what does the underlined mean in the following sentence?
Last year, we strengthened our commitment to innovation by doubling the rate of increase of spending for basic and applied research, compared to the rate in the year before. 
Rate of increase is a mathematical term but mostly used to derive economic parameters such as rate of economic growth/inflation/population growth etc.
· The formula is: Rate of increase = Total number of increase / Total time
e.g.
Population of city A is 150000 in Year 2005 and 180000 in Year 2008.
The rate of increase is (Total number of increase-180000 – 150000=30000) / (Total time-2008 – 2005=3)
= 30000 / 3 = 10000 people per year
If you need the rate of increase per month:
30000/ (3x12) = 30000 / 36 = 833.33 people per month
Here is a chart showing growth of population in Indian sub-continent calculated from per year to per minute
Rate of Increase in Indian Population
Per Year ....................1,55,31,000
Per Month ...............12,73,033
Per Day ....................42,434
Per Hour ..................1,768
Per Minute ..............29