1. http://comp.uark.edu/~cvyas/survey_test/

2. Multiple Regression Analysis Regression analysis with two or more independent variables. Leads to an improvement in accuracy of prediction models, higher R 2 s. Challenges to interpretation due to multicollinearity.

3. Linear model y = the predicted, or dependent variable x = the variable used to predict y, or the independent variable a = the intercept, or point where a “line” cuts the y axis when x = 0 b = the slope, or change in y for any 1 unit change in x

4. Terms for the Linear Model The use of term for y, dependent variable, is consistent with a belief that values of x (independent) determine values of y. Knowing values of x allows us to predict value of y. To develop a statistical model, the dependent variable, y, is “regressed on” values of x (the “regressor”).

5. Linear Model and Additivity x 1, x 2, x 3 are a set of independent regressors that additively influence our prediction of the dependent variable y. bs are coefficients, in the units of y, that convert a one unit change in x into a change in y.

6. Coefficients Unstandardized coefficients are in units of the dependent variable Standardized coefficients or Beta coefficients range from -1.00 to +1.00

7. t-Values Reported with each coefficient Test if the coefficient is significantly different from zero Ratio of the coefficient to the standard error of the coefficient

8. Coefficient of Determination: R 2 Percentage of variance explained, ranges from near zero to 1.00 Squared value of a correlation coefficient in a simple, bivariate regression. Multiple R, is the equivalence of a correlation coefficient for a multiple regression

9. Adjusted R 2 R 2 increases with the addition of each regressor to the model This becomes very important with a small number of observations k = the number of regressors in the model n = the number of observations

10. Multicollinearity Violation of the independence assumption. Significance of coefficients from bivariate models reduced. Minimal improvement in prediction accuracy. Variation Inflation Factors approaching 10 It will be a problem in our models as we move from two to three census regressors.