Correlation Matrix

Figure 1. Correlations for Sales in thousands and Fuel efficiency
A correlation matrix from the Bivariate Correlations procedure.

The Pearson correlation coefficient measures the linear association between two scale variables. The correlation reported in the table is negative(!), although not significantly different from 0 because the p-value of 0.837 is greater than 0.10. This suggests that designers should not focus their efforts on making cars more fuel efficient because there isn't an appreciable effect on sales.

However, the Pearson correlation coefficient works best when the variables are approximately normally distributed and have no outliers. A scatterplot can reveal these possible problems.

  1. To produce a scatterplot of Sales in thousands by Fuel efficiency, from the menus choose:

    Graphs > Chart Builder...

    Figure 2. Chart Builder
    Chart Builder
  2. Select the Scatter/Dot gallery and choose Simple Scatter.
  3. Select Sales in thousands as the y variable and Fuel efficiency as the x variable.
  4. Click the Groups/Point ID tab and select Point ID Label.
  5. Select Model as the variable to label cases by.
  6. Click OK.
Figure 3. Scatterplot for Sales and Fuel efficiency
A scatterplot for Sales and Fuel efficiency. There is a cloud of points in the lower left part of the plot, with a single point in the lower right and a single point in the upper left.

The resulting scatterplot shows two potential outliers, the Metro in the lower right of the plot and the F-Series in the upper left.

The F-Series is found to be generally representative of the vehicles your design team is working on, so you decide to keep it in the data set for now. This point may appear to be an outlier because of the skew distribution of Sales in thousands, so try replacing it with Log-transformed sales in further analyses. The Metro is not representative of the vehicles that your design team is working on, so you can safely remove it from further analyses.

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