1
$\begingroup$

I'd like to learn to evaluate how much there is error if I compute algebraic expressions and round my intermediate steps. For example, I had data of length of couples height as (167,183), (165,165), (167,178), (163,173), (178,180), (165,173). I computed the Pearson correlation of those data points to be $$\frac{\frac{85}{5}}{\sqrt{\frac{287}{10}}\sqrt{41}}.$$ But if I make a table to compute the correlation which has say columns $x,y,x-\bar{x},y-\bar{y},(x_i-x)(y_i-y), (x_i-x)^2,(y_i-y)^2$ and for every point I round the result for example to four decimals, what can I say the error $\epsilon$ of the correlation coefficient? Or if $\epsilon$ should be for example less than $0.01$, how many digits should I take to the intermediate results. I would like to see some tutorial/lecture notes/book to evaluate errors. Also, if person's height is 167 in this data, the height $h$ actually satisfies the inequality $166.5<h<167.5$ so I'd like to learn how much that affects on the correlation.

$\endgroup$
0
$\begingroup$

You might look up "interval arithmetic".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.