### Example:

### Explaining Returns to the Fidelity Select Technology Fund

In our multiple regression example we regressed returns to the Fidelity Select Technology Fund (FSPTX) on returns to the S&P 500 Growth Index (SGX) and S&P 500 Value Index (SVX), in order to know whether the FSPTX behaves more like a large-cap growth fund or a large-cap value fund. We used monthly data from January 2012 through December 2016 for that return-based style analysis.

The result of that regression suggested that the returns to the FSPTX were linked to the returns to the S&P 500 Growth Index (because only the coefficient of SGX was statistically significant) and not closely associated with the returns to the S&P 500 Value Index.

Now suppose we add returns to the S&P 500 (SPX) itself to the returns to above style indices to estimate the equation.

**Y _{t} = b _{0} + b _{1}x _{1t} + b _{2}x _{2t} + b _{3}x _{3t} + ∈ _{t} **

Where

**Y _{t}** = the monthly return to the FSPTX.

**x _{1t}** = the monthly return to the S&P 500 Growth Index.

**x _{2t}** = the monthly return to the S&P 500 Value Index.

**x _{3t}** = the monthly return to the S&P 500.

The S&P 500 includes the component stocks of both style indices, so we are encountering a severe problem of multicollinearity.

Create a regression model to know how much variation in the FSPTX is explained by the S&P 500, Growth and Value indices between 2012 and 2016.