Regression Analysis

Learning Outcome:

After completing this module the students will be able to:

• Determine whether a regression experiment would be useful in a given instance

• Develop a simple linear regression model

• Understand the assumption of simple linear regression model

• Fit regression equations

• Compute a prediction interval for the dependent variable

• Check significance of regression coefficients using t-test

• Test the goodness of fit our model

1. Introduction to Simple Linear Regression

After having established the fact that two variables are strongly correlated with each other, one may be interested in predicting the value of one variable with the help of the given value of another variable. For example, if we know that yield of wheat and amount of rainfall are closely related to each other, we can estimate the amount of rainfall to achieve a particular wheat production level. This estimation becomes possible because of regression analysis that reveals average relationship between the variables.

The term “Regression” was first used by Sir Francis Galton in 1877 while studying the relationship between the height of fathers and sons. The dictionary meaning of regression is the act of returning back to the average. According to Morris Hamburg, regression analysis refers to the methods by which estimates are made of the values of one a variable from a knowledge of the values of one or more other variables and to measurement of the errors involved in this estimation process. Ya Lun Chou elaborates it further adding that regression analysis basically attempts to establish the nature of relationship between the variables and thereby provides mechanism for prediction/ estimation.

In regression analysis, we basically attempt to predict the value of one variable from known values of another variable. The variable that is used to estimate the variable of interest is known as “independent variable” or “explanatory variable” and the variable which we are trying to predict is termed as “dependent variable” or “explained variable”. Usually, dependent variable is denoted by Y and independent variable as X.

It may be noted here that term ‘dependent’ and ‘independent’ refer to the mathematical or functional meaning of dependence; i.e. they do not imply that there is necessarily any cause and effect relationship between the variables. It simply means that

Impressum

Verlag: BookRix GmbH & Co. KG

Texte: Hemant Sharma
Bildmaterialien: Hemant Sharma
Lektorat: Hemant Sharma
Übersetzung: Hemant Sharma
Tag der Veröffentlichung: 28.05.2017
ISBN: 978-3-7438-1537-7

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