In this case, the observed values fall an average of 4.89 units from the regression line. It's a statistic measure calculated from the sampling distributions where the large size samples or proportions reduces the SE of a statistic proportionally and vice versa. The standard error of the regression is the average distance that the observed values fall from the regression line. The standard deviation for each group is obtained by dividing the length of the confidence interval by 3. Setup the test of significance or hypothesis for large & small sample size (student's t & Z statistic) to measure the reliability of sample & population parameter and the estimation the confidence interval for population parameter are some of the major applications of standard error. If the sample size is large (say bigger than 100 in each group), the 95 confidence interval is 3.92 standard errors wide (3.92 2 × 1.96). It is one of an important & most frequently used functions in statistics & probability.
In other words, it's a numerical value that represents standard deviation of the sampling distribution of a statistic for sample mean x̄ or proportion p, difference between two sample means (x̄ 1 - x̄ 2) or proportions (p 1 - p 2) (using either standard deviation or p value) in statistical surveys & experiments. It is calculated as: Standard error of the mean s / n. Standard Error can be used to estimate confidence intervals. The standard error of the mean is a way to measure how spread out values are in a dataset. This is because there is more variability in a small sample size than in a large one. The formula for Standard Error is: The larger the sample size, the smaller the Standard Error will be. It is equal to the population standard deviation () divided by the square root of the number of observations in that sample. It shows how effective the selected sample size n is in the statistical experiments or the reliability of experiment results with respect to the sample size. To calculate Standard Error, you need to know the population standard deviation and the sample size. In probability & statistics, the standard deviation of sampling distribution of a statistic is called as Standard Error often abbreviated as SE.
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