A linear regression equation is usually written Y = a + bX + e

Where Y is the dependent variable

a is the intercept

b is the slope or regression coefficient

X is the independent variable (or covariate)

e is the error term

Different type of lines:

Nonlinear regression aims to describe the relationship between a response variable and one or more explanatory variables in a non-linear fashion.

Example of to assign your "Y" and "X" variable:

Suppose that a diode is examined to assess the relationship between the voltage and the current. The following table shows the current obtained at set voltages.

Voltage (volts) 0.4 0.5 0.6 0.7 0.8

Current (amps) 0.01 0.02 0.05 0.07 0.12

By fitting a regression line to the data, i.e. y = a + bx, a model for the relationship between voltage and current is found. As the voltage is set at the start, it is the explanatory variable (Independent variable) and the current is the response variable (Dependent variable).

Thank you Srinivasan and Ronny,

Then how we would interpret F test? To know what is the best model?

Any one can explain more the difference between each of this models (straight linear, logarithmic curve, exponential, geometric or parabola)?

Ok,:)

let me explain with graphs from a SAS analysis which I've analysed. Firstly I should say that almost always "X" is assigned to the variable which is easier to measure and "Y" is the other one. F test has no absolute interpretation for model selection, although, the more the F statistic the more the reliability of the model. You SHOULD always consider some important criteria: 1- R-square.2- residual distribution plot. 3- AIC ( specially for non linear regression).

the first graph is an example of linear regression. As you see with an increase in X the Y is increased constantly.

This one is a logarithmic regression. However, you can fit 2 or more flexible models for such data. Here, we can fit a hyperbolic or exponential curve, depending on parameter sign (- or +). The better model is the one which have lower AIC and RMSE, and higher adjusted R-sqr.

This one is a Quadratic model. I choose quadratic because we have a maximum point in graph. Don't forget not to use more than quadratic (cubic, etc.) polynomial.

For residual test it's better to use two criteria: 1- residuals must have normal distribution, 2- mean of residuals should be equal to zero.

Graph explanation is a little complicated. If the residuals did not have both of assumption, then it said to be heteroscedastic or your model has heteroscedasticity problem.

I hope it can help you

There are two types of guys - statisticians (who knows about DOE, Regression etc weird stuff) and technologists (chemists, economists, physicist) who knows about the nuts and bolts of the problem from theoretical/practical etc. point of view - they fill the nature of the problem).

So always (and I mean always) the technologists should provide the statisticians with their perception about the dependence of Y from X - is it linear (?) that means if we increase X, Y will increase. Is it Quadratic (?) - which means if we increase X, Y will increase until some point and most probably it will decrease after that. May be it is exponential - if we increase X, Y will increase very sharply, going to infinity - etc. (Sorry I can't express so colorful the logistic relationship). Briefly, the first question to the technologist (in this case Abdullah) is "what is your perception for the relationship?". Then to start to fit the Xs to Ys and based on the results to continue with the research or with publication.

If you have the scatter plot, go for the trendline and see what it appears like.