In multiple regression model What are the characteristics of a good predictor variable

11.3.5.3 Multiple regression analysis of discussion evaluation

Multiple regression analysis was conducted to examine the effects of three factors [decision-making strategy, group to which participants belonged to, and type of agenda] on individuals’ evaluation of the discussion process, evaluation of the discussion results, and overall satisfaction with the discussion. Specifically, multiple regression analysis was conducted with the evaluation of the discussion process, the evaluation of the discussion results, and the overall satisfaction of the discussion as the dependent variables, and the decision-making strategy, the group to which the participants belonged to, and the type of agenda as the independent variables. The models were evaluated by AIC. The models examined were a model predicting by intercept only [model number 1], a model predicting by intercept and decision strategy [model number 2], a model predicting by intercept and participant's group [model number 3], a model explaining by intercept and agenda type [model number 4], a model predicting by intercept, decision strategy, and participant's group [model number 5], a model predicting by intercept, decision strategy, and agenda type [model number 6], a model predicting by intercept, group participants belong to, and agenda type [model number 7], a model predicting by intercept, decision strategy, group participants belong to, and agenda type [model number 8], an interaction between the intercept and the decision strategy, the group to which the participant belongs, the decision strategy and the group to which the participant belongs [model number 9], an interaction between the intercept and the decision strategy, the type of agenda, the decision strategy and the type of agenda [model number 10], and an interaction between the intercept and the group to which the participant belongs, the type of agenda, the group to which the participant belongs and the type of agenda [model number 11]. We compared the partial regression coefficients of the decision strategy in the model with the lowest AIC among the six models that included the decision strategy.

Multiple regression analysis was conducted to examine the influence of the three factors of decision-making strategy, the group to which the participants belonged to, and the type of agenda on the evaluation of the discussion process. As a result of comparing and ranking the AIC of each model, the model with the lowest AIC was the model that predicted the evaluation of the discussion process by the interaction of the decision strategy, the group to which the participants belonged to, and the decision strategy and the group to which the participants belonged to [model number 9], with an AIC of 2767.89. In other words, among the 11 models examined, the model that predicts the evaluation of the discussion process by the interaction of the decision strategy, the group to which the participant belongs to, and the group to which the participant belongs to with the decision strategy can be judged to be the model with the highest predictive ability.

The partial regression coefficients for the decision strategies in this model are shown in Table 5.6. The partial regression coefficients for DIS as the reference were −0.07 for WAD and −0.02 for LEX. There was no significant difference between WAD and DIS for either WAD or LEX [WAD: t[1140]=−0.63, n.s.; LEX: t[1140]=−0.18, n.s.]. There was no significant difference between WAD and DIS [WAD: t[1140]=−0.63, n.s.; LEX: t[1140]=−0.18, n.s.]. This suggests that when comparing WAD and DIS, and LEX and DIS, the ratings of the discussion process did not change, respectively.

Multiple regression analysis was conducted to examine the influence of the three factors of decision-making strategy, the group to which the participants belonged to, and the type of agenda on the evaluation of the outcome of the discussion. The lowest AIC model predicted the evaluation of the discussion process by the interaction of the decision-making strategy and the group to which the participants belonged to [model number 9], with an AIC of 3439.48. In other words, among the 11 models examined, the model that predicts the evaluation of the outcome of the discussion by the interaction of the decision strategy, the group to which the participant belongs to, and the group to which the participant belongs to with the decision strategy can be judged to be the model with the highest predictive ability.

The partial regression coefficients for the decision strategies in this model are shown in Table 5.6. The partial regression coefficients for DIS as the reference were −0.19 for WAD and −0.06 for LEX. There was no significant difference between WAD and DIS for either WAD or LEX [WAD: t[1140]=−1.21, n.s.; LEX: t[1140]=−0.41, n.s.]. There was no significant difference between WAD and DIS [WAD: t[1140]=−1.21, n.s.; LEX: t[1140]=−0.41, n.s.]. This suggests that when comparing WAD and DIS, and LEX and DIS, the evaluation of the results of the discussion did not change, respectively.

Results of Multiple Regression Analysis [MRA]

Recall that MRA is a statistical procedure that assesses the relationship between a dependent variable and several predictor variables. The estimates generated by MRA are called coefficients. Using MRA, we can calculate the amount of variance in the dependent variable that is accounted for [= explained] by the variation in each of the independent variables. This calculation shows the relative importance of each independent variable to the relationship.

It is beyond the scope of this book to provide a detailed treatment of MRA as a statistical technique. For a basic interpretation of MRA results in economics, consult Greenlaw [2009]. For advanced information on MRA and other statistical techniques, you may wish to consult Tabachnick and Fidell’s Using Multivariate Statistics.

In an MRA study, the following information generated by regression software is usually reported.

The size and sign of regression coefficients. The size of regression coefficients shows how much each predictor variable contributes on its own to the variance in the dependent variable after the effects of all the other predictor variables in the model have been statistically removed. In their standardized form [as β], regression coefficients are a measure of the importance of each variable, allowing researchers to compare the relative importance of the predictors. In economics and public policy, the sign of regression coefficients is also important and it is discussed in comparison with the expected [or hypothesized] sign predicted from theory: Do the explanatory variables have the expected sign?

Statistical significance for each estimated coefficient, which is determined by comparing the p-value [or significance probability] associated with a coefficient with the chosen level of significance. If the p-value is smaller, the coefficient is interpreted as being statistically significant; if it is greater, the coefficient is interpreted as being nonsignificant, or as not being significant. There are many variations in the reporting and interpretation of null hypothesis significance testing in public policy and economics. For example, in economics, three significance levels are commonly used: 1%, 5%, and 10% and results are often described as being “statistically significant at the 1% [or 5%, or 10%] significance level.” The 10% significance level is uncommon in other disciplines, for example, in sociology or education, where results with p-values that are greater than .05 [5%] are interpreted as being nonsignificant.

Alternatively, when reporting statistical significance, researchers may simply indicate whether the generated p-values are smaller than the level of significance. In this case, authors indicate statistically significant values with asterisks—a single asterisk [⁎] for p