Worksheet – Case #10 – Creating a regression model with a fitted line

Finding Data

For this example, you will use the S&P 500 Price Return and the S&P Volatility index.

For the S&P 500 Price Return, go to:

Country & Region > United States > Equity Market > Equity Indices > S&P > 500 > Composite > Price Return

Locate and add “Index”. You can also use the short code “spx” in Series list.

Now, for the VIX, go to:

Country & Region > United States > Equity Market > Equity Indices > Volatility Indices > CBOE

Locate and add “S&P 500 Volatility Index (VIX), Close”. You can also use the short code “vix” in Series List.

Data Preparation

Limiting the data sample

In this example, you will only work on a data sample of 15 years. To do so, you can use the Data Range feature in Series List:

  • In Series list, locate the “data range” feature on the top right of the screen
  • for “Range start”, write “–15y”

You will now only have 15 years of observations on a rolling basis.

Analysis

Rate of change

First, you will have to express the two series as week-on-week percentage change:

  • Select “Time chart” in the tree
  • Click on “Insert” and choose Rate of change
  • For “Method”, choose Change over period %
  • For “Length”, select 1 Week

Regression

To create a fitted line in a Scatter Chart, you need to generate a regression model between the two variables:

  • Select “Rate of change” in the tree
  • Click on “Add” and choose Regression

Next step is to set the parameters in the Regression analysis:

  • check the tick-box “Output the dependent series”
  • check the tick-box “Output the explanatory series”
  • Check “Include” for both series
  • Pick the volatility index as dependent series

Fitted line in a Scatter chart

From the Regression analysis, add a scatter chart as Presentation.

To start with, you can make the chart cleaner by displaying the line as dots only:

  • Click on the line graph
  • Change “Graph style” to Custom
  • Set “Line” to None
  • Set “Marker style” to 4px

You can now add the regression line. To do so:

  • Go to “Graph layout”
  • On the 2nd Line graph, create a pair of series with the predicted volatility index and the S&P price return.
  • Make sure the order of the series is the same as the 1st line graph: S&P price return first, and then the VIX index.

Charting

You can change the axis titles to the series names:

  • Click on the Y-axis
  • Change Axis title to “Custom” and click on “Edit...”
  • Hoover the mouse over the “dynamic properties” tab
  • Click on the red cross beside “Graph text” and click OK

By clicking on the axis title you can change where you want the text to be located in the “appearance” window under the presentation properties tab.

Other changes:

Chart title:  VIX and S&P 500: Regression model with fitted line

Subtitle:  One week % change

Legend position: Above, centered

Main scale: Left

Legend text changed

Axis title is set to “outside the edge” and text alignment is set to “center”