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
Obesity is becoming a major problem to many Americans as well as many people around the world. Being the second cause of preventable death in the United States, obesity increases the risk of numerous adverse health problems including breast cancer, heart disease, type II diabetes, osteoarthritis, colon cancer, stroke, and more. Obesity is defined as an excess proportion of total body fat, with a person being considered obese if his or her weight is twenty percent or more above normal body weight. A common way to measure obesity is by calculating the body mass index. An individual is considered overweight if his or her BMI is between twenty five and thirty,
(TCO 2) In Excel, a function can be defined as a _____. (Points : 2)
1. Identify each of the unknown samples(use specific data to justify your answers for A and B).
Bobbi Kristina Brown is in hospice in what may turn out to be her final days. Family members gather around her bedside for a never-ending prayer vigil. It should be a quiet time for her and her family members, but it isn’t. A storm is raging in spite of the soft music playing in the background and the lit candles. Someone entered the room and snapped a picture of Bobbi Kristina. Then he or she tries to sell it to the highest bidder. According to TMZ, July 7, 2015, this resulted in banning all members of Bobby Brown’s family from entering the room. Security at the hospice has orders to keep everyone out, except for a few key members. The only ones exempt from the ban is Bobby Brown, Pat Houston, Cissy Houston, and anyone else involved with Bobbi
Select appropriate tools to collect, record, analyze, and evaluate data. Make directional hypotheses that specify what happens to a dependent variable when an independent variable is manipulated.
179). This is an important statement as it means the researcher needs to start thinking about how they will analyze their data before they even collect it. In order to properly analyze the data, the researcher should transcribe each interview and then compare it to their observations and journal (Badenhorst, 2008). When analyzing the data the researcher must keep in mind the research questions, and create themes through the data that relate to the research question. First, the researcher will analyze each session together, coming up with keynotes and themes from the observations, interviews, and journals (Anderson & Austin, 2012). Once that is analyzed, each piece from each session will then be compared with each other. For example did participants enjoy the program in session 1 but not by session 5? Why did this happen? Was the program too repetitive? Was it the same thing over and over? Was there a different instructor? After the analysis is done the researcher must put the data into a legible discussion
2. Identify all of the major dependent and independent variables and the level of measurement for each variable
Body fat distribution can be estimated by skin fold measures, waist-to-hip circumference ratios, or techniques such as ultrasound, computed tomography, or magnetic resonance imaging.” (www.cdc.gov) The difference is that obesity is a definite problem, whereas being overweight can be directly related to obese but may just be that your lean muscle weight is higher than the average person in you height category.
2. Identify all of the major dependent and independent variables and the level of measurement for each variable
For the day of the dead research paper I chose Mexico because it's one of the most common Spanish speaking countries that celebrate the day of the dead. In this region the day of the dead usually starts on November 1st, and ends on November 2nd. It is celebrated with various festivities, honoring the dead. We watched a video in class recently, showing that people honor the dead with partying, and offerings.
T.S. Han, M.A. Tijhuis, M.E. Lean, et al. Quality of life in relation to overweight and body fat distribution Am. J. Public Health, 88 (1998), pp.
James, W. P. (2008). The epidemiology of obesity: the size of the problem. Journal of Internal Medicine, 336-352. Retrieved from http://eds.a.ebscohost.com.library.gcu.edu:2048/ehost/pdfviewer/pdfviewer?sid=9ede2d6d-4d02-42e9-aff7-dd9b2486a3c3%40sessionmgr4004&vid=8&h
Obesity rates are soaring throughout North America (What Is Obesity?, 2013). With obesity reaching almost epidemic proportions in the United States, and the threat of a global epidemic, we must watch this alarming increase carefully ( Health Risks of Obesity, 2013). Obesity is defined as: "…an excess of adipose tissue…" (A Report of the Surgeon General, 2014). The two most common measures of obesity are Body Mass Index (BMI is a ratio of weight to height) and relative weight index, such as percent desirable weight (Body Mass Index , 2013). BMI is the most frequently used measure of obesity as it has a strong correlation with more direct measures of adiposity, such as underwater weighing (A Report of the Surgeon General, 2013). Some
MEASUREMENTS: changes in obesity (body mass index (BMI) > or =30 kg/m(2)) and normal weight (BMI <25 kg/m(2)) prevalence for men and women by 10-year U.S. birth cohorts were examined. The prevalence of obesity and normal weight in the elderly in 2010 was estimated under three different scenarios of obesity prevalence change.
Source: CDC, National Center for Health Statistics, National Health and Nutrition Examination Survey. Health, United States, 2002. Flegal et. al. JAMA. 2002;288:1723-7. NIH, National Heart, Lung, and Blood Institute, Clinical Guidelines on the Identification, Evaluation and Treatment of Overweight and Obesity in Adults, 1998.