Assuming that r is the maximum rate of increase of the population,

the fraction by which the actual population (N) remains below the maximum (K), then the increase of population per unit of time is

The total population will then be

Figure 4.1 shows the various forms of logistic growth curve for different values of t and r (Weisstein, Eric W., 2009). In a typical logistic growth model, showing growth of population, N increases continuously from zero to a saturating level in a certain manner: initially when N is small, the growth rate is also small, but it continues to increase till a maximum point of growth rate is reached after which although N continues to rise the rate of growth becomes smaller and smaller, ultimately reaching zero. Is this not a realistic assumption for population growth? Almost the same thing can be said about the degree of urbanization, spread of literacy and many other things in population studies. All these processes can be modelled using logistic curve.

Logistic regression is a type of regression model in which log of odds ratio of a binary/qualitative dependent variable is expressed as a linear function of a number of qualitative as well as quantitative variables. During the last fifty years logistic regression has completely replaced the simple multiple regression analysis in sociology.