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# Intermediate Statistics 1

## on Jun 24, 2008

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## Intermediate Statistics 1Presentation Transcript

• Intermediate Statistics Professors:Ramaswami & Walker
• This Morning’s Session
• Review of Course Outline
• Review of Course Expectations
• Review of First Stat’s course
• Break
• Introduction to Generalized Linear Techniques
• Introduction to Regression
• Break
• Simple Regression
• Purpose of the course
• To assist you to develop the tools and knowledge on how to: (a) be intelligent consumers of data; (b) be able to run your own analysis; © understand how to interpret data and (d) be able to derive logical inferences based on data
• Focus of the Course
• Generalized Least Square techniques
• Interpretation using SPSS Outputs
• Knowing SPSS (Statistical Package for the Social Sciences)
• Course Requirements
• Mid-term examination
• Final examination
• Always have handouts in class
• Have a calculator
• Politeness
• Cooperative ethos
• Working independently on exams
• Review of First Stats Course
• What are the different types of measurement?
• What is correlational analysis
• Interpret the following findings:
• Example 1:
• In a study that examined the relationship between number of days present in school and students’ sense of belonging among 135 high school students the following Pearson Correlation statistics was obtained:
• r=.64; p<=.000
• Example 2
• The relationship between time on task and obtaining a grade of C+ or lower was found to be r= -.32; p <= .048 for 50 students in an alternative education program for disruptive students.
• What are generalized least square models?
• Generalized least square models are models that seek to minimize differences between what we observe and what we calculate.
• These models are able to accomplish this, by fitting the data such that the squared deviations between observed and fitted data are minimized.
• Example
• Refer to example on the board-
• Techniques to be Studied
• Regression (Simple, multiple, hierarchical)
• Analysis of Variance (one-way)
• Univariate Analysis of Variance to include Analysis of Covariance
• Possibly- Chi- Square
• Regression
• History- in France, applied to the study of astronomy- orbits of bodies around the sun (least squares method)
• Term regression coined in the 19 th C to describe a biological phenomenon- children of exceptional individuals tended to be less intelligent than their parents- Darwin’s cousin Francis Galton- “regression towards mediocrity”. Work later extended by Pearson and Yukle
• Assumptions of Regression
• Sample must be representative of the population.
• The dependent variable must be continuous.
• The independent variables must be linearly related but not strongly
• The independent variable should be continuous although categorical variables can be used.
• Values of the independent variables are normally distributed
• The Basic Regression Model
• Predicted Y= a+ B1(X1)+ B2(X2)……..error
• Where B1 represent the impact of X1 on Y
• a represents the constant or the intercept.
• Y is our outcome variable
• X is our independent variable
• What do the terms mean?
• B is called the slope or the regression coefficient. It is the change in the dependent variable for a unit change in x or the predictor variable
• Example of slope
• Education Income
• 16 years 20,000
• 18 years 20, 500
• 20 years 21,000
• 22 years 21,500
• 24 years 22, 000
• Questions that can be asked in regression
• What is the impact of the predictor (independent) variables on the outcome (dependent variable)?
• Is the impact significant?
• Is the regression model significant?
• What percent of the variance in the outcome variable is explained by the predictor (s) variable (s).
• Key Terms in SPSS Regression Outputs
• R Square