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 techniquesInterpretation using SPSS OutputsKnowing SPSS (Statistical Package for

the Social Sciences)

Course Requirements

Mid-term examinationFinal examinationAlways have handouts in classHave a calculatorPolitenessCooperative ethosWorking independently on exams

Review of First Stats Course

What are the different types of measurement?

What is correlational analysisInterpret 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 CovariancePossibly- 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 19th 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 SquareAdjusted R SquareRegression modelStandardized Coefficients(Beta)Unstandardized Coefficients (B)FvalueT valueP value