Database Reference
In-Depth Information
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.
•
Medical:
A linear regression model can be used to analyze the effect of a
proposed radiation treatment on reducing tumor sizes. Input variables
might include duration of a single radiation treatment, frequency of
radiation treatment, and patient attributes such as age or weight.
6.1.2 Model Description
As the name of this technique suggests, the linear regression model assumes that
there is a linear relationship between the input variables and the outcome variable.
This relationship can be expressed as shown in
Equation 6.1
.
6.1
where:
is the outcome variable
are the input variables, for
j
=
1, 2, …, p - 1
is the value of
when each
equals zero
is the change in
based on a unit change in
, for
j
=
1, 2, …, p - 1
is a random error term that represents the difference in the linear model
and a particular observed value for
Suppose it is desired to build a linear regression model that estimates a person's
annual income as a function of two variables—age and education—both expressed
in years. In this case, income is the outcome variable, and the input variables
are age and education. Although it may be an over generalization, such a model
seems intuitively correct in the sense that people's income should increase as their
skill set and experience expand with age. Also, the employment opportunities and
starting salaries would be expected to be greater for those who have attained more
education.
However, it is also obvious that there is considerable variation in income levels
for a group of people with identical ages and years of education. This variation is
