Excel interpolation with results in situ - excel

Question

Extrapolation in Excel is easy: have a list of numbers (and optionally their paired "X-values"), and it can easily generate further entries in the list with the GROWTH() function.
GROWTH() works for interpolation too: you just need to tell it the intermediate X-values that you want it to calculate for. My problem with it is the appearance of the data in the spreadsheet. Here's an example:
Say I have some inputs, and through some process get some outputs. Only, there were gaps in the experiment so no outputs were generated for some values:
Out of curiosity, I copied the data to the right, and used Excel's "Extend with Growth Trend": I highlighted the first two entries (only), then right-click-dragged-down the little square over the next four cells (overriding the final value there) and chose "Growth Trend" in the context menu. To remind myself that the values were Excel-generated, I gave them a grey background:
Hmm. The generated values (unsurprisingly) aren't a good extrapolation, since they don't factor in the later value. It's out by over 40%! Also note that this Extend feature of Excel is an ease-of-input mechanism, not a calculation tool in its own right - Excel enters the data as raw numbers (to multiple decimal places).
So I formalised the Extend column by using the GROWTH() function - again only factoring in the first two values, but also using their paired X-values and the desired interpolation entry as parameters:
D4: =GROWTH(D$2:D$3,$A$2:$A$3,$A4)
D5: =GROWTH(D$2:D$3,$A$2:$A$3,$A5)
D6: =GROWTH(D$2:D$3,$A$2:$A$3,$A6)
Thankfully, the results mimic those of the previous column (Microsoft use the same mechanism for both features!) I didn't overwrite the last entry, since after all it has the value that I actually want! The fact that the calculated values are the same as before is the problem I'm trying to fix, and that this question is about.
To improve the calculated values, I need to incorporate the last value - but at the same time I want the "natural" sequence of input values to be maintained. In other words, I want the interpolated values to be placed in situ. That implies that the arguments to the GROWTH() function need to be discontiguous ranges, which Excel does by using the (Range,Range,...) syntax. I tried it, and got #REF! errors. I then tried using a named discontiguous range: same result.
After a bit of Googling (and StackOverflowing!) I found references to using INDIRECT() - a particularly problematic 'solution', since it evaluates strings that would need to be manually maintained. Nevertheless:
E4: =GROWTH(INDIRECT({"E2:E3","E7"}),INDIRECT({"A2:A3","A7"}),A4)
E5: =GROWTH(INDIRECT({"E2:E3","E7"}),INDIRECT({"A2:A3","A7"}),A5)
E6: =GROWTH(INDIRECT({"E2:E3","E7"}),INDIRECT({"A2:A3","A7"}),A6)
…and after all that it didn't work anyway! The values remained the same as the previous version, that didn't incorporate the last value. Maybe the last value doesn't make for better interpolation results? So, as an experiment, I ignored the "in situ" requirement and generated an "ex situ" version, with the known values followed by the desired values, allowing me to use simple ranges. Success! But to highlight that the data is in the wrong order, I asked Excel to create an X-Y plot of the data too:
B13: =GROWTH(B$10:B$12,$A$10:$A$12,$A13)
B14: =GROWTH(B$10:B$12,$A$10:$A$12,$A14)
B15: =GROWTH(B$10:B$12,$A$10:$A$12,$A15)
Of course, the results are exponential not linear, so setting the Y-axis to logarithmic generates a very readable result - and it effectively masks the back-and-forth of the data. But deep down, we both know that the data is wrong - just look at the table!
Maybe, just maybe, if I used Excel's "Sort Data" feature it would break up the range for me, and show me how I should have written the formulae? Sadly, although it looks like it worked, I get a "Circular reference" error for B12 - the range wasn't modified to make it discontiguous, and now B12's result is dependent on the original range which includes itself! I coloured it below to indicate that this isn't a viable solution:
So, my "final" solution is to maintain the previous "ex situ" version, and simply have an "in situ" column as well that does a VLOOKUP() on the ExSitu (named) table - and I needed to tell it to do an exact match with the FALSE parameter, since the list isn't sorted:
F4: =VLOOKUP($A4,ExSitu,2,FALSE)
F5: =VLOOKUP($A5,ExSitu,2,FALSE)
F6: =VLOOKUP($A6,ExSitu,2,FALSE)
Note that I labelled the column with an asterisk since it's a cheat: the values are only in situ by copying from another table.
Phew! After all that, my question:
Is there a way to directly interpolate the "in situ" values, without having to have an "ex situ" lookup table to generate the results? The above example was deliberately straightforward: you can easily imagine a longer list with more gaps to be filled in.

Answer 1

Since you had a good data sense, I'll share my discovery path on this case. I'm more like a visual person. I don't see things 'that' clear via tables. Here is what I do to you data points. :
Input Raw
360 7.16
370 28.9
380
390
400
410 5,380.00
Highlight all and press my favorite button > F11. I choose line chart type. Then with the plus button on the top left of the chart, I add trendline > more options.. From there I choose 'polynomial' and 'exponential' . Plus, a tick on 'display equation on chart' As you can see in the links, both fit seem ok. just take the equation and fit in for other values as needed.
Three things I've noticed :
The polynomial and exponential fit is close enough to what I need. But it doesn't exactly 'map' on the ( 410, 5380.00 ) point.
By having the formula I find it easier to make sense of whether or not the trendline 'proposed' by excel is a close fit to my need. As you play around you can see how far-off the linear & logarithmic trendline can be.
The trendline equation doesn't really map to 360,370,410... point as the x value, it assumes x is 0,1,2,3... (try to test it with the 'equation' of the excel proposed trendline)
IMHO, use excel trend with care. My next best fitting tool -> wolframalpha logarithmic fit.
For the original question :
Is there a way to directly interpolate the "in situ" values, without having to have an "ex situ" lookup table to generate the results?
I think my simple answer will be : Indirectly, Yes. Directly? not sure.
Hope this heals/helps in some ways.. ( :