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Linear Regression
Predictions and Hypothesis Testing
What benefit does a variable provide when developing and examining models?
Statistics can be used to describe a phenomenon or conduct hypothesis testing, but statistics can also used to predict outcomes (Hanneman, Kposowa, & Riddle, 2012, p. 7). To enable predictions to be made, variables are required in the statistical model. Variables allow researchers to model the mathematical relationship between two or more phenomenon. For example, the relationship between tree circumference and the number of leaves could be described by the two variables girth and leaves. This relationship may or may not be causal, but it could be correlational. If a causal relationship is suspected, then maybe reducing the number of leaves inhibits expansion of tree girth. In this case, leaves would be the independent variable and girth the dependent variable. If the model is valid, then the tree girth could be predicted for any value of leaves. Variables therefore allow researchers to test hypotheses...
Explain the purpose of simple linear regression and scatter diagrams. Please provide a simple linear regression model and define each variable used.
Linear regression is a statistical tool for quantifying the relationship between two variables (Journal of Tropical Pediatrics, n.d., p. 3). Linear regression is used to predict the mean response of the dependent variable (Y) given a change in the independent variable (X). Scatter diagrams are useful because the amount of error inherent to the prediction model can be visualized. If the best-fit line is included in the scatter plot, then the magnitudes of the error (residuals) for a given value X can be easily seen. Scatter plots are also useful for troubleshooting the prediction model.
If X = leaves and Y = tree girth, then Y = bX + a, where b = slope of the best-fit line and a = the y-intercept (Journal of Tropical Pediatrics, n.d., p. 5). This is the regression equation and a and b are the regression coefficients. If the regression coefficients…
References
Atmospheric pressure and other state variables. (n.d.). Retrieved 6 May 2014 from http://www.geog.ucsb.edu/~joel/g110_w08/lecture_notes/pressure/pressure.html.
Hanneman, R.A., Kposowa, A.J., & Riddle, M.D. (2012). Research Methods for the Social Sciences: Basic Statistics for Social Research. Somerset, N.J.: Jossey-Bass.
Journal of Tropical Pediatrics. (n.d.). Chapter 2: Simple linear regression. In Research Methods II: Multivariate Analysis. Retrieved 6 May 2014 from http://www.oxfordjournals.org/our_journals/tropej/online/ma.html.
National Heart, Lung, and Blood Institute. (2011). What are the coronary heart disease risk factors? Retrieved 6 May 2014 from http://www.nhlbi.nih.gov/health/health-topics/topics/hd/.
Demand Management Plan for Wild Dog Coffee Company:Impact of Advertising on Product DemandTo analyze the impact of advertising on product demand, a simple linear regression model to forecast the pounds of espresso beans used each month based on advertising expenditures can be used. The model used can be found in the Appendix to this paper.The regression equation is: Y = 542.78 + 0.42X where Y is the pounds of espresso
Regression Analysis: Real Estatee Sales Prices and Distance to City This regression analysis seeks to answer the question of how the sales price of Real Estate listed houses changes with the distance from the city. Does the sales price increase or decrease as the distance from the city increases or is there a relationship between the variables at all? Given the attraction of city living and the general trends of suburban
Its name tells us the criterion used to select the best fitting line, namely that the sum of the squares of the residuals should be least. In other words, the least squares regression equation is the line for which the sum of squared residuals is a minimum (Dallal, 2008). Multiple regression - the general purpose of multiple is to learn more about the relationship between several independent variables and a
Regression, Correlation: Effect of IQ on GPA Effective teaching begins with understanding the thinking and reasoning abilities of one's students and devising ways to ensure that the classroom setting is accommodative of the inherent differences in cognitive capabilities and that all students get to benefit from the learning process. One way of measuring a child's intellectual ability is by administering the Wechsler Intelligence Scale for Children -- Forth Edition (WISC-IV), which
Display The effectiveness of using display as a marketing mix variable is average. It has a coefficient of 0.253. This is in regard to all of the brands. Feature The effectiveness of using feature as a marketing mix variable is noted to be the most efficient for all of the brands. This is due to its high level of significance (0.315).This means that it is the variable which should be perfected by all
Linear, Logistic or Multiple Correlation/Regression Proposal Objective of this paper is to use the statistical test to investigate whether the middle income earners in developing countries are capable of becoming home owners. The paper uses Nigeria as a case study. Unlike the developed countries such as the United States and United Kingdom where middle income earners can become house owners, however, the issues are different in developing countries because various