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Help with method of least squares?

Help with method of least squares? Topic: Problem solving in system analysis
July 16, 2019 / By Holly
Question: I don't understand this concept. Everything I've read on the subject is too advanced for me. My highest math class so far is calc 2. I have a data table and an equation to find an equation using the method of least squares but I can't seem to find the right answers. The problem in question goes like this: First here's the data points: (1, 2.3) (2, 6.2) (3, 18.9) (4, 35.6) (5, 56.5) But then it also says: Using the method of least squares, develop an equation for the best fit line through these data points of the form: y=A0*(x^A1) My answer is consistently wrong; I think this is because I don't understand how the form affects what I need to do. Other problems ask me to solve for different forms. I really need help understanding how this works, particularly in terms of the form alright I understand the conceptual side of what your saying... up until the end. I'm still too uneducated on the subject to follow the math. I calculated the slope as 3.14 and the y intercept at 14.54. What I need to know is what to do, mathematically, from there. Do I need to take the ln of one of those? Or does the first equation change? What I really need is more of a step by step. If Its any help, this is the equation I am using: http://www.fda.gov/ucm/groups/fdagov-public/documents/image/ucm174702.jpg That was a mistake. I actually got the slope is 13.78 and I don't know how to find the intercept. My textbook doesnt mention that
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Best Answers: Help with method of least squares?

Edana Edana | 3 days ago
The textbook should walk you by the hand through the "best fit line" problem, where y= ax+b is the form you are trying to fit with N data points. In that case, you're basically using the form y=ax+b to generate N equations in 2 unknowns: you are given N (x,y) pairs, and your unknowns are (a,b). The method of least squares is the classical method of find a "best fit solution" to this overdetermined system. In a nutshell, the way it works is to consider e = y_{data} - y_{fit line}, then minimize the sum of the squares of the N values of e. Analytically, e(j) = y(j) - a x(j) - b. so you square it, sum over j, across the N data points, then take the partial derivative of the sum with respect a and set that to zero, then take the partial derivative of the sum with respect to b and set that to zero, and now you have 2 equation in the 2 unknowns (a,b). The trick to handling the form y = a x^b is to use logarithms to convert it into the form Y = A X + B, then use the previous analytical result. ln y = ln a + b ln x Y = B + A X Y = ln y B = ln a A = b X = ln x so take the logarithm of (x,y) to form (ln x, ln y) = (Y,X), plug (X,Y) into the least squares analysis to get (A,B), then transform (A,B) back to get (a,b)
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Edana Originally Answered: Gauss' method for finding the sum of whole numbers 1-100. Explain his method.?
It says that for numbers that are opposite (cant think of a better word. For example, 1 and 100, 2 and 99, 3 and 98, 4 and 97, etc.) will all add up to the same number, 101.

Edana Originally Answered: Punnett Squares?
AaBbCc x AaBbCc ... and your teacher wants a Punnett square, then it's going to have to be 8 rows and 8 columns. Show all the possible gametes from each parent. Each gamete must have an a, b, and c. ABc ABC AbC Abc aBc aBC abC abc all 8 of these gametes will be on a colum down and a colum across to make 64 squares. Then each box of the Punnett square will have 6 letters again: There's no way to show you the square in this word-processing format. Just give it a try. also if you want me to show you how to do it, or do it for you online, just IM me on aim @ ebrady247
Edana Originally Answered: Punnett Squares?
You have two different problems here. In the first problem: homozygous long = SS homozygous short = ss Parents SS x ss Gametes S S s s Put first parent's gametes on the side of the square and second parent's gametes on the top to make the column headings. Each of the four boxes in the Punnett square will have Ss (that's the genotype because it tells what the genes say) and will be long-leaved (that's the phenotype because that's the form of the trait that they exhibit). In the second problem, you have a case of polygenic inheritance in which several pairs of genes govern the trait. The individuals AaBbCc are each medium darkness because they have three uppercase and three lowercase letters each. The offspring from these two individuals could have any number of uppercase letters. They could get A from each parent, B from each, and C from each: AABBCC and be the darkest possible, or they could get AABBCc and be one step lighter -- clear down to the possibility of being aabbcc and being as light as possible.
Edana Originally Answered: Punnett Squares?
This is a pretty simple one if you just take a deep breath. Steps: 1. Draw a box with 4 smaller squares in it. 2. Review your terminology to remember what homozygous means Long leaf (dom)=SS Short leaves (rec)= ss 3. On the left side write out one of the seperated parental alleles (each letter, upper or lowercase S= 1 allele) 4. On the top write out the other seperated parental alleles So it should look like this s s S__|__ S | 5. Now add copy the letters down or across the row they are each in 6. Your resulting square will look like this Ss|Ss Ss|Ss 7. So what does this mean? They all have the same genotype (heterozygous) and the same phenotype (they all look like they have tall leaves) You may want to try a couple different simple squares what if you crossed a Ss with an Ss? or a ss with and Ss? What would teh resulting genotypes and phemotypes be here? Have fun with this stuff, it is kinda cool when you think about it a bit.

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