Lecture 7 - Assumptions in the Method of Least Squares

Photo courtesy of F. Espenak at MrEclipse.com

Assumptions
In order to use the Least Squares Method, we must make 4 fundamental assumptions about our data and the underlying relationship between the independent and dependent variables, x and y.

1. Linearity - that the variables are truly related to each other in a linear relationship.
2. Independence - that the errors in the observations are independent from one another.
3. Normality - that the errors in the observations are distributed normally at each x-value. A larger error is less likely than a smaller error and the distribution of errors at any x follows the normal distribution.
4. Equal variance - that the distribution of errors at each x (which is normal as in #3 above) has the identical variance. Errors are not more widely distributed at different x-values.

A useful mnemonic device for remembering these assumptions is the word LINE - Linearity, Independence, Normality, Equal variance.

Note that the first assumption, linearity, refers to the true relationship between the variables. The other three assumptions refer to the nature of the errors in the observed values for the dependent variable.

If these assumptions are not true, we need to use a different method to perform the linear regression.