The proposition is not true.pi and -pi are both irrational. But their sum, = 0, is rational.
Any number multiplied by zero will always give the result of zero.
Not always. For example: sqrt(2)+(-sqrt(2))=0 which is not irrational.
No. While the sum of two qudratics cannot have a power greater than two, it could have a power of 2, 1 or 0. x2 + 1 is one quadratic (2-x)(2+x) is another quadratic. Their sum is 1, a constant (power = 0).
Such a sum is always rational.
the sum of the residuals is always 0(zero) because its how far they are away from the LSRL. that's what makes them residuals in the first place :P
how much in residuals is jason alexander receiving from seinfeld
0 (zero).
'a' can be any number whatsoever. The sum of +a and -a is always zero.
No, it would always equal 0. So if it was like 3 + -3 = 0
Yes.
Not always, if the smaller number is 0 or a negative number. Then their sum will be equal or less than the greater number.
The sum of deviations from the mean, for any set of numbers, is always zero. For this reason it is quite useless.
In estimating a linear relationship using ordinary least squares (OLS), the regression estimates are such that the sums of squares of the residuals are minimised. This method treats all residuals as being as important as others.There may be reasons why the treatment of all residuals in the same way may not be appropriate. One possibility is that there is reason to believe that there is a systematic trend in the size of the error term (residual). One way to compensate for such heteroscedasticity is to give less weight to the residual when the residual is expected to be larger. So, in the regression calculations, rather than minimise the sum of squares of the residuals, what is minimised is their weighted sum of squares.
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The proposition is not true.pi and -pi are both irrational. But their sum, = 0, is rational.
Depends what the number is. If you were multiplying and did (substitute Z with any number)0xZ,the answer would always be zero. Actually the SUM is the answer to a addition problem. So the answer would be the number in which is to 0.