Pls help, this task is killing me

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Blooper987

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Hello!
I dont know if this is good thread for this task but Im confused... Im trying to solve this for two hours and nothing! I just burn out myself... I cant figure out how to begin this task and how to solve it! Can someone explain me step by step I will be grateful to Heaven ?

The set of values of the independent variable is given 2.4; 2.6; 2.8; 3; 3.3; 3.6; 4; 4.2 and the corresponding sequence in the same order for the dependent variable 36000; 5000; 800; 200; 30; 6.5; 1.2; 0.5. Make a transformation of linearization of this dependence knowing that the independent variable should be taken reciprocally and the dependent logarithmized by basis e.

Thank you guys!
 
Blooper987 said:
Hello!
I dont know if this is good thread for this task but Im confused... Im trying to solve this for two hours and nothing! I just burn out myself... I cant figure out how to begin this task and how to solve it! Can someone explain me step by step I will be grateful to Heaven ?

The set of values of the independent variable is given 2.4; 2.6; 2.8; 3; 3.3; 3.6; 4; 4.2 and the corresponding sequence in the same order for the dependent variable 36000; 5000; 800; 200; 30; 6.5; 1.2; 0.5. Make a transformation of linearization of this dependence knowing that the independent variable should be taken reciprocally and the dependent logarithmized by basis e.

Thank you guys!
Click to expand...
Did you calculate the transformed variables (dependent and independent) as instructed and make a list?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Blooper987 said:
Hello!
I dont know if this is good thread for this task but Im confused... Im trying to solve this for two hours and nothing! I just burn out myself... I cant figure out how to begin this task and how to solve it! Can someone explain me step by step I will be grateful to Heaven ?

The set of values of the independent variable is given 2.4; 2.6; 2.8; 3; 3.3; 3.6; 4; 4.2 and the corresponding sequence in the same order for the dependent variable 36000; 5000; 800; 200; 30; 6.5; 1.2; 0.5. Make a transformation of linearization of this dependence knowing that the independent variable should be taken reciprocally and the dependent logarithmized by basis e.

Thank you guys!
Click to expand...
I don't think I've ever seen the word "logarithmized", but presumably you have, or they wouldn't have written that!

Take the reciprocal of each x, and the natural log of each y. Graph the results, and they are linear.
 
I know that it looks like I just trying to get someone to solve this for me but the thing is I need someone to explain me how proccess of linearization looks like, I have given experiment in practicum on my faculty and we have to measure a few times, lets say 10. Then I put that measures in table and if its not linearized function we have to linearize it! How to do that? Can someone explain me on this example that I wrote above?
P.S. I read rules, but I cant show you where I stuck because I dont know how to do it? I just have table with x and y and nothing else! I have confusing formulas for "least square method" but I dont know how to use it! I calculate this and got some linear function that goes like this: y=-11247,81075x+41669,56232
Its messed up I dont know if its right
 
Dr Peterson, Its not english language Im not native speaker I have used translator sorry for misunderstanding
 
Dr.Peterson said:
I don't think I've ever seen the word "logarithmized", but presumably you have, or they wouldn't have written that!
Click to expand...
I think it will catch on! "If \(\displaystyle y= e^x\) then ln(y)= x where I have logarithmized both sides of the equation."
 
Blooper987 said:
I know that it looks like I just trying to get someone to solve this for me but the thing is I need someone to explain me how proccess of linearization looks like, I have given experiment in practicum on my faculty and we have to measure a few times, lets say 10. Then I put that measures in table and if its not linearized function we have to linearize it! How to do that? Can someone explain me on this example that I wrote above?
P.S. I read rules, but I cant show you where I stuck because I dont know how to do it? I just have table with x and y and nothing else! I have confusing formulas for "least square method" but I dont know how to use it! I calculate this and got some linear function that goes like this: y=-11247,81075x+41669,56232
Its messed up I dont know if its right
Click to expand...

What we want primarily is to find out where you need help, particularly whether it is the meaning of the words, or how to carry out one of the steps. (And I agree with Halls, we need such a word, and I have said similar things myself!) You have now told us more about your situation, which is good.

I think you are expecting this problem to be harder than it is; my suggestion (equivalent to Subhotosh's) was intended to help you get started, because once you try doing something, you can often see what it means. One reason we ask to see work is just to get you to try!

What I did was simply to put the data into a spreadsheet, and graph them (which looks exponential). Then I made another pair of columns containing the reciprocal of the first and the natural log of the second. When I graphed this, the result was a straight line, so I had accomplished what they asked.

That is all they are saying: "Make a transformation of linearization of this dependence knowing that the independent variable should be taken reciprocally and the dependent logarithmized by basis e." They told you exactly what to do; they did not ask you to figure out your own way to linearize the data, but told you that if you do what I just said, it will have been linearized!

I also used Excel's "trendline" feature to find an equation; but you were not told to do that, either by hand or by computer. Least squares is a method to make an equation (not to linearize data), which Excel uses or you could do yourself (though we usually teach the manual process only for the sake of understanding, and will real amounts of data, you would always use a computer).

Now, if you have other situations in which you have to linearize something but are not told how to do it, we will want to see those. In general, linearizing depends entirely on the specific data and their meaning; it may be a guess, or a theoretical consideration that tells you how. Each case will be different.
 
The purpose of such an exercise is to show BY EXAMPLE that an obviously non-linear relationship can be specified, at least approximately, by using a method that on the surface can be used only to specify a linear relationship.

As Dr. Peterson explained, the method, when used in practice, requires experimentation (or the application of extra-mathematical theory).

We look for a way to transform the given variables, which do not seem to have a linear relationship, into new variables that do seem to have a linear relationship. We then use the method of least squares to find the best linear relationship between the transformed variables.

In this exercise, you are given the transformations. In actual practice, you would use extra-mathematical theory or pure experimentation to look for such transformations. But all that is intended in this exercise is to show that there is at least one set of transformations that create an approximately linear relationship between the transformed variables.

They want you to see that

[MATH]u = ln(y) \text { and } v = \dfrac{1}{x}[/MATH]
are related (at least approximately) by

[MATH]u = av + b \implies ln(y) = \dfrac{a + bx}{x} \implies y = e^{\{(a + bx)/x\}}.[/MATH]
The only way for you to get a lick of value from this exercise is to calculate u and v and plot them on a graph.

In fact, based on what you have told us about the problem, that is all the exercise tells you to do. There is nothing to solve. Just do what is asked.
 
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