Multiple Regresion

Executive Summary

Regression analysis is used to predict the behavior of a dependent variable, based on one or more independent variables. In this study, multiple regression is being used to predict behavior in a real life, daily situation; availability of treadmills at the local gym is being predicted depending on the hour of the day and day of the week, during peak hours. Data was collectedby observation during one month.
The results were analyzed following these steps:
* Analyze variables to assure independence, constant variation, a linear relation and a normal distribution through the use of residual plots.
* Verify how much the dependent variable’s variation depends on the predictor variables
* Validate the model through statistical tests
* Analyze thevariables to see if any of them should be removed from the model
This paper contains the results obtained from this analysis. The multiple regression model was simplified to a simple regression model, since the indicator variables, days of the week, were found not useful in predicting availability of treadmills at the local gym.
Speculations as to why this may have occurred are presented in thisproject, as well as conclusions related to the research.

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Multiple Regression Analysis to predict treadmill availability at the local gym |
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Author: |
ING. Carla P. García C.Advisor:Professor Rita TakakuwaTurn-in date:December 5th, 2011 |

Contenido
Executive Summary 1
Introduction 3
Problem statement 5
Methodology 5
Results and Analysis 5Conclusions and Recommendations 13
The following recommendations are presented: 13
Bibliography 14

Introduction

Multiple regression analysis is used to study the relationship between several independent variables that work as predictors, and one dependent variable. It is widely used in research with three main approaches:
1. Identify explanatory variables: which allows the researcherto create a model where the variables selected have an impact on the final result, thus allowing those variables that do not influence the result directly, to be eliminated.
2. Detect interaction among independent variables: helps identify if there is some type of relation between the independent variables that are being used in the analysis, and therefore in case it exists, see if it impactsthe final result.
There are four principal assumptions that have to be proved in order to successfully use linear regression to analyze a certain situation:
1. Linearity: the relationship between the dependent and independent variables have to be linear.
2. Independence: correlation between the errors should not exist.
3. Homoscedasticity : constant variance of the errors
4.Normality
This type of regression accepts continuous and discrete variables, but in case discrete variables are used, dummy variables have to be used and binary codes of 1 and 0 should be assigned in order to proceed with the analysis.
In the following research, multiple regression was applied to a real life situation, which will be explained in the next section.

Problem statement

At thelocal gym in my neighborhood, treadmills are rarely available at the peak hour of the week days, resulting in discontent among clients. The following research was made in order to determine if the availability of treadmills is related to the hour of the day and the days of the week. For the purpose of this study, the first three days of the week were analyzed, given that these days are the ones thatare visited the most by customers, thus resulting in a shortage of available treadmills.
It is important to state that the gym has a total of 10 treadmills available for clients.
Methodology

As mentioned, the research consists of one dependent variable and two independent variables.
Dependent variable: Number of treadmills available for usage in the gym
Independent variables:
*...