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Hi, I need to find the rate of this table. The numbers are
X:-4, 1, 5
Y:-3, 1, 4
Thanks
The rate would appear to be x goes from -4 to 1 by adding 5, and from 1 to 5 by adding 4.
For y, we have -3 to 1 adds 4 and 1 to 4 adds 3. This says as x increases by a integer,
y increases by 1 less.
To approximate it mathematically, solve the matrix
Ai + Bj = D
Bi + Cj = E
where A is the count, B is the sum of the x, C is the sum of the x²,
D is the sum of the Y, and E is the sum of the xy.
It can be seen that A=3, B=-4+1+5=2, C=(-4)²+1²+5²=16+1+25=42, D=-3+1+4=2,
and E = -4*-3 + 1*1 + 5*4 = 12 + 1 + 20 = 33.
This gives us [1] 3i + 2j = 2, [2] 2i + 42j = 33.
Computing -3/2 of [2] gives -3i - 63j = -99/2. Adding this to [1] gives -61j = -95/2,
and that gives j = 95/122. This gives i = 18/122.
Checking the equations out in Excel, they both come out right.
This gives the linear approximation as y = (18 + 95x)/122.
That approximates the y values as -2.967213115, 0.926229508, 4.040983607,
and those are fairly close to -3, 1, and 4.
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Scott A Wilson
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