Question

Multiple Regression is complex. Discuss why we use it and what it tells us, and contrast this with Multiple Correlation and the reasons we might use it. Let’s think of examples in clinical work where these techniques might enhance our ability to predict some future outcome. Show me you understand the information these measures yield.

Answer 1

Reality in the public sector is complex. Often there may be several possible causes associated with a problem; and likewise there may be several factors necessary for a solution. Complex statistical applications are needed which can:

-deal with interval and ratio level variables

-assess causal linkages

-forecast future outcomes

    Ordinary least squares linear regression is the most widely used type of regression for predicting the value of one dependent variable from the value of one independent variable. It is also widely used for predicting the value of one dependent variable from the values of two or more independent variables. When there are two or more independent variables, it is called multiple regression.

Correlation measures the closeness (link) of the relationship between two or many variables without knowing the functional relationships. In contrast, regression can show the form of the relationship of one independent variable with one dependent variable. The forms of the intrinsic linear relationship such as polynomial, exponential and logarithmic regression tend to have low correlation. For example, the quadratic function has a low correlation coefficient values, but has a coefficient of determination (multiple correlation coefficient) is high on the regression function.

Regression analysis can also involve many independent variables simultaneously: y = f (x1, x2, ...), including complex functions of polynomial regression such as response surface curves.

Practically, the dotplots chart can be used to identify trends among one or many independent variables X with dependent variable Y. If it tends to form a linear distribution patterns, analysis of the relationship may only use correlation analysis. But if there is a intrinsic linear distribution tendency, preferably using regression analysis.

Dotplots graphs and correlation matrix can also be used to determine the possibility of multicolinearity between independent variables in multiple regression analysis. However, with several approaches in the stepwise regression analysis such as regression analysis, was able to overcome this multicolinearity problem.