Suppose the dependent variable is smoking status. the dependent variable are age, educational level and income. the coefficients are age=.02, educational level =1.8, income=.35. how can i interpret it?
You will also have to check on which of these are significant using their p values
The coefficient for the constant = the log-odds of an event (with event usually coded outcome variable = 1, non-event as outcome =0) when all explanatory variables are set to 0 (or their reference categories for categorical variables. You haven't told us the coefficient for your constant, so we can't work out the log-odds for that one.
The coefficients for the explanatory variables are the logs of the odds ratios for those variables.
- Coefficient for age=.02: e.02 = 1.0202 = the odds ratio for a 1-unit (probably 1-year?) increment in age (while holding all other variables constant).
- Coefficient for educational level =1.8: e1.8 = 6.05= odds ratio for a 1-unit increment in educational level (while holding all other variables constant).
- Coefficient for income=.35: e.35 = 1.419 = odds ratio for a 1-unit increment in income (while holding all other variables constant).
A 1-unit increment depends on how the variables were scaled. E.g., if you have income recorded in thousands of dollars rather than dollars, a 1-unit increment is an increment of 1000 dollars.
HTH.
The goal of a multiple logistic regression is to find an equation that best predicts the probability of a value of the Y variable as a function of the X variables. You can then measure the independent variables on a new individual and estimate the probability of it having a particular value of the dependent variable
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