Calculating Variance From Standard Error
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average squared deviation from the mean). Variance in a population is: [x is a value from the population, μ is the standard error excel mean of all x, n is the number of x in the population,
Standard Error Vs Standard Deviation
Σ is the summation] Variance is usually estimated from a sample drawn from a population. The unbiased estimate standard error symbol of population variance calculated from a sample is: [xi is the ith observation from a sample of the population, x-bar is the sample mean, n (sample size) -1 is degrees of
Standard Error Matlab
freedom, Σ is the summation] The spread of a distribution is also referred to as dispersion and variability. All three terms mean the extent to which values in a distribution differ from one another. SD is the best measure of spread of an approximately normal distribution. This is not the case when there are extreme values in a distribution or when the standard error regression distribution is skewed, in these situations interquartile range or semi-interquartile are preferred measures of spread. Interquartile range is the difference between the 25th and 75th centiles. Semi-interquartile range is half of the difference between the 25th and 75th centiles. For any symmetrical (not skewed) distribution, half of its values will lie one semi-interquartile range either side of the median, i.e. in the interquartile range. When distributions are approximately normal, SD is a better measure of spread because it is less susceptible to sampling fluctuation than (semi-)interquartile range. If a variable y is a linear (y = a + bx) transformation of x then the variance of y is b² times the variance of x and the standard deviation of y is b times the variance of x. The standard error of the mean is the expected value of the standard deviation of means of several samples, this is estimated from a single sample as: [s is standard deviation of the sample mean, n is the sample size] See descriptive statistics. Copyright © 2000-2016 StatsDirect Limited, all rights reserved. Download a free trial here.
average squared deviation from the mean). Variance in a population is: [x is a value from the population, μ is the
Error Variance Definition
mean of all x, n is the number of x in the population,
Standard Error Interpretation
Σ is the summation] Variance is usually estimated from a sample drawn from a population. The unbiased estimate error variance psychology of population variance calculated from a sample is: [xi is the ith observation from a sample of the population, x-bar is the sample mean, n (sample size) -1 is degrees of http://www.statsdirect.com/help/basic_descriptive_statistics/standard_deviation.htm freedom, Σ is the summation] The spread of a distribution is also referred to as dispersion and variability. All three terms mean the extent to which values in a distribution differ from one another. SD is the best measure of spread of an approximately normal distribution. This is not the case when there are extreme values in a distribution or when the http://www.statsdirect.com/help/basic_descriptive_statistics/standard_deviation.htm distribution is skewed, in these situations interquartile range or semi-interquartile are preferred measures of spread. Interquartile range is the difference between the 25th and 75th centiles. Semi-interquartile range is half of the difference between the 25th and 75th centiles. For any symmetrical (not skewed) distribution, half of its values will lie one semi-interquartile range either side of the median, i.e. in the interquartile range. When distributions are approximately normal, SD is a better measure of spread because it is less susceptible to sampling fluctuation than (semi-)interquartile range. If a variable y is a linear (y = a + bx) transformation of x then the variance of y is b² times the variance of x and the standard deviation of y is b times the variance of x. The standard error of the mean is the expected value of the standard deviation of means of several samples, this is estimated from a single sample as: [s is standard deviation of the sample mean, n is the sample size] See descriptive statistics. Copyright © 2000-2016 StatsDirect Limited, all rights reserved. Download a free trial here.
Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack http://stats.stackexchange.com/questions/114688/calculating-the-variance-standard-error-estimation 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 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 standard error up and rise to the top Calculating the Variance (Standard Error Estimation) up vote 0 down vote favorite 1 I am studying the book "An Introduction to Statistical Learning: with Applications in R", on page 66 While the book explains how to calculate $\beta_0$ and $\beta_1$, it skips how the actual calculation happened and only displays the equations to calculate them and then the result in the next page. I got lost calculating variance from when $\sigma^2$ is calculated. I don't know how it was calculated, as I quote the book: In general, $\sigma^2$ is not known, but can be estimated from the data. This esti- mate is known as the residual standard error and is given by the formula $\text{RSE} = \sqrt\frac{RSS}{n-2}$ so I calculated $\sigma^2$ as $\text{RSE} = \sqrt\frac{RSS}{n-2}$ which gives 3.258 but it doesn't add up when I try to use this value instead of $\sigma^2$ in the equations (3.8) in the same page. P.S: This example belongs to the Advertising data set, and it is Sales (Y) as a function of TV (X) advertising. Available here variance share|improve this question edited Sep 8 '14 at 14:31 asked Sep 8 '14 at 12:07 Kenan Deen 1286 3 Sloppy writing: It should say "In general, σ is not known, but can be estimated from the data. This esti- mate is known as the residual standard error". See also stats.stackexchange.com/questions/5135/… –conjugateprior Sep 8 '14 at 13:11 add a comment| 3 Answers 3 active oldest votes up vote 2 down vote accepted Looking at ISL's parent book, ESL (Elements of Statistical Learning, Hastie et al, 2009, pp. 44-48), the $N-2$ in the denominator comes from the fact that if there are $p$ variables not including the intercept (so ther