Intro to general linear models (GLM)
Simple linear regression and multiple regression are subsets of general linear models. A typical GLM has K+1 parameters and looks something like this
y=B0+B1x1+B2x2+B3x3...BkXk+epsilon
and "linear" here means linear in the parameters (x's can be of higher order and the model can be called linear). B0 is still the slope (value when all Xi=0), but now B1---Bk are partial slopes, meaning each Bi they represent the change in y per unit change in Xi, holding all other Xj constant.
GLMs an be additive (y=B0+B1x1i+B2x2i+error) which indicates the belief that the effect of the explanatory variables are additive or GLMS can include an interaction term (y=B0+B1x1+B2x2+B3X1X2), meaning the explanatory variables affect each other in an increasing or decreasing way.
Dummy variables are sometimes used when using categorical variables, like groups. The use of dummy variables get around the following problem: if we have 4 regions and code them 1,2,3,4 then we are forcing the difference between groups 2 and 3 to be the same as the difference between 1 and 4.
By assigning categories a dummy variable, we can measure the difference between the baseline category and another dummy variable, holding x constant.
