Multivariate Analysis
Content
III. Multivariate Analysis Table 4: Table Showing Values for Total Regression and Relative Impact of Each Independent Variable on the Model
Variables Included In Regression Analysis Medicare Part D Eligible, February 2010 Beneficiaries with Known Creditable Drug Coverage, February 2010 Total (Cumulative Effect)1 beta .137 t .056 sig. .956 Very Low HMO Penetration Rate2 beta t sig. 8.305 2.408 .030 Low HMO Penetration Rate3 beta t sig. -2.90 -.123 .922 High HMO Penetration Rate4 beta t sig. 8.522 9.078 .070 Very High HMO Penetration Rate5 beta t -3.85 -1.197
sig. .244
-.779
.319
.751
-7.334
-2.126
.052
3.842
.163
.897
-7.617
-8.114
.078
4.779
1.486
.152
*Categorical variable used was HMO Penetration Rate, January 2009.
A. Multiple Regression Analysis The cumulative effect of the variables Medicare Part D Eligible and Beneficiaries with Known Creditable Drug Coverage, on the model shows that Medicare Part D Eligible affects Estimated Uninsured Population less than Beneficiaries with Known Creditable Drug Coverage. Beneficiaries with Known Creditable Drug Coverage have a more significant contribution to the model, since its t is higher in relation to the total t (t is 0.319 compared to Total Regression t, -1.946) and has a smaller significance (significance is at 0.751, compared to 0.956). The beta shows that there is also a negative effect on the model (beta is -.779). Looking at the R of the total model (R = 0.916), we can also see that the independent variable has a significant contribution to the model. The model shows that Beneficiaries with Known Creditable Drug Coverage affects the model more than Medicare Part D Eligible. B. Contextual Analysis The categorical variable used for contextual analysis was HMO Penetration Rate. In states where there is a very low HMO penetration rate, like Alabama, Alaska, and Idaho, the regression values (beta = 8.305, t = 2.408, significance = 0.030) show that the model described in the total regression analysis (Beneficiaries with Known Creditable Drug Coverage affects the model more than Medicare Part D Eligible), does not apply in this context. The beta value for Medicare Part D Eligible, which is 8.305, is higher compared to the beta value of Beneficiaries with Known Creditable Drug Coverage, which is -7.334. It is also very different since it shows a positive effect on the model. Medicare Part D Eligible is the significant independent variable in this context (0.030 against 0.052). There is also a more significant contribution of Medicare Part D Eligible on this context, because the t value is higher than the Total Regression t value (2.408 compared to -1.946). In states where there is a low HMO penetration rate, like Illinois and Nevada, the regression values (beta = 3.842, t = 0.163, significance = .897) show that model described in the total regression analysis, does apply in this context. The beta value for Medicare Part D Eligible (-2.90) is lower compared to the beta value of Beneficiaries with Known Creditable Drug Coverage (3.842), and shows the same negative relationship. Comparing the t of Beneficiaries with Known Creditable Drug Coverage in this context (0.163) with the model's t (-1.946), we can say that the independent variable does not affect the model very much. The significance also shows that the independent variables are not very significant in this context (0.922, 0.897). In states where there is a high HMO penetration rate, like Kansas and West Virginia, the regression values (beta = 8.522, t = 9.078, sig. = 0.070) show that the model described, does not apply in this context. The beta value for Medicare Part D Eligible (8.522) is higher than the beta value for Beneficiaries with Known Creditable Drug Coverage (-7.617), and shows that there is a positive
1 2
R = .916; R-squared = .840 R = .979; R-squared = .959
3 4
R = .944; R-squared = .891 R= .999; R-squared = .998 5 R = .934; R-squared = .873
relationship between the model and the independent variable. Comparing the t of Medicare Part D Eligible (9.078) in this context, with the model's t (-1.946) we can say that the independent variable affects the model significantly. The independent variables are also not significant in this context, because they are beyond the 0.05-significance level (0.070, 0.078). In states where there is a very high HMO penetration rate, like New Jersey and New York, the regression values (beta = 4.779, t = 1.486, sig. = 0.152) show that the model described, does apply in this context. The beta value for Beneficiaries with Known Creditable Drug Coverage (4.779) is higher than the beta value for Medicare Part D Eligible (-3.85), and shows that there is a positive relationship between the model and the independent variable. Comparing the t of Beneficiaries with Known Creditable Drug Coverage (1.486) in this context, with the model's t (-1.946) we can say that the independent variable does not affect the model significantly. The independent variables are also not significant in this context, because they are beyond the 0.05-significance level (0.244, 0.152).
Variables Included In Regression Analysis Medicare Part D Eligible, February 2010 Beneficiaries with Known Creditable Drug Coverage, February 2010 Total (Cumulative Effect)1 beta .137 t .056 sig. .956 Very Low HMO Penetration Rate2 beta t sig. 8.305 2.408 .030 Low HMO Penetration Rate3 beta t sig. -2.90 -.123 .922 High HMO Penetration Rate4 beta t sig. 8.522 9.078 .070 Very High HMO Penetration Rate5 beta t -3.85 -1.197
sig. .244
-.779
.319
.751
-7.334
-2.126
.052
3.842
.163
.897
-7.617
-8.114
.078
4.779
1.486
.152
*Categorical variable used was HMO Penetration Rate, January 2009.
A. Multiple Regression Analysis The cumulative effect of the variables Medicare Part D Eligible and Beneficiaries with Known Creditable Drug Coverage, on the model shows that Medicare Part D Eligible affects Estimated Uninsured Population less than Beneficiaries with Known Creditable Drug Coverage. Beneficiaries with Known Creditable Drug Coverage have a more significant contribution to the model, since its t is higher in relation to the total t (t is 0.319 compared to Total Regression t, -1.946) and has a smaller significance (significance is at 0.751, compared to 0.956). The beta shows that there is also a negative effect on the model (beta is -.779). Looking at the R of the total model (R = 0.916), we can also see that the independent variable has a significant contribution to the model. The model shows that Beneficiaries with Known Creditable Drug Coverage affects the model more than Medicare Part D Eligible. B. Contextual Analysis The categorical variable used for contextual analysis was HMO Penetration Rate. In states where there is a very low HMO penetration rate, like Alabama, Alaska, and Idaho, the regression values (beta = 8.305, t = 2.408, significance = 0.030) show that the model described in the total regression analysis (Beneficiaries with Known Creditable Drug Coverage affects the model more than Medicare Part D Eligible), does not apply in this context. The beta value for Medicare Part D Eligible, which is 8.305, is higher compared to the beta value of Beneficiaries with Known Creditable Drug Coverage, which is -7.334. It is also very different since it shows a positive effect on the model. Medicare Part D Eligible is the significant independent variable in this context (0.030 against 0.052). There is also a more significant contribution of Medicare Part D Eligible on this context, because the t value is higher than the Total Regression t value (2.408 compared to -1.946). In states where there is a low HMO penetration rate, like Illinois and Nevada, the regression values (beta = 3.842, t = 0.163, significance = .897) show that model described in the total regression analysis, does apply in this context. The beta value for Medicare Part D Eligible (-2.90) is lower compared to the beta value of Beneficiaries with Known Creditable Drug Coverage (3.842), and shows the same negative relationship. Comparing the t of Beneficiaries with Known Creditable Drug Coverage in this context (0.163) with the model's t (-1.946), we can say that the independent variable does not affect the model very much. The significance also shows that the independent variables are not very significant in this context (0.922, 0.897). In states where there is a high HMO penetration rate, like Kansas and West Virginia, the regression values (beta = 8.522, t = 9.078, sig. = 0.070) show that the model described, does not apply in this context. The beta value for Medicare Part D Eligible (8.522) is higher than the beta value for Beneficiaries with Known Creditable Drug Coverage (-7.617), and shows that there is a positive
1 2
R = .916; R-squared = .840 R = .979; R-squared = .959
3 4
R = .944; R-squared = .891 R= .999; R-squared = .998 5 R = .934; R-squared = .873
relationship between the model and the independent variable. Comparing the t of Medicare Part D Eligible (9.078) in this context, with the model's t (-1.946) we can say that the independent variable affects the model significantly. The independent variables are also not significant in this context, because they are beyond the 0.05-significance level (0.070, 0.078). In states where there is a very high HMO penetration rate, like New Jersey and New York, the regression values (beta = 4.779, t = 1.486, sig. = 0.152) show that the model described, does apply in this context. The beta value for Beneficiaries with Known Creditable Drug Coverage (4.779) is higher than the beta value for Medicare Part D Eligible (-3.85), and shows that there is a positive relationship between the model and the independent variable. Comparing the t of Beneficiaries with Known Creditable Drug Coverage (1.486) in this context, with the model's t (-1.946) we can say that the independent variable does not affect the model significantly. The independent variables are also not significant in this context, because they are beyond the 0.05-significance level (0.244, 0.152).
