Coefficient Standard Error Significance
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Coefficient Standard Error T Statistic
vote favorite 2 Gelman & Hill 2007 mention several times throughout their book that: "Roughly speaking, if a coefficient estimate is more than 2 standard errors away from zero, then it is called statistically significant. " However, when they use this rule throughout this book I find the conclusions inconsistent. For example from the ouput: (formula = kid.score ~ mom.hs + mom.iq) coef.est coef.se (Intercept) 25.7 5.9 mom.hs 5.9 2.2 mom.iq 0.6 0.1 n = 434, k = 3 residual sd regression coefficient standard error = 18.1, R-Squared = 0.21 They conclude that mom.hs is statistically significant with an estimate of 5.9 and an a standard error of 2.2 Then in a second output: lm(formula = log.earn ~ height + male) coef.est coef.se (Intercept) 8.153 0.603 height 0.021 0.009 male 0.423 0.072 n = 1192, k = 3 residual sd = 0.88, R-Squared = 0.09 they say that height is statistically significant with an estimate of 0.021 and a standard error of 0.009 then in a third example: lm(formula = log(weight) ~ log(canopy.volume) + log(canopy.area) + log(canopy.shape) + log(total.height) + log(density) + group) coef.est coef.se (Intercept) 5.35 0.17 log(canopy.volume) 0.37 0.28 log(canopy.area) 0.40 0.29 log(canopy.shape) -0.38 0.23 log(total.height) 0.39 0.31 log(density) 0.11 0.12 group -0.58 0.13 n = 46, k = 7 residual sd = 0.33, R-Squared = 0.89 they say that none of the variables are significant even though to me they seem to have even higher values than the other examples. What am I getting wrong? statistical-significance share|improve this question asked Nov 15 '11 at 12:45 Dbr 95481629 add a comment| 1 Answer 1 active oldest votes up vote 5 down vote accepted For each of the examples, you can easily perform abs(estimate) - 2 * standarderror. If this is higher than zero (i.e. the estimate is more than two standard errors away from zero), it is very unlikely that the true value is zero, i.e. it is statistically significantly nonzero (at nearly the 95% con
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 standard error significance rule of thumb coefficient. The smaller the standard error, the more precise the estimate.
Standard Error And Significance Level
Dividing the coefficient by its standard error calculates a t-value. If the p-value associated with this t-statistic
Coefficient Standard Deviation
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 http://stats.stackexchange.com/questions/18407/using-coefficient-estimates-and-standard-errors-to-assess-significance assess the strength of the 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 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/ Stiffness 0.2385 0.0197 12.13 0.000 1.00 Temp -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.Engli
6Chapter 7Chapter 8AppendixHuman valuesSocial and Political TrustLatent variable modellingDataUser guideOnline analysisWeightsGlossary Standard error and significance level In order to know how accurate our single sample based regression coefficient is as an estimate of the population coefficient, we need to http://essedunet.nsd.uib.no/cms/topics/regression/4/1.html know the size of the standard error. Fortunately, although we cannot find its exact value, we can get a fairly accurate estimate of it through analysis of our http://people.duke.edu/~rnau/411regou.htm sample data. This estimate, which is reported in the SPSS regression analysis coefficients table, makes it possible to tell how likely it is that the difference between the standard error population regression coefficient and our sample regression coefficient is larger or smaller than a certain, freely chosen value. This makes it possible to test so called null hypotheses about the value of the population regression coefficient. Such testing is easy with SPSS if we accept the presumption that the relevant null hypothesis to test is the hypothesis coefficient standard error that the population has a zero regression coefficient, i.e. that there is no linear association between the independent and the dependent variable. Our test criterion will be that the null hypothesis shall be refuted if there is less than a certain likelihood (e.g. 5% likelihood) that a population with a coefficient value of 0 would give rise to a sample with a regression coefficient whose absolute value is equal to or larger than the one we actually found in our sample. We call this chosen likelihood level our ‘significance level’. Note that we cannot conclude with certainty whether or not the null hypothesis is true. This criterion says that we should refute the null hypothesis if the chances that we would observe the estimated regression coefficient if the null hypothesis really were true is less than our chosen significance level. Thus, if we choose 5 % likelihood as our criterion, there is a 5% chance that we might refute a correct null hypothesis. Refuting a correct null hypothesis
1: descriptive analysis · Beer sales vs. price, part 2: fitting a simple model · Beer sales vs. price, part 3: transformations of variables · Beer sales vs. price, part 4: additional predictors · NC natural gas consumption vs. temperature What to look for in regression output What's a good value for R-squared? What's the bottom line? How to compare models Testing the assumptions of linear regression Additional notes on regression analysis Stepwise and all-possible-regressions Excel file with simple regression formulas Excel file with regression formulas in matrix form If you are a PC Excel user, you must check this out: RegressIt: free Excel add-in for linear regression and multivariate data analysis What to look for in regression model output Standard error of the regression and other measures of error size Adjusted R-squared (not the bottom line!) Significance of the estimated coefficients Values of the estimated coefficients Plots of forecasts and residuals (important!) Out-of-sample validation For a sample of output that illustrates the various topics discussed here, see the "Regression Example, part 2" page. (i) Standard error of the regression (root-mean-squared error adjusted for degrees of freedom): Does the current regression model yield smaller errors, on average, than the best model previously fitted, and is the improvement significant in practical terms? In regression modeling, the best single error statistic to look at is the standard error of the regression, which is the estimated standard deviation of the unexplainable variations in the dependent variable. (It is approximately the standard deviation of the errors, apart from the degrees-of-freedom adjustment.) This what your software is trying to minimize when estimating coefficients, and it is a sufficient statistic for describing properties of the errors if the model's assumptions are all cor