Two Variables

So far, the statistics we’ve studied have all dealt with describing one variable at a time. Measures of association describe the relationship between two variables.

Definition 3.5.1.

  • sample covariance: measures the direction of the linear relationship between two variables
    \begin{equation*} \text{In Excel: COVARIANCE.S} \end{equation*}
  • sample correlation coefficient: measures both the strength and direction of the linear relationship between two variables
    \begin{equation*} \text{In Excel: CORREL} \end{equation*}
Figure 3.5.2. Correlation (Made in GeoGebra by Zbynek Konecny)

Exercise 3.5.3.

(Donnelly 3.50)
A regional manager at Acme markets would like to develop a model to predict weekly sales of pet food based on the shelf space. The data in the Excel file below shows the results collected from nine randomly selected stores.

(a)

Calculate the sample covariance.
Answer.
\begin{equation*} =COVARIANCE.S(A2:A10,B2:B10)=3.75 \end{equation*}

(b)

Calculate the sample correlation coefficient.
Answer.
\begin{equation*} =CORREL(A2:A10,B2:B10)\approx 0.54 \end{equation*}

(c)

Describe the relationship between \(x\) and \(y\text{.}\)
Answer.
Since r is almost exactly in the middle of 0 and 1, there is a moderate positive relationship between shelf space and sales.
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