# Can you tell me a method that estimates the linearity of a series ?

Hello everybody,

I'm dealing with hundreds of series that have approximately the same % of increase in a given time, but they all differ in terms of linearity.

To make it clear, I attached an image here. The blue line represents the ideal series, the green line the worst, the red line the average.

I would like to know if there is a built-in method (or similar) that, given as input a series, tells me how close it is to be a linear series. (ie: output from 0 to 1, where 1 is the perfect linear series)

I hope I explained myself.

Thank you...

Files:
grwthL.jpg  29 kb

You mean like linear regression?

trevor88: I'm dealing with hundreds of series that have approximately the same % of increase in a given time, but they all differ in terms of linearity. To make it clear, I attached an image here. The blue line represents the ideal series, the green line the worst, the red line the average. I would like to know if there is a built-in method (or similar) that, given as input a series, tells me how close it is to be a linear series. (ie: output from 0 to 1, where 1 is the perfect linear series). I hope I explained myself.
Just as stated in the previous post, you can use Linear Regression and analyse the regression metrics such as deviation, mean vs median, skew, etc. All of those metrics can will help you decide which of the series is most linear.

Linear regression to get the line. RMS of residuals to get your quality.

Sorry, but what I'd like to know is if there is a method that takes as input an Array of values and outputs a coefficient that tell me how close that array is to be a linear set of values.

That linear regression page is for building and indicator that doesnn't show me what I asked...

trevor88 #: Sorry, but what I'd like to know is if there is a method that takes as input an Array of values and outputs a coefficient that tell me how close that array is to be a linear set of values.

That linear regression page is for building and indicator that doesnn't show me what I asked...

Ignore the green linear regression link, as that is generated automatically by the website and is not a link provided by the posters. Instead pay attention the words and details provided by the posters and do some research on "Linear Regression" and study the various metrics associated with it, like for example Root Mean Square Error (RMSE).

One known method is the Pearson Correlation Coefficient.

Take a look here:

I think Kaufman's Efficiency Ratio might be one solution.

The less deviations within a trend, the higher the efficiency.

The output is 0 for most inefficient to 1 perfectly efficient.

maximo #: I think Kaufman's Efficiency Ratio might be one solution. The less deviations within a trend, the higher the efficiency. The output is 0 for most inefficient to 1 perfectly efficient.

Kaufman's Efficiency Ratio has nothing to do with this. It does not measure how "linear" data is. You are mixing apples and oranges.

Ratio estimation works best if the data are well fit by a 'straight line' through the origin.

Efficiency Ratio = Direction / Noise

'Direction' is the current sum of plot XY useful as a linear estimator. Ordinary Least Squares is another estimator. Direction represents the line of best fit though not calculated in the same way as least squares.
'Noise' is the sum of absolute changes from one data point to the next. Noise in statistics can also be calculated as standard deviations from the mean.

I can make juice from both fruit.

Reason: