Contents
Where does the standard error on the mean come from?
The standard error on the mean may be derived from the variance of a sum of independent random variables, given the definition of variance and some simple properties thereof. If which due to the Bienaymé formula, will have variance
What does σ 2 mean in linear regression?
The image is a copied and pasted youtube lecture on Linear Regression. I can sort of understand what the lecturer says during the lecture, but I wonder how I actually calculate the σ 2 in the read box of the image. X _ means a matrix. The linear regression is homoscadastic with no serial correlation.
Which is a practical result of decreasing the standard error?
A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample. Or decreasing the standard error by a factor of ten requires a hundred times as many observations.
When is the standard error of a Gaussian distribution?
When the true underlying distribution is known to be Gaussian, although with unknown σ, then the resulting estimated distribution follows the Student t-distribution. The standard error is the standard deviation of the Student t-distribution. T-distributions are slightly different from Gaussian, and vary depending on the size of the sample.
How is the variance of the sum of squares calculated?
Variance. The sum of squares gives rise to variance. The first use of the term SS is to determine the variance. Variance for this sample is calculated by taking the sum of squared differences from the mean and dividing by N-1: Standard deviation.
How to calculate the standard error of a random variable?
In many cases, to calculate the standard error of a random variable defined in terms of other random variables requires starting from scratch, but some special cases are particularly simple. For example, if Y = a×X+b, where a and b are constants, then SE(Y) = |a|×SE(X).
Where does standard error go in pooled variance statistic?
Once the standard error is calculated, it goes in the denominator of our test statistic, as shown above and as was the case in all previous chapters. Thus, the only additional step to calculating an independent samples t-statistic is computing the pooled variance. Let’s see an example in action.