non-linear result of regression data analysis

I am not sure I am statistically literate enough to comment, as I am not sure what you are trying to describe here (An example data set with regression output might be helpful). Or perhaps you are using terms differently than I tend to use them, I am not sure.

When I run a regression on a random set of data, I get a "linear model" consisting of slope and intercept (y=mx+b). I do not expect the residuals (differences between the predicted y's and the measured y's) to be linear. Especially for random data, I expect the residuals to be randomly distributed above and below 0, which is what I get.

What do you mean by "the residual plot gives and estimated model which is far from linear"? Where are you seeing "Excel calculate a higher-order plot with just two coefficients"?

Short answer: The chart and the regression appear to be using different x values, so the chart does not actually match the regression.

longer answer:

how Excel generates the estimated model data (marked in yellow) in the 'residuals' section.

The values in G30:G37 are calculated by y=mx+b. m is the slope of the line in H22, b is the y intercept in H21, and x are the values in C6:C14.

The chart data is linked to another spreadsheet on your computer, so I cannot look to see exactly what the chart is using. It appears to be using the values in F29:F37 for the x values (not the same x values used in the regression or for calculating estimated cell density) and the values in G29:G27 for the "estimated" series Y values and D6:D14 for the measured cell densities. I am not sure why your regression tool did this, because when I run the regression tool, it uses C6:C14 as the x values for the chart.