Define mathematical model in statistics.

A mathematical model in statistics is a representation of a real-world situation using mathematical equations.

Mathematical models are used in statistics to describe and predict the behaviour of a system or process. They are often used to make predictions about future events or to test hypotheses about the relationships between variables. Mathematical models can be simple or complex, depending on the complexity of the system being modelled.

One common type of mathematical model in statistics is the linear regression model. This model is used to describe the relationship between two variables, where one variable is considered to be the independent variable and the other is the dependent variable. The model takes the form of a straight line equation, y = mx + c, where y is the dependent variable, x is the independent variable, m is the slope of the line, and c is the y-intercept.

Another type of mathematical model in statistics is the logistic regression model. This model is used to describe the relationship between a binary dependent variable (i.e. a variable that can take on only two values, such as yes or no) and one or more independent variables. The model takes the form of a logistic function, which is an S-shaped curve that describes the probability of the dependent variable taking on a particular value.

In conclusion, mathematical models are an important tool in statistics for describing and predicting the behaviour of real-world systems and processes. They can take many different forms, from simple linear equations to complex models involving multiple variables and non-linear relationships.