Voltmeter scaling resistor front-end and ADC calibration coefficients
This is a late answer, but here is something you may use to determine your calibration coefficients.
As @NickJohnson has already written, a linear function can be used to convert values ready by the ADC to "true" values. Thus, let me rename the parameters:

$$V_\text{true}=C_\text{gain}\cdot V_\text{read}+C_\text{offset}$$

The simplest way to calculate the coefficients is to make two measurements,  one at the low, the other at the high end of the ADC range. (But make sure you're not measuring at the limits, i.e. measure at 0.1V and 4.9V for a 0-5V range). The coefficients are

$$C_\text{gain}=\frac{V_\text{true}^\text{high}-V_\text{true}^\text{low}}{V_\text{read}^\text{high}-V_\text{read}^\text{low}}$$

$$C_\text{offset}=V_\text{true}^\text{low}-C_\text{gain}\cdot V_\text{read}^\text{low}$$

Using the first and last set of numbers from your comment, I get \$C_\text{gain}=1.11303\$ and \$C_\text{offset}=-0.469206\$

But, is that the maximum precision you can get? Here is a plot showing the residuum - the difference between the values calculated by the formula from the read values and the true values. The first and last values have a residuum of zero, as they have been used to calculate the coefficients. But for the other points, the calculated value is up to 16mV (or 0.65%) too low!





Now, let's take into account all of your measured values. My result is \$C_\text{gain}=1.11224\$ and \$C_\text{offset}=-0.456815\$, which differs a little from the values above. 

Here is the plot again. The first point is off by 12mV or 1.2%, but the others are about -5mV...-8mV  or up to 0.2% off. 



How is it done? In Excel, you can simply draw your values as  "xy-plot". Make sure, the read values are on the x-axis, and the true values on the y-axis. by right-click on the diagram, you can draw a "line of best fit" or similar (I don't know the english term) and display the parameters.

I myself love gnuplot for such tasks. For using it, create a simple text file with your data:


1    1.320 
2    2.207
3    3.105
4    4.000
5    4.902
6    5.805
7    6.707
8    7.605
9    8.500
10   9.406

in gnuplot, do


    # Cosmetics only
    unset key
    set ytics nomirror
    set y2tics

    set xlabel "V_{read}"
    set ylabel "Residuum  V_{true} - f(V_{read}) [V]" tc rgb "red"
    set y2label "Residuum  (V_{true}-f(V_{read})) / V_{read} [%]" tc rgb "blue"



    # Now, define function, fit it to the data, and plot everything

    f(x)=m*x+b

    fit f(x) "adc.csv" via m, b

    plot "adc.csv" u 1:($2-f($1)) w lp pt 7, "adc.csv" u 1:(($2-f($1))/$2*100) axes x1y2 w lp pt 7 lt 3


When executing the fit command, you get lots of output, resulting in 


Final set of parameters            Asymptotic Standard Error
=======================            ==========================

m               = 1.11224          +/- 0.0007126    (0.06407%)
b               = -0.456815        +/- 0.004237     (0.9275%)


which is the result.

Additionally:


measure as many points as possible
measure each point several times
if a linear function does not match your data well, consider using a non-linear function.