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Continuous Independent Variables -- variables that lie on a continuum such as age, weight, height, income and the like are all considered continuous variables. These could take any numeric form, including decimals within a logical range (e.g. age would not be negative).
Quasi-continous Indendent Variables -- variables that appear to lie on a continuum, such as years of schooling or number of children in the household, but are actually not continuous. The interval of 1 to 2 years of schooling and 5 to 6 years of schooling might not actually be estimating the same amount of change, but the years of schooling is used to estimate a level of education. The years are in whole numbers and not actually measured on a continuum, just as you would not bear half of a child.
Categorical Independent Variable -- variables that have distinct number of categories that are usually arbitrarily assigned numbers to represent each category, for example roof, water source, delivery location. Categorical variables may seem to have a heirachy to the numbering scheme, but it is not always consistent with different populations. An example is that a grass or thatch roof might be assigned a low number, then a higher number for a tin roof, and a higher number for an iron roof, but this would not necessarily mean that those with iron roofs are better-off.
Dichotomous Independent Variable-- variables that have two(di) forms (chotomy) and therefore are usually responses to yes/ no questions or another type of on/off type of response. This might be breastfed 0-4 months is yes or no...there are no alternative answers to that.
Dummy variables-- variables that might represent several mutually exclusive categories, so that the responses of the dummy variables can only take on a value of yes (1) for one of the variables at once-- it would infer that all the other variables therefore are 0. For example, the variable for water source might have had 3 responses possible -pipe, well, tap, but you recode this into three separate variables (dummy variables) that are now either yes or no responses for each (dichotomous). So at any one time, pipe could be a 1 for yes, but that would infer that well and tap are both no or 0, since they are mutually exclusive. These are useful in regression analysis, but you always include all but one of the possible dummy variables in the model...never all of the variables.