1. Simple Bivariate Regression
PSGE 7211

2. Most widely used statistical technique in the social sciences
What is Regression?
(Multiple) regression is a statistical method for studying the relationship between a single dependent variable and one or more independent variables
Most widely used statistical technique in the social sciences

3. Clarification of Terms
Dependent Variable (DV)
Response, Outcome
Independent Variable (IV)
Predictor, Explanatory, Regressor, Covariate

4. What is Regression good for?
Prediction: you can combine many variables to produce optimal predictions of the dependent variable
Causal Analysis: it separates the effects of independent variables on the dependent variable so you can isolate the unique contribution of each variable

5. The Power of Regression

6. Predict and Explain
Understanding the causes of poor academic performance will allow us to predict who will have trouble in school
Motivational beliefs
Goals, Task value, Interest
Anxiety

7. Variables in Regression Analysis
You can use...
Nominal
Interval
Ratio/Continuous
Categorical
Continuous

8. Why is regression linear?
Regression analysis is also known as linear regression because it is based on a linear equation (y = a + bx)
If you graph a linear equation, you get a ...

9. Why is Regression linear?
A straight line!

10. INCOME = 8,000 + (1,000 x SCHOOLING)
An example
DV = person’s annual income
IV = number of years of schooling completed
Regress INCOME on number of years of schooling completed
INCOME = 8,000 + (1,000 x SCHOOLING)

11. INCOME = 8,000 + (1,000 x SCHOOLING)
Income & Schooling
INCOME = 8,000 + (1,000 x SCHOOLING)
Years of Schooling
Income 1 2 3 4 5 6 7
8,000 + (1,000 x 0) =
8,000
8,000 + (1,000 x 1) =
9,000
8,000 + (1,000 x 2) =
10,000
8,000 + (1,000 x 3) =
11,000
8,000 + (1,000 x 4) =
12,000
8,000 + (1,000 x 5) =
13,000
8,000 + (1,000 x 6) =
14,000
8,000 + (1,000 x 7) =
15,000

12. Income & Schooling
EXPLAIN: How would you explain the relation between income and schooling?
PREDICT: If a person has 10 years of schooling, what would be his/her income?

13. INCOME y DV = 8,000 a intercept + 1,000 b slope (SCHOOLING) x
Linear Equation
INCOME y DV =
8,000 a
intercept +
1,000 b
slope
(SCHOOLING) x
(variable x)
Point on the vertical axis which “intercepts” the line or the value of y when x is 0.
The amount of change in y we get for every 1-unit change in x
The larger the slope, the steeper the line!

14. Income & Schooling y
Slope
Intercept
x = # years schooling

15. IV = # hours per week on math homework
Another example
DV = Math Achievement
IV = # hours per week on math homework
Regress math achievement on number of hours spent per week on math homework
ACHV’T = a + b(HW)

16. Achievement & Homework
Step 1 – Look at descriptives

17. Achievement & Homework
Step 2 – Look at correlations

18. Achievement & Homework
Math Achv’t
For bivariate regressions, the R is equivalent to correlation coefficient (Pearson’s R)
The R-Square coefficient denotes the variance explained in the outcome variable by the predictor variable; Homework explains .102 or 10.2% of the variance in math achv’t HW
.102

19. Is the model significant?
Variance explained
Variance unexplained
Look at the F-Statistic. Is it significant? What does this mean? Null hypothesis for Regression: Slope of the regression line = 0 (or no relation)

20. y’ = a + bx + e The Regression Equation
Predicted value of math achv’t = (# of homework hours)
Note that the statistic is also significant as determined by the following formula:

21. Regression Line

22. b = unstandardized coefficients
b and Betas
b = unstandardized coefficients
β= standardized coefficients (b transformed into standard deviation units)

23. Interpreting Regression output
In order to examine what effect X had on Y, I regressed the DV on the IV
Results suggest that the overall model [was/was not] statistically significant, F (1, 98)=11.18, p=.001
The R-squared was .10, indicating that…
X [was/was not] statistically significant predictor of Y

24. In pairs, discuss the output – how would you interpret the output?
Lab Time
In pairs, discuss the output – how would you interpret the output?
Discuss what bivariate regression analysis you will run
Confirm that you understand the steps for running SPSS

25. SPSS – Bivariate Regression
STEP 1

26. SPSS – Bivariate Regression
STEP 2

27. SPSS – Bivariate Regression
STEP 3

28. SPSS – Bivariate Regression
STEP 3

29. Exit Ticket Interpret the output
What does this analysis do?
What should you report when you write up a regression analysis?
If you want, go to 1025 and run your HW 4 output.