REGRESSION ANALYSIS

Regression Analysis

Regression Analysis

Introduction

The study is related to the regression analysis, which particularly focuses on the data that relates to the restaurant industry. Moreover, the paper is intended to get the knowledge about the customers so that the target market of restaurant business can be estimated.

Research Question

Is there an association between an average monthly spending by the customers and their income level?

Is there an association between an average monthly spending by the customers and their family size?

Hypotheses

Ho1: There is relation between an average monthly spending by the customers and their income.

HA1: There is no relation between an average monthly spending by the customers and their income.

Ho2: There is relation between an average monthly spending by the customers and their family size.

HA2: There is no relation between an average monthly spending by the customers and their family size.

Model Specification

The general model of the regression is given below:

Y = a + b x + c

The specific model of the regression for the average monthly spending by the customers, income and family size of the customers is given below:

Average monthly spending by the customers = a + b (Income level) + b (Family size) + c

Regression analysis is a statistical method for analyzing the relationship between a response variable that is the dependent variable (y) and one or more explanatory variables are held. Regression analysis is the generic name for a general type of models and methods, with many applications in empirical science and technology. The idea of a regression analysis is to describe or explain the observed variation in the y-data using the corresponding x-data. This is done by adapting a functional relationship y = ƒ (x) of a certain type that is linear; moreover, the relationship is often perfect (Freund, Wilson and Sa, 2006).

To express this relationship is very important to establish a mathematical model. This type of modeling is called regression, and helps to understand how certain variables influence another variable, that verifies the behavior of a variable that can change the behavior of another. This relationship can be seen as a process (Wang and Jain, 2003). In this process, the values of X1, X2 and so on are called the input variables or regressive (inputs) and Y- Variable are the output or response (Kleinbaum, Kupper and Mullerm, 2007).

Regression analysis enables to find a reasonable relationship between the input variables and output through empirical relationships. Using this approach requires data collection and the use of statistical methods for linear regression analysis (Allen, 2004). The data collection provides information about the nature of the relationship between variables and studies able to accommodate unexpected situations, such as variability in the raw material, temperature, and machine operators. However, if we are interested only in the relationship of an input variable with the response variable we have the case of simple linear regression. But if we want to relate the response variable with more than one variable then the multiple linear regression analysis is used. On the contrary, if the response variable is ...