develop the estimated simple linear regression equation

For example, X 2 appears in the equation for b 1. In the two variable case, the other X variable also appears in the equation. It's simpler for k=2 IVs, which we will discuss here.įor the one variable case, the calculation of b and a was:Īt this point, you should notice that all the terms from the one variable case appear in the two variable case. The prediction equation is:įinding the values of b is tricky for k>2 independent variables, and will be developed after some matrix algebra. Again we want to choose the estimates of a and b so as to minimize the sum of squared errors of prediction. We still have one error and one intercept. Note that we have k independent variables and a slope for each. We can extend this to any number of independent variables: Where Y is an observed score on the dependent variable, a is the intercept, b is the slope, X is the observed score on the independent variable, and e is an error or residual. With one independent variable, we may write the regression equation as: How is it possible to have a significant R-square and non-significant b weights? What are the three factors that influence the standard error of the b weight? Write a regression equation with beta weights in it. Why do we report beta weights (standardized b weights)?

What happens to b weights if we add new variables to the regression equation that are highly correlated with ones already in the equation? multiple regression?ĭescribe R-square in two different ways, that is, using two distinct formulas. What is the difference in interpretation of b weights in simple regression vs.

Write a raw score regression equation with 2 ivs in it. Regression with Two Independent Variables

Develop the estimated simple linear regression equation