*This Blog entry is from the Linear Regression section in **Learn Palisade**.*

This Blog thus far has focused on performing analysis of just a single independent variable. This would be referred to as Univariate Analysis. Bivariate analysis would refer to bringing two values together to estimate their relationship. In terms of visualisation of a relationship, this could be achieved by visually inspecting a scatter plot comparing one value to another as dots on a chart with two axes.

The Scatter Plot Analysis is available in the StatTools Ribbon, click the button Summary Graphs towards the centre of the ribbon, then ScatterPlot in the sub menu:

The ScatterPlot window will open which will ask for parameters for the X and Y:

Y is the vertical axis; X is the horizontal axis. In this example, the Dependent Variable (titled Dependent, being the actual price change observed) is to be on the Y axis, with the Skew (this is the prices tending towards higher or lower) on the X axis.

At this stage it is not necessary to display the Correlation Coefficient, however, the default is acceptable, where Display Correlation Coefficient is checked. Click OK to perform the analysis, a Scatter Plot will be drawn and returned:

The intention is to visually inspect the scatter plot to see if the mass tends with an increase. in the Skew. Furthermore, it shows how the values are clustered together, in some instances there may be distinct groups emerge which need to be split (i.e. maybe a different model for one cluster).

In this example, it is visually quite hard to draw any conclusion as the scatter plot is far too dense, having too many dots overlaying each other. A solution is to take a random sample, to reduce the size of the dataset without losing any significance of meaning. Creating a scatter plot on the smaller dataset makes the Scatter Plot much easier to understand.

In the above example while there are far fewer points on the scatter plot, the overall shape is broadly the same.