# Res 342 Week 4

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RES/342 Week Four

Regression analysis in Research

INTRODUCTION

Have you ever had to forecast sales? Have you ever wondered if there was a positive relationship between the number of hours that you studied for a certain exam and your final course grade? Have you ever wondered if there was a negative relationship between the number of cups of caffeinated coffee that you consume in a given day and the incidence of developing gallstones? These types of questions can be answered by statistical techniques referred to as linear regression, and correlation analysis. Regression analysis predicts the value of some dependent variable, Y, given some independent variable, X. Correlation analysis measures how strong the relationship is between the two variables.

Week in Relation to the Course

In previous weeks, we used hypothesis testing to draw conclusions about sample data. This week, we use linear regression to make predictions from a sample of data. Additionally, we use hypothesis testing to determine the validity of the regression line in terms of its slope and an ANOVA table to depict key values used to develop the regression equation. Linear regression is a key element of time series analysis presented next week.

Methodology

Regression analysis is used for prediction purposes. A regression model is a statistical model that is used to predict the values of a dependent or response “Y” variable on an independent or explanatory “X” variable. Simple linear regression uses a single independent “X” variable to predict the numerical dependent “Y” variable. Multiple regression models use several explanatory variables or independent “X’s” to predict a numerical dependent variable “Y” (Levine, Berenson, & Stephan, 1999, p. 772). In regression analysis, a scatter diagram is used to plot the independent variable, X, on the x-axis or horizontal axis and the dependent variable, Y, on the y-axis (vertical). This graph will indicate the relationship between the...

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