Broyles Textbook Exercises

Week 7: Broyles Textbook Exercise

Introduction

            In order to know the nature of relationship between variables, there is use of a statistical application known as regression analysis. There are lots of methods in this statistical tool for doing analysis and modeling of the variables. These methods are particularly used when it is tried to find the relationship between one dependent variable and more than one independent variable. With the help of regression analysis, it is possible to know the way in which change in a dependent variable is caused due to the change in the independent variable.

Case Overview

            In the case discussed, there was need to analyze the relation between the age of individual and the number of times visits are done by physician. Here, the managed care organization has some members and age of those individuals is considered in this case. And visits refer to the number of times physician care was used by those individuals. So for the analysis, there was selection of 15 members randomly (Broyles, 2006).

Test statistic

            For the analysis of this data, the test statistic is selected and so regression analysis is used for this. For knowing the nature of relationship between variables, regression analysis can be used. There are lots of methods in this statistical tool for doing analysis and modeling of the variables. These methods are particularly used when it is tried to find the relationship between one dependent variable and more than one independent variable. With the help of regression analysis, it is possible to know the way in which change in a dependent variable is caused due to the change in the independent variable (Triola & Triola, 2006).

Assumptions in regression analysis

            When the regression analysis is applied on a particular data then there are three fundamental assumptions that are made. These assumptions are:

• In the sample, there should be necessarily one independent variable.
• There should be linear relationships between the variables in the sample.
• The data which is used in the sample should be either a ratio or internet based level of measurement.

Analysis 

            The age of the individuals and the visit by physician was taken as data for the regression analysis. In the data, there was R square as 0.91. This shows that the relationship between the data is good. So, the age and the number of visits by physician can give explanation about the major portion of variation in the managed care hospital and this is about 91%. It was marked that the level of significance F was set at 2.92857E-08 in the application of analysis of variance in the data. The variable of age was associated with a statically important p value and it was observed to be 2.92857E-08. On the other hand, there was no statistically important value of the visits variable and so the relative p value of it was 0.034085. The inference gained from F value is that there is much importance of the results and can be relied and there should be use of this set of independent variable. After the analysis the regression line was formed and this is:

y = Visit= -1.22 + 0.14 * Age

This indicates that there is increase in number of members by 0.14 for every increase in the number of visits. There can be presence of some standard error of 0.79. This indicates about the measure of the standard deviation and refers to the variability that exists in the sample.

References

Broyles, R. W. (2006). Fundamentals of statistics in health administration. Sudbury, Mass: Jones and Bartlett.

Triola, M. &Triola, M. (2006). Biostatistics for the Biological and Health Sciences. Addison-Wesley Longman, Incorporated.