This graph doesn't show it very well, but the regression problem can be thought of as a sort of response surface problem. We can (sort of) view the plot in 3D space, where the two predictors are the X and Y axes, and the Z axis is the criterion, thus: We have 3 variables, so we have 3 scatterplots that show their relations.īecause we have computed the regression equation, we can also view a plot of Y' vs. Job Perf' = -4.10 +.09MechApt +.09Coscientiousness. We can now compute the regression coefficients: The numbers in the table above correspond to the following sums of squares, cross products, and correlations: We can collect the data into a matrix like this: Suppose we want to predict job performance of Chevy mechanics based on mechanical aptitude test scores and test scores from personality test that measures conscientiousness. This equation is a straight-forward generalization of the case for one independent variable. The equation for a with two independent variables is: Also note that a term corresponding to the covariance of X1 and X2 (sum of deviation cross-products) also appears in the formula for the slope. Note that terms corresponding to the variance of both X variables occur in the slopes. 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
0 kommentar(er)
