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# Intermediate Statistics 1

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### Intermediate Statistics 1

1. 1. Intermediate Statistics Professors:Ramaswami & Walker
2. 2. This Morning’s Session <ul><li>Review of Course Outline </li></ul><ul><li>Review of Course Expectations </li></ul><ul><li>Review of First Stat’s course </li></ul><ul><li>Break </li></ul><ul><li>Introduction to Generalized Linear Techniques </li></ul><ul><li>Introduction to Regression </li></ul><ul><li>Break </li></ul><ul><li>Simple Regression </li></ul>
3. 3. Purpose of the course <ul><li>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 </li></ul>
4. 4. Focus of the Course <ul><li>Generalized Least Square techniques </li></ul><ul><li>Interpretation using SPSS Outputs </li></ul><ul><li>Knowing SPSS (Statistical Package for the Social Sciences) </li></ul>
5. 5. Course Requirements <ul><li>Mid-term examination </li></ul><ul><li>Final examination </li></ul><ul><li>Always have handouts in class </li></ul><ul><li>Have a calculator </li></ul><ul><li>Politeness </li></ul><ul><li>Cooperative ethos </li></ul><ul><li>Working independently on exams </li></ul>
6. 6. Review of First Stats Course <ul><li>What are the different types of measurement? </li></ul><ul><li>What is correlational analysis </li></ul><ul><li>Interpret the following findings: </li></ul>
7. 7. Example 1: <ul><li>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: </li></ul><ul><li>r=.64; p<=.000 </li></ul>
8. 8. Example 2 <ul><li>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. </li></ul>
9. 9. What are generalized least square models? <ul><li>Generalized least square models are models that seek to minimize differences between what we observe and what we calculate. </li></ul><ul><li>These models are able to accomplish this, by fitting the data such that the squared deviations between observed and fitted data are minimized. </li></ul>
10. 10. Example <ul><li>Refer to example on the board- </li></ul>
11. 11. Techniques to be Studied <ul><li>Regression (Simple, multiple, hierarchical) </li></ul><ul><li>Analysis of Variance (one-way) </li></ul><ul><li>Univariate Analysis of Variance to include Analysis of Covariance </li></ul><ul><li>Possibly- Chi- Square </li></ul>
12. 12. Regression <ul><li>History- in France, applied to the study of astronomy- orbits of bodies around the sun (least squares method) </li></ul><ul><li>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 </li></ul>
13. 13. Assumptions of Regression <ul><li>Sample must be representative of the population. </li></ul><ul><li>The dependent variable must be continuous. </li></ul><ul><li>The independent variables must be linearly related but not strongly </li></ul><ul><li>The independent variable should be continuous although categorical variables can be used. </li></ul><ul><li>Values of the independent variables are normally distributed </li></ul>
14. 14. The Basic Regression Model <ul><li>Predicted Y= a+ B1(X1)+ B2(X2)……..error </li></ul><ul><li>Where B1 represent the impact of X1 on Y </li></ul><ul><li>a represents the constant or the intercept. </li></ul><ul><li>Y is our outcome variable </li></ul><ul><li>X is our independent variable </li></ul>
15. 15. What do the terms mean? <ul><li>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 </li></ul>
16. 16. Example of slope <ul><li>Education Income </li></ul><ul><li>16 years 20,000 </li></ul><ul><li>18 years 20, 500 </li></ul><ul><li>20 years 21,000 </li></ul><ul><li>22 years 21,500 </li></ul><ul><li>24 years 22, 000 </li></ul>
17. 17. Questions that can be asked in regression <ul><li>What is the impact of the predictor (independent) variables on the outcome (dependent variable)? </li></ul><ul><li>Is the impact significant? </li></ul><ul><li>Is the regression model significant? </li></ul><ul><li>What percent of the variance in the outcome variable is explained by the predictor (s) variable (s). </li></ul>
18. 18. Key Terms in SPSS Regression Outputs <ul><li>R Square </li></ul><ul><li>Adjusted R Square </li></ul><ul><li>Regression model </li></ul><ul><li>Standardized Coefficients(Beta) </li></ul><ul><li>Unstandardized Coefficients (B) </li></ul><ul><li>Fvalue </li></ul><ul><li>T value </li></ul><ul><li>P value </li></ul>