Calculate Standard Error Of Regression Coefficients
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Standard Error Of Regression Coefficient Formula
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Standard Error Of Regression Coefficient Definition
posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, standard error of regression coefficient excel machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How to derive the standard error of linear regression coefficient up vote 2 down standard error of regression coefficient matlab vote favorite 3 For this univariate linear regression model $$y_i = \beta_0 + \beta_1x_i+\epsilon_i$$ given data set $D=\{(x_1,y_1),...,(x_n,y_n)\}$, the coefficient estimates are $$\hat\beta_1=\frac{\sum_ix_iy_i-n\bar x\bar y}{n\bar x^2-\sum_ix_i^2}$$ $$\hat\beta_0=\bar y - \hat\beta_1\bar x$$ Here is my question, according to the book and Wikipedia, the standard error of $\hat\beta_1$ is $$s_{\hat\beta_1}=\sqrt{\frac{\sum_i\hat\epsilon_i^2}{(n-2)\sum_i(x_i-\bar x)^2}}$$ How and why? standard-error inferential-statistics share|improve this question edited Mar 6 '15 at 14:38 Christoph Hanck 9,13332149 asked Feb 9 '14 at 9:11 loganecolss 5531926 stats.stackexchange.com/questions/44838/… –ocram Feb 9 '14 at 9:14 @ocram, thanks, but I'm not quite capable of handling matrix stuff, I'll try. –loganecolss Feb 9 '14 at 9:20 1 @ocram, I've already understand how it comes. But still a question: in my post, the standard error has $(n-2)$, where according to your answer, it doesn't, why? –loganecolss Feb 9 '14 at 9:40 add a comment| 1 Answer 1 active oldest votes up vote 7 down vote accepted 3rd comment above: I've already understand how it c
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How To Calculate Standard Error Of Regression Slope
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How To Calculate Standard Error In Regression Analysis
Problems and solutions Formulas Notation Share with Friends Regression Slope: Confidence Interval This lesson describes how to construct a confidence interval around the slope of a regression line. http://stats.stackexchange.com/questions/85943/how-to-derive-the-standard-error-of-linear-regression-coefficient We focus on the equation for simple linear regression, which is: ŷ = b0 + b1x where b0 is a constant, b1 is the slope (also called the regression coefficient), x is the value of the independent variable, and ŷ is the predicted value of the dependent variable. Estimation Requirements The approach described in this lesson is valid http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP whenever the standard requirements for simple linear regression are met. The dependent variable Y has a linear relationship to the independent variable X. For each value of X, the probability distribution of Y has the same standard deviation σ. For any given value of X, The Y values are independent. The Y values are roughly normally distributed (i.e., symmetric and unimodal). A little skewness is ok if the sample size is large. Previously, we described how to verify that regression requirements are met. The Variability of the Slope Estimate To construct a confidence interval for the slope of the regression line, we need to know the standard error of the sampling distribution of the slope. Many statistical software packages and some graphing calculators provide the standard error of the slope as a regression analysis output. The table below shows hypothetical output for the following regression equation: y = 76 + 35x . Predictor Coef SE Coef T P Constant 76 30 2.53 0.01 X 35 20 1.75 0.04 In the output above, the standa
The standard error of the coefficient is always positive. Use the standard error of the coefficient to measure the precision of the estimate of the coefficient. The http://support.minitab.com/en-us/minitab/17/topic-library/modeling-statistics/regression-and-correlation/regression-models/what-is-the-standard-error-of-the-coefficient/ smaller the standard error, the more precise the estimate. Dividing the coefficient by its standard error calculates a t-value. If the p-value associated with this t-statistic is less than your alpha level, you conclude that the coefficient is significantly different from zero. For example, a materials engineer at a furniture manufacturing site wants to assess the strength of the standard error particle board that they use. The engineer collects stiffness data from particle board pieces with various densities at different temperatures and produces the following linear regression output. The standard errors of the coefficients are in the third column. Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 20.1 12.2 1.65 0.111 Stiffness 0.2385 0.0197 12.13 0.000 1.00 Temp standard error of -0.184 0.178 -1.03 0.311 1.00 The standard error of the Stiffness coefficient is smaller than that of Temp. Therefore, your model was able to estimate the coefficient for Stiffness with greater precision. In fact, the standard error of the Temp coefficient is about the same as the value of the coefficient itself, so the t-value of -1.03 is too small to declare statistical significance. The resulting p-value is much greater than common levels of α, so that you cannot conclude this coefficient differs from zero. You remove the Temp variable from your regression model and continue the analysis. Why would all standard errors for the estimated regression coefficients be the same? If your design matrix is orthogonal, the standard error for each estimated regression coefficient will be the same, and will be equal to the square root of (MSE/n) where MSE = mean square error and n = number of observations.Minitab.comLicense PortalStoreBlogContact UsCopyright © 2016 Minitab Inc. All rights Reserved.EnglishfrançaisDeutschportuguêsespañol日本語한국어中文(简体)By using this site you agree to the use of cookies for analytics and pers
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