Simple Bivariate Regression PSGE 7211

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

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

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

The Power of Regression

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

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

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 ...

Why is Regression linear? A straight line!

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)

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

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?

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!

Income & Schooling y Slope Intercept x = # years schooling

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)

Achievement & Homework Step 1 – Look at descriptives

Achievement & Homework Step 2 – Look at correlations

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

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)

y’ = a + bx + e The Regression Equation Predicted value of math achv’t = 47.032 + 1.990(# of homework hours) Note that the statistic is also significant as determined by the following formula:

Regression Line

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

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

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

SPSS – Bivariate Regression STEP 1

SPSS – Bivariate Regression STEP 2

SPSS – Bivariate Regression STEP 3

SPSS – Bivariate Regression STEP 3

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.