Multiple Regression Term Paper Example | Topics and Well Written Essays - 5000 words

Multiple Regression - Term Paper Example Oftentimes, when a model is too simple that it only contains one independent variable, such a model is of limited value because the predictions made from such models are too inaccurate to be useful in a real-world setting. Thus, when one wants to be able to predict an outcome at a more precise level, it is more advantageous to use the information that may be provided by two or more variables in an explanatory framework (Burt, Barber, & Rigby, 2009). Thus, multiple regression analysis should allow an analyst to arrive at better predictions. For example, a student may want to find out the perfect model to getting high grades in school. Using the results of his individual exams as the dependent variable, he may hypothesize that amount of time spent studying, amount of sleep taken the night before the exam, amount of beer drank the night before the exam, caloric intake (or a fancy phrase for how heavy his meal was) prior to taking the exam, and even the presence of his lucky rabbitâ€⠄¢s foot are possible factors for scoring well in the exam. Using multiple regression analysis, the student may find out that amount of time spent studying, amount of sleep taken the night before the exam, and amount of beer drank the night before the exam are significant predictors of his exam scores. ... For example, oncologists may be interested in the best predictors of lung cancer, educators may want to know what are the best predictors of SAT scores, and psychologists would want to find out which factors best predict depression among a particular age group. These questions may all be answered with the help of multiple regression. 2.0 Computational approach The main goal of linear regression, in this case, multiple regression, is to be able to fit a regression line through a number of given points (Wang & Jain, 2003). This regression line is sometimes called the line of best fit and this is the line that represents the regression model of a given problem. These points are usually best represented graphically in a scatter plot. While it is quite easy to produce a scatter plot when there is only one independent and one dependent variable, multiple regression presents the challenge of having more than one independent variable thus making the practice of making a scatterplot impractic al (Dekking, 2005). 2.1 Least Squares In regression modeling, the basic estimation procedure used is the least squares method (Black, 2010). Since the main goal of linear regression is to fit a line through the points, least squares estimation is used to compute this line in such a way that the squared deviations of the observed points from this line are minimized (Wang & Jain, 2003). 2.2 The Regression Equation The bivariate form of simple linear regression produces a two-dimensional line in a two-dimensional space. This equation is defined by: Y = a + bX, where Y is the dependent variable being forecasted by the regression model, X is the independent variable