pilinyir1
2022-09-20
Answered

Why is linear interpolation and extrapolation not useful in making predictions?

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Julianne Mccoy

Answered 2022-09-21
Author has **10** answers

Linear interpolation is not useful in making pblackictions because it only suggests data values within an already known range (typical within time). For example, if you knew data values for the years 1980, 1990, 2000, and 2010, interpolation could be used to determine likely values between 1980 and 2010 (that's what interpolation means).

Linear extrapolation is normally not useful in making pblackictions because so very few time based function are linear in nature and, even in "near future" pblackictions graphs of values like stock market prices are not smooth.

Linear extrapolation is normally not useful in making pblackictions because so very few time based function are linear in nature and, even in "near future" pblackictions graphs of values like stock market prices are not smooth.

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we have a system of linear equations as such:

$x+2y+(a-1)z=1\phantom{\rule{0ex}{0ex}}-x-y+z=0\phantom{\rule{0ex}{0ex}}-ax-(a+3)y-az=-3\phantom{\rule{0ex}{0ex}}-ax-(a+2)y+0\cdot z={a}^{2}-5a-2$

and i have to find the solution in $\mathbb{R}$ and ${\mathbb{Z}}_{\mathbb{5}}$ so i have no problem for $\mathbb{R}$ i get the matrix

$\left(\begin{array}{cccc}1& 2& a-1& 1\\ 0& 1& a& 1\\ 0& 0& a& 0\\ 0& 0& a& {a}^{2}-5\cdot a\end{array}\right)$

but the questions i have are as follows:

1. Can i use what i found for the augmented matrix and the discussion by parameter a in $\mathbb{R}$ to deduce ${\mathbb{Z}}_{\mathbb{5}}$?

2. Or is there some other way i must reduce to row echelon form for ${\mathbb{Z}}_{\mathbb{5}}$ and then have the discussion for parameter a?

3. If i had an 3x3 or 4x4 system to solve over a low prime ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{1}}}$ and ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{2}}}$ (eg 5 and 7) how would i go about doing it with the matrix gauss elimination?could i use the same augmented matrix and reduce it to row echelon over $\mathbb{R}$ and then use that augmented matrix for the rest like above or not?

4. If i recall correctly there was a theorem about the rank of the original matrix and augmented that says something about the number of solutions but i do not recall how that would help me find solutions just eliminate the a's where there is none?

$x+2y+(a-1)z=1\phantom{\rule{0ex}{0ex}}-x-y+z=0\phantom{\rule{0ex}{0ex}}-ax-(a+3)y-az=-3\phantom{\rule{0ex}{0ex}}-ax-(a+2)y+0\cdot z={a}^{2}-5a-2$

and i have to find the solution in $\mathbb{R}$ and ${\mathbb{Z}}_{\mathbb{5}}$ so i have no problem for $\mathbb{R}$ i get the matrix

$\left(\begin{array}{cccc}1& 2& a-1& 1\\ 0& 1& a& 1\\ 0& 0& a& 0\\ 0& 0& a& {a}^{2}-5\cdot a\end{array}\right)$

but the questions i have are as follows:

1. Can i use what i found for the augmented matrix and the discussion by parameter a in $\mathbb{R}$ to deduce ${\mathbb{Z}}_{\mathbb{5}}$?

2. Or is there some other way i must reduce to row echelon form for ${\mathbb{Z}}_{\mathbb{5}}$ and then have the discussion for parameter a?

3. If i had an 3x3 or 4x4 system to solve over a low prime ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{1}}}$ and ${\mathbb{Z}}_{{\mathbb{p}}_{\mathbb{2}}}$ (eg 5 and 7) how would i go about doing it with the matrix gauss elimination?could i use the same augmented matrix and reduce it to row echelon over $\mathbb{R}$ and then use that augmented matrix for the rest like above or not?

4. If i recall correctly there was a theorem about the rank of the original matrix and augmented that says something about the number of solutions but i do not recall how that would help me find solutions just eliminate the a's where there is none?

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