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Regression Analysis (Spring, 2000)
Regression Analysis (Spring, 2000)

Chapter 4: z-scores and Probability
Chapter 4: z-scores and Probability

... **This chapter corresponds to chapter 8 (“Are Your Curves Normal?”) of your book. What it is: z-scores (also called “standard scores”) are raw scores that have been adjusted for the mean and standard deviation of the distribution from which the raw scores came. z-scores are expressed in standard dev ...
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PPT slides for 13 September - Psychological Sciences

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Chapter 4 - City University of Hong Kong
Chapter 4 - City University of Hong Kong

... R2 = SSR/SST R2 is defined as the ratio of the variation explained by the regression line (i.e. SSR) to the total variation (i.e. SST)  Some remarks on R2 (a) R2 takes values in [0, 1] (b) R2 = 1 => SSR = SST => Perfect fit (c) Large R2 => Large proportion of the total variation can be explained by ...
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Data and Error Analysis in Science

... because a very slow reaction distorts the mean in the direction of that large value. In this case, we call that very large value an outlier because it lies so far away from the rest of the measurements. Why might one group of students have recorded such a large value? Note: If the researchers can de ...
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Logistic Regression

BA Economics QUESTION BANK Quantitative Methods for Economic Analysis – I
BA Economics QUESTION BANK Quantitative Methods for Economic Analysis – I

... 143. For the following correlation coefficients, which of the following indicates the strongest relation? (a) r = 0.5 b) r = 0.09 (c) r = −0.6 (d) r = 0.2 144. A researcher finds a correlation of 0.40 between personal income and the number of years of college completed. Based upon this finding he ca ...
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Lecture5-12-09 - University of Washington

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1. Students taking an intro stats course reported the number of credit

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Linear Regression

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Lecture Notes

... We are very close to doing some statistical analyses to test specific hypothesis. The next step is to play with scenarios such as: You sample 36 scores from a population that has a μ=80 and σ=12. For what value of the sample mean is there only a 5% chance that you would obtain a sample mean that is ...
ANOVA
ANOVA

... Testing for a difference in more than two means • Previously we have seen how to test for a difference in two means, using a 2 sample t-test. But what if we want to test to see if there are differences in a set of more than two means? • The tool for doing this is called ANOVA, which is short for “a ...
Mean - Illinois State University Department of Psychology
Mean - Illinois State University Department of Psychology

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Descriptive Statistics

< 1 ... 17 18 19 20 21 22 23 24 25 ... 111 >

Regression toward the mean

In statistics, regression toward (or to) the mean is the phenomenon that if a variable is extreme on its first measurement, it will tend to be closer to the average on its second measurement—and if it is extreme on its second measurement, it will tend to have been closer to the average on its first. To avoid making incorrect inferences, regression toward the mean must be considered when designing scientific experiments and interpreting data.The conditions under which regression toward the mean occurs depend on the way the term is mathematically defined. Sir Francis Galton first observed the phenomenon in the context of simple linear regression of data points. Galton developed the following model: pellets fall through a quincunx forming a normal distribution centered directly under their entrance point. These pellets could then be released down into a second gallery (corresponding to a second measurement occasion. Galton then asked the reverse question ""from where did these pellets come?"" ""The answer was not 'on average directly above'. Rather it was 'on average, more towards the middle', for the simple reason that there were more pellets above it towards the middle that could wander left than there were in the left extreme that could wander to the right, inwards"" (p 477) A less restrictive approach is possible. Regression towards the mean can be defined for any bivariate distribution with identical marginal distributions. Two such definitions exist. One definition accords closely with the common usage of the term “regression towards the mean”. Not all such bivariate distributions show regression towards the mean under this definition. However, all such bivariate distributions show regression towards the mean under the other definition.Historically, what is now called regression toward the mean has also been called reversion to the mean and reversion to mediocrity.In finance, the term mean reversion has a different meaning. Jeremy Siegel uses it to describe a financial time series in which ""returns can be very unstable in the short run but very stable in the long run."" More quantitatively, it is one in which the standard deviation of average annual returns declines faster than the inverse of the holding period, implying that the process is not a random walk, but that periods of lower returns are systematically followed by compensating periods of higher returns, in seasonal businesses for example.
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