35k 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 ...
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 ...
126k 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 ...
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 ...
2k views

738 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?
657 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 ...
632 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 ...
655 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?