Linear Regression Analysis Paper

Linear Regression Analysis

Linear regression analysis is a technique that fits a straight-line relationship (a regression line) to a set of paired observations, using the simple straight-line equation y=a+-bx. The quantity a denotes the point that the regression line crosses the y-axis (the y intercept) and the quantity b is the slope (steepness) of the regression line. If b is positive then increasing x means increasing y. If b is negative the increasing x means decreasing y. The purpose of all regression is to enable the user to predict values of y from values of x. Regression may also be used to explore the possible causation of changes in y by changes in x, or explain some of the variation in y by x. However, the fitting of a regression line to a set of paired observations, and calling on the dependent variable, does not mean that y is caused by x. From the point of view of causation there are two fundamentally different ways of obtaining a set of paired observations. First, the team could manipulate values of an independent variable (x), and subsequently measure the response of a dependent variable (y). This is the more usual situation for regression and is more correctly termed model in regression. Second, the team could simply collect pairs of co-varying observations and call one of them y and one of them x. This second situation is often more correctly analyzed using correlation, unless one specifically wants to predict one variable from another, when one should use a model II regression (1998).

Regression analysis is also a forecasting technique used to establish the relationship between quantifiable variables. In regression analysis, data on dependent variables is plotted on a scatter graph or diagram, and trends are indicated through a line of best fit. The use of a single independent variable is known as simple regression analysis, although the use of two or more independent variables is called multiple regression analysis (2009). Team C...