Definition Standard Error Regression
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the estimate from a scatter plot Compute the standard error of the estimate based on errors of prediction Compute the standard error using Pearson's correlation Estimate the standard error of the estimate based on a sample Figure 1 shows two regression
Standard Error Of Regression Coefficient
examples. You can see that in Graph A, the points are closer to the line standard error regression formula excel than they are in Graph B. Therefore, the predictions in Graph A are more accurate than in Graph B. Figure 1. Regressions
Meaning Of Standard Error In Regression Analysis
differing in accuracy of prediction. The standard error of the estimate is a measure of the accuracy of predictions. Recall that the regression line is the line that minimizes the sum of squared deviations of prediction regression in stats (also called the sum of squares error). The standard error of the estimate is closely related to this quantity and is defined below: where σest is the standard error of the estimate, Y is an actual score, Y' is a predicted score, and N is the number of pairs of scores. The numerator is the sum of squared differences between the actual scores and the predicted scores. Note the similarity of the formula for standard error of coefficient σest to the formula for σ.  It turns out that σest is the standard deviation of the errors of prediction (each Y - Y' is an error of prediction). Assume the data in Table 1 are the data from a population of five X, Y pairs. Table 1. Example data. X Y Y' Y-Y' (Y-Y')2 1.00 1.00 1.210 -0.210 0.044 2.00 2.00 1.635 0.365 0.133 3.00 1.30 2.060 -0.760 0.578 4.00 3.75 2.485 1.265 1.600 5.00 2.25 2.910 -0.660 0.436 Sum 15.00 10.30 10.30 0.000 2.791 The last column shows that the sum of the squared errors of prediction is 2.791. Therefore, the standard error of the estimate is There is a version of the formula for the standard error in terms of Pearson's correlation: where ρ is the population value of Pearson's correlation and SSY is For the data in Table 1, μy = 2.06, SSY = 4.597 and ρ= 0.6268. Therefore, which is the same value computed previously. Similar formulas are used when the standard error of the estimate is computed from a sample rather than a population. The only difference is that the denominator is N-2 rather than N. The reason N-2 is used rather than N-1 is that two parameters (the slope and the intercept) were esti
the estimate from a scatter plot Compute the standard error of the estimate based on errors of prediction Compute the standard error using Pearson's correlation Estimate the standard error of the estimate based
Standard Error Of Estimate Interpretation
on a sample Figure 1 shows two regression examples. You can see that linear regression standard error in Graph A, the points are closer to the line than they are in Graph B. Therefore, the predictions
Standard Error Of Regression Interpretation
in Graph A are more accurate than in Graph B. Figure 1. Regressions differing in accuracy of prediction. The standard error of the estimate is a measure of the accuracy of predictions. Recall http://onlinestatbook.com/2/regression/accuracy.html that the regression line is the line that minimizes the sum of squared deviations of prediction (also called the sum of squares error). The standard error of the estimate is closely related to this quantity and is defined below: where σest is the standard error of the estimate, Y is an actual score, Y' is a predicted score, and N is the number of pairs http://onlinestatbook.com/2/regression/accuracy.html of scores. The numerator is the sum of squared differences between the actual scores and the predicted scores. Note the similarity of the formula for σest to the formula for σ.  It turns out that σest is the standard deviation of the errors of prediction (each Y - Y' is an error of prediction). Assume the data in Table 1 are the data from a population of five X, Y pairs. Table 1. Example data. X Y Y' Y-Y' (Y-Y')2 1.00 1.00 1.210 -0.210 0.044 2.00 2.00 1.635 0.365 0.133 3.00 1.30 2.060 -0.760 0.578 4.00 3.75 2.485 1.265 1.600 5.00 2.25 2.910 -0.660 0.436 Sum 15.00 10.30 10.30 0.000 2.791 The last column shows that the sum of the squared errors of prediction is 2.791. Therefore, the standard error of the estimate is There is a version of the formula for the standard error in terms of Pearson's correlation: where ρ is the population value of Pearson's correlation and SSY is For the data in Table 1, μy = 2.06, SSY = 4.597 and ρ= 0.6268. Therefore, which is the same value computed previously. Sim
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta http://stats.stackexchange.com/questions/85943/how-to-derive-the-standard-error-of-linear-regression-coefficient Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or 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, machine learning, data analysis, data mining, and standard error 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 vote favorite 3 For this univariate linear regression model $$y_i standard error of = \beta_0 + \beta_1x_i+\epsilon_i$$ 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 9,14332149 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