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Non-Linear Regression

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.

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Non-Linear Regression

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  1. Non-Linear Regression

  2. 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 r2 which is how closely the line fits the data.

  3. It is the coefficient of Determination (r2). It is defined as being Variation in y explained by variation in x = r2 Total variation in y If the line is a perfect fit, yest and y will be identical for each value of x.

  4. If the curve is a poor fit, the total of (yest – ybar)2 will be smaller than the total of (y – ybar)2, therefore r2 will be close to 0. The curve of best fit will be the one that has the highest value for r2. It can only be from 0 and 1.

  5. Power Regression – uses the line of y = axb as the line that models the information. Exponential Regression – uses the line of y = abx or y = aekx 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.

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

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