What Is Polynomial Regression
A polynomial is a mathematical expression that is a sum of more than one monomial (Wikipedia). A monomial can be a constant, or a variable (also called indeterminate). In a monomial, the coefficients should be involved with only the operations of addition, subtraction, multiplication, and non-negative integer exponents (Wikipedia). For example, X2+5X-7 is a polynomial, and it is a quadratic one. Polynomial regression is the regression technique that tries to figure out the polynomial that fits the relationship of one dependent variable (Y) and one or more independent variables (X1, X2…). When there is only one independent variable, it is called a univariate polynomial (Wikipedia). When there are more than one independent variable, it is called a multivariate polynomial (Wikipedia). Polynomial regression is widely used in biology, psychology, technology, and management field (Jia, 2011).
The Relationship Between Polynomial Regression and Other Regressions
How do we use a polynomial regression? If we want to understand polynomial regression, first we need to know what’s the relationship between polynomial regression and other regressions. A simple linear regression studies the relationship of one independent variable and one dependent variable. In a simple regression model, we assume that there is only one independent variable that contributes to the changes of the dependent variable and the relationship between them is linear. However, that is usually an idealized case. In the real world practice, a dependent variable can be influenced by so many factors. For example, wool yield is controlled by weight, chest circumference, and body length of sheep(Jia, 2011). This is the t...
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...ly with the increasing of indeterminates (Jia, 2011). And in the meantime the calculations become very difficult as well.
Now we can use techniques from linear regression to solve the problem. After the transformation, the least squares method will be used to predict those unknown betas. The core concept of the least squares method is to make the sum of (y-ye)2 the least (Jia, 2011). There is no need to calculate them by ourselves because the process is complex. We usually use computer to assist us to get the results of the least squares method.
An example of using polynomial regression in SPSS
(use online data, show SPSS steps, result interpretations)
Reference
Jia, J. (2011). Statistics. Beijing, China: China Remin University Press.
http://en.wikipedia.org/wiki/Polynomial
http://en.wikipedia.org/wiki/Polynomial_regression
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