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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ SIMPLE LINEAR REGRESSION ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ SIMPLE LINEAR REGRESSION Documents prepared for use in course C22.0103.001 , New York University, Stern School of Business Fictitious example, n = 10. Page 3 This shows the arithmetic for fitting a simple linear regression. Summary of simple regression arithmetic page 4 This document shows the formulas for simple linear regression, including the calculations for the analysis of variance table. Another example of regression arithmetic page 8 This example illustrates the use of wolf tail lengths to assess weights. Yes, these data are fictitious. An illustration of residuals page 10 This example shows an experiment relating the height of suds in a dishpan to the quantity of soap placed into the water. This also shows how you can get Minitab to list the residuals. The simple linear regression model page 12 This section shows the very important linear regression model . It’s very helpful to understand the distinction between parameters and estimates. Regression noise terms page 14 What are those epsilons all about? What do they mean? Why do we need to use them? More about noise in a regression page 18 Random noise obscures the exact relationship between the dependent and independent variables. Here are pictures showing the consequences of increasing noise standard deviation. There is a technical discussion of the consequences of measurement noise in an independent variable. This entire discussion is done for simple regression, but the ideas carry over in a complicated way to multiple regression. Does regression indicate causality? page 26 This shows a convincing relationship between X and Y . Do you think that this should be interpreted as cause and effect? An interpretation for residuals page 28 The residuals in this example have a very concrete interpretation. x 1
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≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ SIMPLE LINEAR REGRESSION ≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈ Summary of regression notions for one predictor page 3 1 This is a quick one-page summary as to what we are trying to do with a simple regression. The residual versus fitted plot page 3 2 Checking the residual versus fitted plot is now standard practice in doing linear regressions. An example of the residual versus fitted plot page 3 6 This shows that the methods explored on pages 3 2 -3 5 can be useful for real data problems. Indeed, the expanding residuals situation is very common. Transforming the dependent variable page 4 1 Why does taking the log of the dependent variable cure the problem of expanding residuals? The math is esoteric, but these pages lay out the details for you.
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