# Tag Info

Accepted

### Calculate standard deviation with only the averages from a number of samples

To proceed in general, suppose we have $n$ samples that each contain $m$ values, generated as IID variables from an underlying superpopulation with mean parameter $\mu$ and standard deviation ...
• 97.7k

### Compute expected standard deviation from proportion data

Very late response, but regarding the goodness-of-fit test to the binomial distribution, it turns out that this $$s^2(n-1)/\sigma^2$$ has a $\chi^2$ distribution with $n-1$ degrees of freedom, where ...
• 1

### Why is standard error of the mean always calculated from the population variance?

The "standard error" of an estimator is just the standard deviation of that estimator. Typically this depends on the unknown parameters in the model, and so the true standard error is a ...
• 97.7k

### Why is standard error of the mean always calculated from the population variance?

Well, typically, we only have a single realization of the sample mean to work with - we are not often in a situation where we have several datasets drawn from the same population. Even if we did have ...
• 356

### Why Confidence Level 95% is -1.65?

As a bit of an expansion to the answer by @Tim : First, the sources are assuming that the observed values follow a normal distribution. Second, the sources are using "confidence level" in a ...
• 7,448
1 vote

### Why Confidence Level 95% is -1.65?

The sources you mention assume normal distribution, or use the normal distribution to approximate the underlying distribution. You are probably familiar with the 68-95-99.7 rule, mean $\pm 1.65$ ...
• 115k
Accepted

### Is the 'Std. Error' provided by lmer in lme4 actually Standard Deviation?

The "standard error" of a parameter is the standard deviation of the parameter's sampling distribution (e.g. wiki). In other words, theoretically, if you were to sample new data and rerun ...
• 5,541
Accepted

### Help with table interpretation

A mean of 0 means that on average the effect of your variable REI1 and REI2 is 0. But the standard deviation comes from the fact that for each sample this effect may differ from zero. See the image ...
1 vote

### Should we always minimize squared deviations if we want to find the dependency of mean on features?

Yes, it is possible for estimators obtained by minimizing some different than squared deviation to give a better estimator of model parameters. The question of whether a given estimator can be beaten ...
• 642

### Should we always minimize squared deviations if we want to find the dependency of mean on features?

Your estimator is the OLS estimator in nonlinear regression Your problem is essentially just the OLS estimation problem in nonlinear regression. To see this, suppose you have nonlinear regression ...
• 97.7k

### Should we always minimize squared deviations if we want to find the dependency of mean on features?

A similar question (if not the same) is: If the predicted value of machine learning method is E(y | x), why bother with different cost functions for y | x? The theoretical mean of a distribution ...
• 48.8k
1 vote

### Should we always minimize squared deviations if we want to find the dependency of mean on features?

NO It is important to keep in mind that an estimator of a parameter can take on many forms. In fact, constants can be estimators! Consequently, we might find that calculating something other than the ...
• 32.6k

### Should we always minimize squared deviations if we want to find the dependency of mean on features?

Can it be the case that a use of something different from squared deviation gives a better estimate of model parameters (for example more accurate (smaller width) and with smaller or no systematic ...
• 904

### Variance of a bounded random variable

The key elements here are that $f(x) = x^2$ is convex, $EX$ minimises $E(X-t)^2$ and $X(\omega) \in [a,b]$. Let $x \in [a,b]$, then \$f(x-{1 \over 2}(a+b)) \le {1 \over 2} (f({x-a \over 2}) + f({x-b \...
• 181

### Should we always minimize squared deviations if we want to find the dependency of mean on features?

Minimizing the MSE in the cases you describe indeed produces a consistent estimator for the model parameters. The consistency is related to the fact that the derivative of the MSE, and therefore the ...
• 4,157
1 vote

### What are the variance and standard deviation for the bin counts for n rolls on a standard six-sided die?

"That doesn't make sense: if the die starts at zero-based numbering, then the variance changes. But, variance shouldn't depend on the numbering of the die as all faces are equally probable. – ...
• 11

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