Calculate Standard Error Of Beta 1
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How To Calculate Standard Error In R
there is a significant relationship between the independent and dependent variables. Test Requirements The approach described in this lesson is valid 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 test procedure consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero. H0: Β1 = 0 Ha: Β1 ≠ 0 The null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero. Formulate an Analysis Plan The analysis pla
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How To Calculate Standard Error Without Standard Deviation
the company Business Learn more about hiring developers or posting ads with us Cross calculate standard error of estimate Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, calculate standard error confidence interval 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 http://stattrek.com/regression/slope-test.aspx?Tutorial=AP and rise to the top How to derive the standard error of linear regression coefficient up vote 2 down 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 http://stats.stackexchange.com/questions/85943/how-to-derive-the-standard-error-of-linear-regression-coefficient 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 comes. But still a question: in my post, the standard error has (n−2), where according to your answer, it doesn't, why? In my post, it is found that $$ \widehat{\text{se}}(\hat{b}) = \sqrt{\frac{n \hat{\sigma}^2}{n\sum x_i^2 - (\sum x_i)^2}}. $$ The denominator can be written as $$ n \sum_i (x_i - \bar{x})^2 $$ Thus, $$ \widehat{\text{se}}(\hat{b}) = \sqrt{\frac{\hat{\sigma}^2}{\sum_i (x_i - \bar{x})^2}} $$ With $$ \hat{\sigma}^2 = \frac{1}{n-2} \sum_i \hat{\epsilon}_i^2 $$ i.e. the Mean Square Error (MSE) in the ANOVA table, we end up with your expression for $\widehat{\text{se}}(\hat{b})$. The $n-2$ term accounts for the loss of 2 degrees of freedom in the estimation of the intercept and the slope. share|i
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