1277 Words6 Pages

Chapter 4
Multiple Linear Regression
Section 4.1
The Model and Assumptions
Objectives
Participants will: understand the elements of the model understand the major assumptions of doing a regression analysis learn how to verify the assumptions understand a median split
3
The Model y o 1x1 ... p x p or in Matrix Notation
Dependent Variable nx1 Unknown Parameters (p+1) x 1
Y X e
Independent Variables – n x(p+1)
Error – nx1
4
Questions
How many unknown parameters are there? Can you name them? How many populations will be sampled? What are conceptual populations?
5
Major Requirements for Doing a Regression Analysis
The errors are normally distributed (not Y). Constant*…show more content…*

Problems if VIF > 10. Some people use the condition index. In order to avoid false positives, use the COLLINOINT option. 24 Variance Inflation Factor (VIF) Example 25 Collinearity Diagnostics – Not Adjusted 26 Collinearity Diagnostics – Adjusted 27 Body Fat Example Variables 28 Percent body fat from Siri’s (1956) equation – dependent Age (years) Weight (lbs) Height (inches) Neck circumference (cm) Chest circumference (cm) Abdomen 2 circumference (cm) Hip circumference (cm) Thigh circumference (cm Knee circumference (cm) Ankle circumference (cm) Biceps (extended) circumference (cm) Forearm circumference (cm) Wrist circumference (cm) What Is Being Tested by |t| 30 continued... What Is Being Tested by Pr >|t| 31 Partial F-Tests H o : 3 0 | all other 's are in the model 32 Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 33 ... Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 34 ... Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 35 ... Graphs Predicted versus Y Residual versus Independents Student versus Independents Cook’s D versus Weight Leverage versus Weight 36 Moral of the Story Removing more than one variable at a time is a

Problems if VIF > 10. Some people use the condition index. In order to avoid false positives, use the COLLINOINT option. 24 Variance Inflation Factor (VIF) Example 25 Collinearity Diagnostics – Not Adjusted 26 Collinearity Diagnostics – Adjusted 27 Body Fat Example Variables 28 Percent body fat from Siri’s (1956) equation – dependent Age (years) Weight (lbs) Height (inches) Neck circumference (cm) Chest circumference (cm) Abdomen 2 circumference (cm) Hip circumference (cm) Thigh circumference (cm Knee circumference (cm) Ankle circumference (cm) Biceps (extended) circumference (cm) Forearm circumference (cm) Wrist circumference (cm) What Is Being Tested by |t| 30 continued... What Is Being Tested by Pr >|t| 31 Partial F-Tests H o : 3 0 | all other 's are in the model 32 Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 33 ... Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 34 ... Interpretation – The Stable Table Do I need this leg to have a stable table? Nope! 35 ... Graphs Predicted versus Y Residual versus Independents Student versus Independents Cook’s D versus Weight Leverage versus Weight 36 Moral of the Story Removing more than one variable at a time is a

Related

## Linear Regression

1142 Words | 5 PagesLinear-Regression Analysis Introduction Whitner Autoplex located in Raytown, Missouri, is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac, GMC, and Buick franchises as well as a BMW store. Using data found on the AutoUSA website, Team D will use Linear Regression Analysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing

## Linear Regression

1330 Words | 6 PagesLinear Regression deals with the numerical measures to express the relationship between two variables. Relationships between variables can either be strong or weak or even direct or inverse. A few examples may be the amount McDonald’s spends on advertising per month and the amount of total sales in a month. Additionally the amount of study time one puts toward this statistics in comparison to the grades they receive may be analyzed using the regression method. The formal definition of Regression

## Linear Regression Model

1029 Words | 5 PagesDue in class Feb 6 UCI ID_____________________________ MultipleChoice Questions (Choose the best answer, and briefly explain your reasoning.) 1. Assume we have a simple linear regression model: . Given a random sample from the population, which of the following statement is true? a. OLS estimators are biased when BMI do not vary much in the sample. b. OLS estimators are biased when the sample size is small (say 20 observations)

## Project Assignment On Multiple Linear Regression

1844 Words | 8 PagesProject Assignment on Multiple Linear Regression Table of Contents 1.0 Introduction: 3 2.0 Data and Methods 3 2.1 Data 3 2.2 Methods 3 3.0 Results 4 3.1 Graphical results: 4 3.2 Correlation results: 8 3.3 Multiple regression results: 8 4.0 Discussion 10 5.0 Conclusion 10 Appendix: 11 1.0 Introduction: Standing in the contemporary world, while several cities in the America have evidenced declined, crime rate, there is a significant number of cities specifically that are small in size, experienced

## Linear Regression ( LR ) Equation In Excel

1145 Words | 5 PagesIntroduction The general intention of this Module Two Case Assignment is to generate a Linear Regression (LR) equation in Excel. We will be formulating this equation by exploiting data gathered by our client, the New Star Grocery Company, this organization relies that their consumer influx correlates with their monthly sales. Thus, we will commence this assignment by deliberating upon the means, in which we developed this equation. Development Henceforth, in developing this equation, we gathered

## Introduction to Linear Regression and Correlation Analysis

3134 Words | 13 PagesIntroduction to Linear Regression and Correlation Analysis Goals After this, you should be able to: • • • • • Calculate and interpret the simple correlation between two variables Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant Goals (continued) After this, you should be able to: • Calculate and

## Project Proposal : Simple Linear Regression Project

2377 Words | 10 PagesPROJECT PROPOSAL Fall 2014 / IE 5318 (APPLIED LINEAR REGRESSION) Dr. VICTORIA CHEN STUDENT NAME(S): PROJECT NAME: SIMPLE LINEAR REGRESSION PROJECT I) PROJECT-PROPOSAL: ABSTRACT: We have considered the NBA statistics for the year 2013. We here perform an analysis to find the response of variables when different predictor variables are chosen. Here, we make observations corresponding to 38 players in the year 2013. The data set we have chosen includes: Predictor variables:

## The Simple Linear Regression Model

1243 Words | 5 PagesPURPOSE This report will discuss the simple linear regression model; throughout two variables, the predictor variable (independent) and one response variable (dependent) will be used to explain the models. In so doing, it explains the underlying assumptions when fitting both variables into models and statistical tools. In addition to findings from statistical analyses, this report communicates in clear terms the significance of data on the retention rate (%) and the graduation rate (%) for the sample

## Essay On Multi-Linear Regression

1009 Words | 5 PagesA sample size equaling 50 + 8m is required to do a multi-linear regression, where m is the number of independent variables chosen. At least 3 independent variables can be analyzed (assuming a moderate effect size) taking males and females separately if an equal number of males and females are chosen (Green, 1991). Thus the sample size is adequate for a multi-linear regression analysis. Therefore a sample size of 154 stable mentally ill patients is thus both practical and also would be among the highest

## My Regression Model Is A Simple Additive Linear Regression

1475 Words | 6 Pagesminority legislators or more women legislators, based on the way candidates get elected according to the state rules. I would expect to see that states with more black legislators have fewer women legislators and vice versa. My regression model is a simple additive linear

### Linear Regression

1142 Words | 5 Pages### Linear Regression

1330 Words | 6 Pages### Linear Regression Model

1029 Words | 5 Pages### Project Assignment On Multiple Linear Regression

1844 Words | 8 Pages### Linear Regression ( LR ) Equation In Excel

1145 Words | 5 Pages### Introduction to Linear Regression and Correlation Analysis

3134 Words | 13 Pages### Project Proposal : Simple Linear Regression Project

2377 Words | 10 Pages### The Simple Linear Regression Model

1243 Words | 5 Pages### Essay On Multi-Linear Regression

1009 Words | 5 Pages### My Regression Model Is A Simple Additive Linear Regression

1475 Words | 6 Pages