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# Non Linear Curve

### Explanation.

NL Curve fits a non linear curve to a dataset, calculates the appropriate regression coefficients and performs an analysis of variance to determine the amount of variance explained by the curve.

### Input.

Two columns of data are required, the first column is considered to be a numerical explanatory X variable which explains a numerical dependent Y variable in the second column. Weights can optionally be added in a third column. The numbers in the input field have to be separated by spaces, returns, semicolons, colons, or tabs, but can NOT be separated by comma’s or full stops. Cases with non-numerical values are ignored. The data for all this can be copied for example from a spreadsheet or word processor or the data can be typed manually into the "Input data here:" field. The data in the input field is read row wise, so first the data in the first row followed by the second, the third and all the other rows. The variables in the columns can be identified in the output by giving the variables names in the first row and checking the "Var labels in 1st row" option. Names can be text or numbers.

### Output.

First an overview of the data read and the linear and non-linear correlation between the variables. From this point one can move onwards to the correlations page for confidence intervals, sample size calculations or to compare correlations. Read the help page related to this correlation page for instructions.

Then, dependent on what you requested:

Ln-Y gives the Growth Function. The B coefficient in the Regression table gives you the proportional increase (or decrease) in Y with each unit change in X. For example, it shows you how your money grows in the bank given a certain interest rate. The program estimates the average interest from the “amount” in the graph. Multiply B with 100 to get the average percentage change. Cases were Y=0 or Y<0 are ignored.

Ln-X is the logarithmic function. The B coefficient in the Regression table gives you the unit increase (or decrease) in Y relative to proportional changes in X. Cases were X=0 or X<0 are ignored.

Ln-Y Ln-X gives the Elasticity Function. The B coefficient in the Regression table gives you the proportional increase (or decrease) in Y relative to proportional changes in X. Multiply B with 100 to get the average percentage change. Cases were X=0 or X<0 or were Y=0 or Y<0 are ignored.

Ln-Y 1/X gives the S-Function. Cases were X=0 or were Y=0 or Y<0 are ignored.

1/X the inverse X function. Cases were X=0 are ignored.

1/Y the inverse Y function. Cases were Y=0 are ignored.

Ln-Y exponential is basically the Growth function only rewritten to get the Exponential Function. Cases were Y=0 or Y<0 are ignored.

Ln-Y Ln-X power is basically the Elasticity function only rewritten to get the Power Function. Cases were X=0 or X<0 or were Y=0 or Y<0 are ignored.

X X-squared or quadratic function. Fits a parabolas (U shaped curve) to the data. Produces the function a+bX+cXX which can be used as the basis for a number of calculations to describe the curve, this is done in a separate table.

cosX sinX or cosinor function. Fits a sinusoid or wavy curve to the data. Often used in chronobiology. You have to give a period. If your unit of measurement is hours and you are interested in days the period is 24. Give a very long period if you want to fit a U-shaped curve. The factual regression is a+b*cos(X/period*2PI)+c*sin(X/period*2PI). The result (in radians) is recalculated into your unit of measurement in a separate table.

Add Linear. Adds a straight linear line to the graph and an additional Anova and Regression analysis, if these options are checked. If you prefer a linear analysis only check “none” for the non-linear analysis. 