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关于回归分析的话题

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licheng 发表于 2015-12-24 08:31:04 | 显示全部楼层 |阅读模式
From: Cheng Li
Date: Fri, Dec 26, 2014 at 6:19 PM
Subject: Regression analysis topics

Yinan taught very well today using theories, data examples and simulation.

The following webpages contain nice discussion and examples about topics in regression analysis. The "Predicated R square" concept seems useful.

Multiple Regression Analysis: Use Adjusted R-Squared and Predicted R-Squared to Include the Correct Number of Variables
http://blog.minitab.com/blog/adventures-in-statistics/multiple-regession-analysis-use-adjusted-r-squared-and-predicted-r-squared-to-include-the-correct-number-of-variables

Regression Analysis: How Do I Interpret R-squared and Assess the Goodness-of-Fit?
http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit

How to Interpret a Regression Model with Low R-squared and Low P values
http://blog.minitab.com/blog/adventures-in-statistics/how-to-interpret-a-regression-model-with-low-r-squared-and-low-p-values

Three Things the P-Value Can't Tell You about Your Hypothesis Test
http://blog.minitab.com/blog/understanding-statistics/three-things-the-p-value-cant-tell-you-about-your-hypothesis-test

Five Guidelines for Using P values
http://blog.minitab.com/blog/adventures-in-statistics/five-guidelines-for-using-p-values

Regression Analysis: How to Interpret the Constant (Y Intercept)
http://blog.minitab.com/blog/adventures-in-statistics/regression-analysis-how-to-interpret-the-constant-y-intercept

Why You Need to Check Your Residual Plots for Regression Analysis
http://blog.minitab.com/blog/adventures-in-statistics/why-you-need-to-check-your-residual-plots-for-regression-analysis

Applied Regression Analysis: How to Present and Use the Results to Avoid Costly Mistakes, part 1
http://blog.minitab.com/blog/adventures-in-statistics/applied-regression-analysis-how-to-present-and-use-the-results-to-avoid-costly-mistakes-part-1

Four Tips on How to Perform a Regression Analysis that Avoids Common Problems
http://blog.minitab.com/blog/adventures-in-statistics/four-tips-on-how-to-perform-a-regression-analysis-that-avoids-common-problems

Confound It Some More: How a Factor That Wasn't There Hampered My Analysis
http://blog.minitab.com/blog/adventures-in-statistics/confound-it-some-more-how-a-factor-that-wasnt-there-hampered-my-analysis

Common Statistical Mistakes You Should Avoid
http://blog.minitab.com/blog/real-world-quality-improvement/common-statistical-mistakes-you-should-avoid

Why Statistics Is Important
http://blog.minitab.com/blog/adventures-in-statistics/why-statistics-is-important

Not All P Values are Created Equal
http://blog.minitab.com/blog/adventures-in-statistics/not-all-p-values-are-created-equal
【Cheng's note:
p-value is defined as Prob(observing such data or more extreme | H0) = Prob(T>t) = 1 - F(t) in a one-sided test, where F is the CDF of the test statistic T under H0, and t is the observed test statistic based on data. T is designed to be small when H0 is true and large when H0 is false, so large t will lead to small p-value.

If we "reject H0" when p-value<alpha (alpha is a cutoff such as 0.05), then Type I error = Prob(reject H0 | H0) = Prob(p-value<alpha | H0) = Prob(T>t_alpha) = alpha, where t_alpha is determined by the CDF of T so that the last equal sign hold true. Read more about p-value athttp://en.wikipedia.org/wiki/P-value.

In the table of the above page, "Pvalue obtained" is alpha, "Final Minimum Probability of true null" seems to refer to Prob(H0 | reject H0), or Prob(H0 | p-value < alpha), which is dependent on Type I error and Prob(H0) = 1 - P(real) through Bayes formula.】


More topics from this website:
http://blog.minitab.com/blog/regression-analysis-3
http://blog.minitab.com/blog/adventures-in-statistics
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