linear interpolation function in excel

[tskoglund]

Given a series of x and y data, how can I interpolate to find y given a value
of x based only on a line between the two adjacent points in the data series?
This would be like the TREND() function, only I don't want regression of the
entire data series, just the (x,y) data points immediately above and below
the input x value.

This seems such fundamental and essential function that I've been
exasperated for years that Excel doesn't have it or directions how to find
it. I realize that Excel calculates these individual lines every time it
connects the dots in a graph, but not having a function to achieve the same
result on a worksheet is puzzling. Am I missing something?

 

[Gary''s Student]

I have good news.

The FORECAST() function, which is usually used to extrapolate outside a
range of known points also interpolates for a point between two known points.
Checkout help for the function syntax.

(this is an un-advertised feature of the function)

 

[tskoglund]

Gary"s Student, you do not have good news , but maybe you don't understand
the question being asked. Like TREND, FORECAST uses all the data points in
the array and finds a best fit considering the entire array of data points.
Suppose A1:A4 = 1,2,2,1 (known y values) and B1:B4 = 1,2,3,4 (known x
values). FORECAST(2.5,A1:A4,B1:B4) returns a y value of 1.5. The function
everybody and their cousin wants - INTERPOLATE(2.5,A1:A4,B1:B4) - would
return a y value of 2.

Put these numbers in the spreadsheet and try it. Hopefully this makes sense
to you so you'll spreading wrong information about interpolation on this
board. I really wish you were right, though.

 

[Bernie Deitrick]

Google groups is your friend. Copy the code below into a code module, and
use as your describe.

HTH,
Bernie
MS Excel MVP

Function Interpolate(Xnow As Double, _
XRates As Range, YRates As Range) As Double
Application.Volatile
Dim hi As Long
Dim lo As Long
Count = XRates.Count
If XRates.Count <> YRates.Count Then
Interpolate = _
"Ranges need to be the same size"
Exit Function
End If

For hi = 1 To Count
If XRates(hi) > Xnow Then Exit For
Next
If hi > Count Then
Interpolate = YRates(Count)
Exit Function
End If
If hi = 1 Then
Interpolate = YRates(hi)
Exit Function
End If
lo = hi - 1
Interpolate = YRates(lo) + (Xnow - XRates(lo)) / _
(XRates(hi) - XRates(lo)) * _
(YRates(hi) - YRates(lo))
End Function

 

[Ron Rosenfeld]

Given a series of x and y data, how can I interpolate to find y given a value
of x based only on a line between the two adjacent points in the data series?
This would be like the TREND() function, only I don't want regression of the
entire data series, just the (x,y) data points immediately above and below
the input x value.

This seems such fundamental and essential function that I've been
exasperated for years that Excel doesn't have it or directions how to find
it. I realize that Excel calculates these individual lines every time it
connects the dots in a graph, but not having a function to achieve the same
result on a worksheet is puzzling. Am I missing something?

If X is your range of X's, Y your range of Y's, and NewX is the new value,
then:

=TREND(OFFSET(Y,MATCH(NewX,X),0,-2),OFFSET(X,MATCH(NewX,X),0,-2),NewX)

This formula assumes your X's are in ascending order.

This formula will give an #N/A error if NewX is less than the minimum X.

This formula will give a #VALUE! error if NewX is equal to or greater than the
maximum X.

These errors are in accord with your specifications that the New X be "between"
two adjacent points, but I would eliminate the error when it matches the
maximum X with this addition to the above formula:

=IF(NewX=MAX(X),INDEX(Y,MATCH(NewX,X)),
TREND(OFFSET(Y,MATCH(NewX,X),0,-2),
OFFSET(X,MATCH(NewX,X),0,-2),NewX))


--ron