A statistical model is a theoretical construction of the relationship of explanatory variables to variables of interest created to better understand these relationships.
They typically consist of a collection of probability distributions and are used to describe patterns of variability that data may display.
The statistical model is expressed as a function. For example, a researcher may model a linear relationship using the regression function below:
y = b0 + b1x1 + b2x2 … + bixi
In this model, y represents an outcome variable and xi represents its corresponding predictor variables. The term b0 is an intercept for the model. The term bi is a regression coefficient and represents the numerical relationship between the predictor variables and the outcome for the ith term.
Statistical modelling is a major topic. Readers who want to know more will find extensive accounts of statistical models including linear regression and logistic regression in statistical texts and online.
Sources: Science Direct; Magoosh Statistics Blog.