What's the difference between gross fixed capital formation and gross private domestic investment? Cited from Wikipedia, we know:

Gross private domestic investment is the measure of physical investment used in computing GDP in the measurement of nations' economic activity. This is an important component of GDP because it provides an indicator of the future productive capacity of the economy. It includes replacement purchases plus net additions to capital assets plus investments in inventories.

Gross fixed capital formation (GFCF) is a macroeconomic concept used in official national accounts. GFCF is a component of the expenditure on gross domestic product (GDP), and thus shows something about how much of the new value added in the economy is invested rather than consumed. GFCF is not a measure of total investment, because only the value of net additions to fixed assets is measured, and all kinds of financial assets are excluded, as well as stocks of inventories and other operating costs (the latter included in intermediate consumption).

If I wanna study the relationship between Effective federal funds rate and investment, in particular, whether there is a linear relationship between the annual percent change of these two quantities, which one should I choose to estimate the investment? Thanks.

Data source: https://fred.stlouisfed.org/series/USAGFCFQDSMEI

https://fred.stlouisfed.org/series/GPDI
The term gross private domestic investment (GPDI) seems to be used only by the US. The term gross fixed capital formation (GFCF) is used by the rest of the world (but not by the US). (This is thus simply the US being exceptional as usual by using its own terminology and methodology.)

Roughly, the difference is this: Ignoring inventories, GFCF includes government investment, while GPDI does. More precisely, the difference is this: $$\begin{alignat*}{1}
\text{GFCF} &amp; =\text{Gross private domestic fixed investment}+\text{Gross government fixed investment}\\
 &amp; =\text{GPDI}-\text{Change in private inventories}+\text{Gross government fixed investment}.
\end{alignat*}$$

To elaborate just a little, the rest of the world follows the UN System of National Accounts (SNA, 2008), while the US does not. In the usual identity $Y=C+I+G+NX$, we have the following differences between the UN SNA and the US:





If you are looking at countries other than the US, then you may not be able to find data for GPDI so easily. In which case, you may want to use GFCF.

Conversely, if you're looking at only the US, then you'll probably want to use GPDI.

Of course, in your analysis, you should be clear about what precisely your statistic, be it GFCF or GPDI, is supposed to measure.