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Regression

Regression. 11/14/2013. Readings. Chapter 8 Correlation and Linear Regression (Pollock) (pp. 182-187 ) Chapter 8 Correlation and Regression (Pollock Workbook). Homework Due Today. Paper Assignment. Opportunities to discuss course content. Office Hours For the Week. When Friday 9-10

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Regression

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  1. Regression 11/14/2013

  2. Readings • Chapter 8 Correlation and Linear Regression (Pollock) (pp. 182-187) • Chapter 8 Correlation and Regression (Pollock Workbook)

  3. Homework Due Today • Paper Assignment

  4. Opportunities to discuss course content

  5. Office Hours For the Week • When • Friday 9-10 • Monday 8-10, 11-1 • Tuesday 8-12 • And by appointment

  6. Course Learning Objectives • Students will be able to interpret and explain empirical data. • Students will achieve competency in conducting statistical data analysis using the SPSS software program.

  7. Scatterplots

  8. A Way of Visualizing a Correlation

  9. More on Scatterplots • We can think of this line as a prediction line. • The closer the dots to the line, the stronger the relationship, the further the dots the weaker the line. • If all the data points are right on the regression line, then there is a perfect linear relationship between the two variables. • This only graphs a correlation...... this means that it does not mean causality nor should it be used for testing!

  10. Ratio and Intervals! Bivariate Regression analysis

  11. If we shouldn’t use scatterplots or correlation for testing.. What should we use?

  12. Remember this?

  13. Bivariate Linear Regression • Bivariate linear regression is an important statistical technique in the Social Sciences. It allows us to measure the effects of an independent variable on a dependent variable. • It regresses all the values on to a line that best describes the relationship.

  14. The Regression Equation! The Constant, where the line crosses the y-axis The Dependent Variable The independent variable The Slope and direction of the line

  15. The Y Term • the value of the dependent variable. • It can also be the predicted score if you use the model as an equation

  16. The Alpha Value • the constant • the point at which the line crosses the y-axis. • This number can be positive or negative and does not have to take on a realistic value based on your data! • This is the value of Y (the dependent variable) if the value of the independent variable is 0

  17. The Beta value • the slope and direction of the line • Positive slopes mean the line goes up, Negative slopes mean the line goes down. • The higher the value of beta, the steeper the slope. • The Regression coefficient • This tells us how much Y changes with each unit change in X.

  18. The Regression Equation for the Scatterplot

  19. Rules for Regression • If you have a Ratio/Interval Dependent variable that takes on at least 11 values • You need ratio level independent variables (some argue that you can use ordinals, but be careful) • If you have 30 or more cases (N>30) • If you have a linear relationship. It will not work with curvilinear or exponential relationships.

  20. Computing Regression in SPSS

  21. How to do it • You must have a ratio-level dependent variable • Analyze • Regression • Linear

  22. Variable Placement • Here you can Test, it is not symmetrical! • You place your dependent and independent variables in the appropriate places and select ok.

  23. The Output

  24. The Constant (Alpha) • Value is 42.435 • This is the value of the d.v. if the iv is zero

  25. Betas and Independent variables • this tells us how much change in the dependent variable, is explained by the independent variable. • Every increase in religious attendance causes the d.v to move by .470 • Do we have a positive or negative relationship?

  26. Is it a significant Relationship (T-Statistic) • This gives us a T-Statistic that tells us if we can reject the null hypothesis. • You look at the significance value to check to see if there is a relationship. The magic number for significance is .05 to reject the null and say there is a relationship! • Sig<.05, the independent variable is significant!

  27. One More • % without health insurance (DV) • Unemployment rate (IV)

  28. Using regression to predict

  29. Data from our equation Y= Percent of state legislators who are women. a= 42.435 the constant (the value in where our line crosses the y-axis) b= -.470 (the slope of the line). It is negative, so that as religious attendance increases, the% of women in the legislature decreases by that amount. A Predicted Value X (50)= oh, lets say a score of 50 above (1/2 of the people go to church frequently)

  30. Using the Value to Predict • Y= 42.435 + (-.470 *50) • Y= 42.435 + (-23.5) • Y= 18.935

  31. An Example

  32. Union and Per Capita Income • Null Hypothesis- There is no relationship between a state's Union population and the per capita income • What would the predicted per capita income be for a state with a union % of 25?

  33. Minority population and health care access • Null Hypothesis? Slope? Practical significance

  34. Cars of the 1970’s • Lets all try one out with the Cars database • Run a regression

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