Q:

Creating weighted sum analysis using DEM and population data using QGIS?

I have a shapefile containing population points for Vietnam, and I am aiming to perform a weighted sum analysis using a Digital Elevation Model. 
Basically, I'd like to combine elevation, population densities and slope to find the best areas for terraced cultivation. I have a full DEM for Vietnam, and population densities. 
The ideal locations would be medium slope angles without high population densities. 
However I'm a bit stuck on what path to follow.

A:

Here's an outline of a basic method. 

Filter each of your layers based on your conditions. 
Slope
i. Create a slope raster from the DEM. 
ii. Use the Raster calculator to create a raster with values of 1 when slope is acceptable (between 10 and 15 degrees), and 0 when the slope is unacceptable.
@rasterband * (@rasterband > 10 AND @rasterband < 15)

Population
i. Convert your subjective condition (high/low population density) to an objective range of numerical values. Define what an acceptable range of population density would be. 
ii. Create a raster with values of 1 when population density is acceptable , and 0 when the population density is unacceptable. 
Elevation
i. Define a range of acceptable elevations.
ii. Use the Raster calculator to create a raster with values of 1 when elevation is acceptable, and 0 when the elevation is unacceptable.
Find the area where the filtered layers overlap.
Use the r.series tool to sum the three rasters together. 

The output is a raster with values between 0 and 3. Any cell with a value of 3 meets all 3 of your criteria.
Note that this method can be modified to create a more nuanced output. Instead of making rasters with only 0 or 1, you can use a range of values between 0 and 1, such that 0 means a cell doesn't meet conditions at all, and 1 means the cell has optimal conditions. It's up to you to decide what you define as "optimal" for each condition.

