What is the difference between a linear and a non-linear regression in econometrics, no wikipedia please.?

Question

What is the difference between a linear and a non-linear regression in econometrics, no wikipedia please.?

Answer 1

Imagine that you want to relate a single variable to its cause, for example, how well students do on a standardized test (dependent variable y) as a function of hours studied (independent variable x).

Now assume that you have plotted each student on a piece of paper, where her test score is on the y axis, and her hours studied are on the x axis. (Similar to the scatter plot available here: http://mynasadata.larc.nasa.gov/images/L...

A linear regression analysis fits a straight line through these data points so that the squared distance of all points from the line is minimized. The regression equation is

y = a +bx + e

where a is the intercept (where the regression line intersects with the y axis), b is the "regression coefficient", and e is the error term.

The regression coefficient b tells you by how many points the test result is expected to increase for an additional hour of studying.

The crucial assumption of the linear regression model is that this effect does not depend on how many hour the student already studied: Let's assume the coefficient is 3, implying that an additional hour of studying is expected to raise the test score by 3 points. The linear model assumes that studying 2 instead of 1 hour OR studying 20 instead of 19 hours will both increase your test score in the same way.

The non-linear regression approach acknowledges that this assumption doesn't always make sense. For example, there are decreasing benefits from studying for a test: You get more "bang for your buck" for the first couple of hours. A non-linear regression model doesn't fit a straight line, but a curve through the scatter plot. (You said you don't want to look at Wikipedia, put at least take a look at the picture at http://en.wikipedia.org/wiki/Nonlinear_r...

If the relation between a dependent variable (test score) and an independent variable (study time) is approximately linear, a linear regression model is appropriate. If the relation is likely to be non-linear, you should run a non-linear regression (or transform one or both of your variables so that the relation is approximately linear).