Database Reference
In-Depth Information
6.1 Linear Regression
Linear regression is an analytical technique used to model the relationship between
several input variables and a continuous outcome variable. A key assumption is
that the relationship between an input variable and the outcome variable is linear.
Although this assumption may appear restrictive, it is often possible to properly
transform the input or outcome variables to achieve a linear relationship between
the modified input and outcome variables. Possible transformations will be covered
in more detail later in the chapter.
The physical sciences have well-known linear models, such as Ohm's Law, which
states that the electrical current flowing through a resistive circuit is linearly
proportional to the voltage applied to the circuit. Such a model is considered
deterministic in the sense that if the input values are known, the value of the
outcome variable is precisely determined. A linear regression model is a
probabilistic one that accounts for the randomness that can affect any particular
outcome. Based on known input values, a linear regression model provides the
expected value of the outcome variable based on the values of the input variables,
but some uncertainty may remain in predicting any particular outcome. Thus, linear
regression models are useful in physical and social science applications where there
may be considerable variation in a particular outcome based on a given set of input
values. After presenting possible linear regression use cases, the foundations of
linear regression modeling are provided.
6.1.1 Use Cases
Linear regression is often used in business, government, and other scenarios. Some
common practical applications of linear regression in the real world include the
following:
•
Real estate:
A simple linear regression analysis can be used to model
residential home prices as a function of the home's living area. Such a
model helps set or evaluate the list price of a home on the market. The
model could be further improved by including other input variables such as
number of bathrooms, number of bedrooms, lot size, school district
rankings, crime statistics, and property taxes.
•
Demand forecasting:
Businesses and governments can use linear
regression models to predict demand for goods and services. For example,
restaurant chains can appropriately prepare for the predicted type and
