Standard Curve Generation:

A standard curve is a graphic representation of the relationship between the distance of migration from the well of  molecular weight standards and the apparent size of the molecular weight standards. Due to the inverse square degeneration of electromagnetic field strength with distance and the wide range (3 magnitudes) or size-resolving power of electrophoretic gels,  a base 10 logarithmic transformation of molecular weights lends a prettier picture. The distance of migration is not transformed so the plot is semilogrithmic. Semilog graph paper with two-three cycles is available, so that mathematical transformation of the data before plotting is obviated.  Here is a sample plot:

Another way to make a standard curve is with a computer program. Common programs like Microsoft's Excel have a linear regression function based on the least squares algorithm in the data analysis add-in.

The data is entered in a table as below:

An then may be scatter-plotted using the graph wizard.

A linear regression analysis gives the equation of the line for easy interpolation of unknown migration values to size values. Here's a sample of the regression output:

Notice the fit of the line is not great (R²=0.69). A log transformation of the molecular weights or a geometric regression would be better. You need a fancier program than Excel. Anyway, the coefficient of x is -3783 and the y intercept is 21963, so the  equation of the line relating molecular weight to migration is:

Molecular Weight = -3783(Migration) + 21963

for  a migration of 3 cm, then:

Molecular Weight = -3783(3) + 21963

= 4466 BP, this is way off!, the expected value is 6500 (see the original data),

the residual is 2034 bp.

Let's try a log10 transformation of the molecular weights:

Now the linear regression looks better!

And the equation of the line is:

log10Molecular Weight = -0.22 (Migration) + 4.56

or, for example, a 6 cm migration

log10 Molecular Weight = -0.22 (6) + 4.56

= antilog10(3.24)

=1737

This is a little better. Compare it to your hand made graph. Still, connecting the data points,  point to point, with straight lines, as in the scatter plot above, is often more accurate than regression, because of inconsistencies (non-linearity) in the gel system. Gel analyses programs designed for molecular biologists often offer this connect-the-dots mode of standard curve interpolation. Statistics programs do not. Here is a link to a web site providing such an approach to the connect-the dots method.