Non-Linear Regression. How would we be able to find the line of best fit for data that is supposed to be curved? This is non-linear regression! In most.

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Presentation transcript:

Non-Linear Regression

How would we be able to find the line of best fit for data that is supposed to be curved? This is non-linear regression! In most cases we don’t know what the value of a certain point would be on a line of best fit, so we have to guess! It becomes an estimate. Modern technology can help us out a lot by finding the info for us. It even provides us with r 2 which is how closely the line fits the data.

It is the coefficient of Determination (r 2 ). It is defined as being Variation in y explained by variation in x = r 2 Total variation in y If the line is a perfect fit, y est and y will be identical for each value of x.

If the curve is a poor fit, the total of (y est – ybar) 2 will be smaller than the total of (y – ybar) 2, therefore r 2 will be close to 0. The curve of best fit will be the one that has the highest value for r 2. It can only be from 0 and 1.

Power Regression – uses the line of y = ax b as the line that models the information. Exponential Regression – uses the line of y = ab x or y = ae kx There are limits to the regression curves. It can give inaccurate results to your data. We get a different answer if we use a linear regression. Polynomial regression could give us the wrong info if we perceive it to be exponential! Your model should show a logical relationship between the variables with the best fit possible.

Homework Pg 191 # 1,2,3,4,5,9