It is highly unlikely that her child will have an IQ of exactly 75, as
there is always error in the regression procedure. Error may be
incorporated into the information given the woman in the form of
an “interval estimate.” For example, it would make a great deal
of difference if the doctor were to say that the child had a ninety-
five percent chance of having an IQ between 70 and 80 in contrast
to a ninety-five percent chance of an IQ between 50 and 100. The
concept of error in prediction will become an important part of the
discussion of regression models.
It is also worth pointing out that regression models do not make
decisions for people. Regression models are a source of information
about the world. In order to use them wisely, it is important to
understand how they work.

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REGRESSION ANALYSIS
205
NMIMS Global Access – School for Continuing Education
After studying this chapter, you should be able to:
Understand the concept of regression analysis
Discuss the applicability of regression
Describe simple linear regression and nonlinear regression
model.
Learn about coefficient of regression and linear regression
equations
7.1
INTRODUCTION
The word regression was first used as a statistical concept in 1877 by
Francis Galtan. Later if more than one variable is used to predict, the
word multiple regression is used. In regression analysis we develop an
equation called as an estimating equation used to relate known and
unknown variables. Then correlation analysis is used to determine
the degree of the relationship between the variables.
Using the chi-square test we can find whether there is any relationship
between the variables. Correlation and regression analysis show how
to determine the nature and strength of the relationship between the
variables. In this chapter we will learn, how to calculate the regression
line mathematically.
7.2
REGRESSION ANALYSIS
We need to have statistical model that will extract information from
the given data to establish the regression relationship between
independent and dependent relationship. The model should capture
systematic behaviour of data. The non-systematic behaviour cannot be
captured and called as errors. The error is due to random component
that cannot be predicted as well as the component not adequately
considered in statistical model. Good statistical model captures the
entire systematic component leaving only random errors.
In any model we attempt to capture everything which is systematic
in data. Random errors cannot be captured in any case. Assuming
the random errors are ‘Normally distributed’ we can specify the
confidence level and interval of random errors. Thus, our estimates
are more reliable.
If the variables in a bivariate distribution are correlated, the points
in scatter diagram approximately cluster around some curve. If the
curve is straight line we call it as linear regression. Otherwise, it is
curvilinear regression. The equation of the curve which is closest to
the observations is called the ‘
best fit’
.

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