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# Distance from linear trend

Posted on 2014-07-31
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How do I calculate the distance from a linear trend in a line chart that goes up and down but steadily increasing?
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Question by:fitaliano
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Expert Comment

ID: 40233136
There are a number of ways, all under goodness of fit (which I forgot some decades back).

The simplest way (if the numbers are positive and you have a good regression line) is to calculate the y value on the line for the x value of the point.

The vertical distance between the line is y(line) - y(point).

That is one way and that is not the only way.
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Accepted Solution

Glenn Ray earned 500 total points
ID: 40233427
Excel has a function - TREND - which will calculate the linear trend value for any given x-value, based on a set of existing x and y values.  Using this, one can calculate the delta (distance) between any given y-value in the set and the linear trend value for the same value of x.  Here's the syntax:

=TREND((known_y's, [known_x's], [new_x's], [const]), where

known_y's is the range containing the y-values
known_x's is the range containing the x-values (optional if x is understood to be 1,2,3,4...)
new_x's is the range containing the "new" x-values to use for calculating the given linear trend point
const is TRUE is forcing the formula to intercept at y=0

In your case, you'll use your existing data for all the x and y values, then use each individual value of x to produce the linear trend value.  From there you just substract that value from the original y-value to get the delta (distance).

See this example of how you'd do it:
Note the formula entered in cell C2 (and copied down)
=TREND(\$B\$2:\$B\$11,\$A\$2:\$A\$11,A2,TRUE)

You can see from the chart and linear trend on it the the deltas agree with what's seen visually.  Example file attached.,

Regards,
-Glenn

Microsoft Reference: TREND function
EE-TrendExample.xlsx
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