Unit 3 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.
•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 modelling are provided.
Use Cases
Linear regression is often used in business, government, and other
scenarios. Some common practical applications of linear regression in
the real world inc lude 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 bed
rooms, lot size, school district ran kings, 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 quantity of food that customers will consume
based upon the weather, the day of the week, whether an item is
offered as a special, the time of day, and the reservation volume.
Similar models can be built to predict retail sales, emergency room
visits, and ambulance dispatches.
