Linear Regression

Linear regression analyzes the relationship between an independent and dependent variable to find the line that best fits between them. It has been used to predict a continuous dependent variable from a number of independent variables. This report will discuss the different tools used for such analysis and will also describe histograms and bivariate plots. It will also discuss the value of a slope which is shown as the ratio of change in the y-value over the change in the x-value. Lastly, this report will show how linear regression can be utilized in the management environment.

Linear regression is an independent variable x and those values which are fixed, and a dependent variable y (Macmillan Dictionary of Toxicology, 1999). These standards can be subjected to unsystematic changes. The equation that determines the regression line is:

Y = a + bX (Macmillan Dictionary of Toxicology, 1999). The slope of the line occurs where the Y intercept meets the regression coefficient (Macmillan Dictionary of Toxicology, 1999). The regression coefficient can be solved by multiplying X deviation and the Y deviation and dividing by the deviations of X squared (Macmillan Dictionary of Toxicology, 1999).

Correlation coefficient is a quantitative assessment of the direction and magnitude of the relationship between two variables (Macmillan Reference Ltd, 2000). There are different types of correlation coefficients; however, the most common one is Pearson product moment correlation (Macmillan Reference Ltd, 2000). The Pearson product moment correlation points toward a linear connection between two variables. For example: what can the birth weight of a baby tell, or what does stress have to do with the outcome of a test, a job, or everyday living, and will the SAT scores dictate how a person will do in college or in life.

The grade point average and the SAT can be used as an example of how correlation coefficient works. The chart below...