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### Sample Creative Writing Paper on Regression Models

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##### Benefits of a Variable

In mathematical modeling, dependent and independent variables are the basic types of variables used. In the development and examination of models, variables can be beneficial in the following ways;

1. Reduces the dimensionality of data: A large number of observables can be integrated in a model thereby simplifying the concept
2. A variable may be altered to in order to study the corresponding effect it has on another variable, this helps in designing models suited for solving specific problems
##### Simple linear regression model

In regression analysis modeling, a regression model is referred to as a simple regression if it involves only a single independent variable. A linear regression model is one that straight-line relationships between its variables. Therefore a simple linear regression model is a regression model that uses a single independent variable in its equation and expresses the relationship between the independent and dependent variables as a straight line relationship (Montgomery & Elizabeth A. Peck, 2011).

Simple linear regression is the most commonly used technique and has three main purposes

1. Describing the linear dependence of one variable on another variable
2. For predicting the values of one variable from the values of another variable, whose data set of data values is available
3. For correcting of the linear dependence of one variable on another, this so as to clarify other features of its variability

When both the dependent and independent variables are given, a scatter diagram of the data may be plotted. A scatter diagram is simply a plot of the two variables on the x-y plane. A scatter diagram is used to;

1. Visually identify the relationships between the dependent and the independent variables of a set of paired data values.
2. Draw a regression line which helps us to find the y-intercept and the coefficient of the independent variable.

A simple linear regression model is based on the equation of a straight (Slinker & Glantz, 2008). An example of a simple linear regression model may be expressed as;

Y = A + BX

Where:

Y is the dependent or response variable

A is the Y intercept, the hypothetical value of Y when X = 0

X is the independent or explanatory variable

B is the slope of the regression line, that is, the change in Y divided by the change in X. it is the value of the change in Y for a unit change in X.

For a simple linear regression model, A and B are constants and do not vary as the independent variable.

##### Multiple Regression Model

Multiple regression modeling is a flexible technique of data analysis that may be suitable whenever the dependent is to be studied in relationship to the independent or predictor variables (Berger, 2003). It is a type of linear regression that involves more than one independent variable in its formulation. A multiple regression equation for forecasting the value of Y can be expressed as follows (Slinker & Glantz, 2008):

Where

Y is the dependent variable

X1, X2 and X3 are the independent variables

A, B1, B2 and B3 are constants

Multiple regression models serve the following purposes

1. Analyzing the relationships between metric or multiple independent variables and a given dependent variable
2. It is used to test theoretical causal models of different outcomes such as a person’s job performance, aggressive or violent conduct, and heart illnesses
3. It is used by professionals to determine equitable compensation
4. It used in research in social and natural sciences in determining the best predictor variables

##### References

Montgomery, D. C., & Elizabeth A. Peck, G. G. (2011). Introduction to Linear Regression Analysis: Fifth Edition. Oxford: Wiley-Blackwell,.

Slinker, B. K., & Glantz, S. A. (2008). Multiple Linear Regression. Circulation , 1732-1737 .

Berger, E. Dale (2003). Introduction to Multiple Regression. Claremont Graduate University. Retrieved on April, 25, 2014

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