Linked Questions

29
votes
4answers
34k views

Why squared residuals instead of absolute residuals in OLS estimation? [duplicate]

Why are we using the squared residuals instead of the absolute residuals in OLS estimation? My idea was that we use the square of the error values, so that residuals below the fitted line (which are ...
15
votes
4answers
4k views

square things in statistics- generalized rationale [duplicate]

Why do you square things in stats? I have run across this a lot, in both data mining and statistics classes, but no one has ever been able to give me an answer. One specific example is when summing ...
4
votes
2answers
120k views

What does the size of the standard deviation mean? [duplicate]

According to Wikipedia (my emphasis), In statistics, the standard deviation ... is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard ...
4
votes
2answers
1k views

Why Standard Deviation is more popular than Mean Absolute Deviation? [duplicate]

$$ Mean\;Absolute\;Deviation = \frac{1}{n}\sum_{i=1}^n |x_i-mean(X)| $$ Almost all textbooks and papers are using Standard Deviation as a measurement of dispersion. And of course, almost all the ...
4
votes
2answers
2k views

Why not use modulus for variance? [duplicate]

I am trying to wrap my mind around the variance definition. Given a set of values S and n = #(S), the variance is defined as: $$ \operatorname{var}(S) = \frac{\sum_{i=1}^n( S_i - \operatorname{mean}(...
7
votes
2answers
443 views

Why is the standard deviation defined using differences^2 instead of differences^4? [duplicate]

I've read some post about why to take the std. deviation and its benefits, here's one of them: Why square the difference instead of taking the absolute value in standard deviation?, and another by ...
2
votes
3answers
1k views

Why should I prefer the standard deviation over other measures of variance? [duplicate]

The most common kind of deviation is the standard deviation. $$ \text{Sd}(x) = \sqrt{\text{Mean}((x - \text{Mean}(x))^2)}$$ The standard deviation is very similar to the mean absolute deviance or $$...
0
votes
3answers
664 views

Why is standard deviation defined as sqrt(var(x)) and not as abs(X-u)? [duplicate]

Why is standard deviation usually defined as sqrt(var(x)) and not simply as abs(X-u) while the latter is simpler to understand and both give same values?
-1
votes
1answer
633 views

Why we need variance in this world? [duplicate]

Why we need variance in this world? What is the purpose to make such function and how does it work? I know that it is a measure of how the data spread, but why we don't just use the absolute ...
2
votes
1answer
599 views

Why linear regression one variable uses squared cost function? [duplicate]

This is about linear regression course given by Andrew Ng on Coursea about machine learning. why cost function is $$ \frac{1}{m} \sum _{i=1}^m \left(h_\theta(X^{(i)})-Y^{(i)}\right)^2 $$ and not ...
0
votes
1answer
639 views

Why is the variance squared, and does it mean the same thing as the standard deviation? [duplicate]

I am still confused, despite similar questions being asked, about the difference between the variance and standard deviation in statistics. Why is the variance squared?
1
vote
1answer
180 views

Why do we use squared deviations to compute the SD, given that it amplifies the effect of outliers? [duplicate]

Suppose I have the following hypothetical data: One thousand times value 15 (i.e., 15 occurs 1000 times) and a single outlier value - 115 (i.e., 115 occurs just once - an outlier) Thus the mean is: $...
0
votes
0answers
71 views

Squared Error vs Absolute Error loss functions [duplicate]

The two most popular types of loss functions are 1) squared error: $L(y,f(x))=(y-f(x))^2$ --> best estimate is the $E(Y|x) $ 2) absolute error: $L(y,f(x))=|y-f(x)|$ --> best estimate is the $median(Y|...
0
votes
0answers
66 views

Intuition for Euclidean Distance as a measure of spread (Standard Deviation) [duplicate]

I've been studying descriptive statistics and am having a hard time understanding the actual intuition behind standard deviation. I'm trying to get a practical feeling for it and so I'm trying to draw ...
1
vote
1answer
45 views

Squaring floats between -1 and 1 reduces sum of squares, so why do it? [duplicate]

I have been learning basic statistical testing as it relates to agriculture and have become familiar with the common practice of summing squared raw deviation values, whether in something simple like ...

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