How to determine the mathematical relationship using a data table?

[cantthinkofausernamern]

Here is the data table:

L(meters) ------- Resistance (x10^-6)
0 ------- 0
0.5 ------ 1.4
1 ------- 3.2
1.5 ------- 4.6
2 ------- 5.8
2.5 ------- 7.6
3 ------- 8.9
The question is to determine if it was a direct relationship or a quadratic relationship. I think it's a direct relationship but don't know how to prove my answer. I know that if it was a quadratic relationship, the second difference of the data numbers would be the same and if it was a direct relationship, the first difference would be teh same. But I cannot use this fact to prove my answer since this is a data collected from an experiment and the differences between numbers are not always the same. What can I do to prove that the relationship between L and R is a directly relationship? Thanks ^-^

 

[Deleted member 4993]

Here is the data table:

L(meters) ------- Resistance (x10^-6)
0 ------- 0
0.5 ------ 1.4
1 ------- 3.2
1.5 ------- 4.6
2 ------- 5.8
2.5 ------- 7.6
3 ------- 8.9
The question is to determine if it was a direct relationship or a quadratic relationship. I think it's a direct relationship but don't know how to prove my answer. I know that if it was a quadratic relationship, the second difference of the data numbers would be the same and if it was a direct relationship, the first difference would be teh same. But I cannot use this fact to prove my answer since this is a data collected from an experiment and the differences between numbers are not always the same. What can I do to prove that the relationship between L and R is a directly relationship? Thanks ^-^

If it was direct relationship - what would the equation look like relating L (Length) and R (resistance)?

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:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[Dr.Peterson]

You've demonstrated that it is not (exactly) a direct proportion, but close. So you can't prove that it is!

What you can do is to find an equation of a linear relationship that is close, and show how close it is.

If you know about things like linear regression, or "trendlines" in Excel, you can use that, and find the value of r or of r^2, and use that to state how close it is.

If you don't have any of that available, then you can just plot a graph, and say, "Look! It's almost a straight line!"

So, tell us what you have learned. (That's really the only thing you've omitted from our rules, unless you have failed to show us the actual wording of the entire problem you are working on, which might give us clues about what is expected.)

 

[cantthinkofausernamern]

You've demonstrated that it is not (exactly) a direct proportion, but close. So you can't prove that it is!

What you can do is to find an equation of a linear relationship that is close, and show how close it is.

If you know about things like linear regression, or "trendlines" in Excel, you can use that, and find the value of r or of r^2, and use that to state how close it is.

If you don't have any of that available, then you can just plot a graph, and say, "Look! It's almost a straight line!"

So, tell us what you have learned. (That's really the only thing you've omitted from our rules, unless you have failed to show us the actual wording of the entire problem you are working on, which might give us clues about what is expected.)

I tried to find the differences between the numbers and also put it on the calculator to see how the graph might look like. Here is the question and what I did. The only way I could think of is to actually draw a graph and say something like ''it looks like a straight line''. I just want to know if there is another way to do it. I will try to learn the excel way. Thanks for your help

 

[Dr.Peterson]

I tried to find the differences between the numbers and also put it on the calculator to see how the graph might look like. Here is the question and what I did. The only way I could think of is to actually draw a graph and say something like ''it looks like a straight line''. I just want to know if there is another way to do it. I will try to learn the excel way. Thanks for your help

As I indicated before, the big thing we need to know is, what have you been taught about this? If they ask you to "prove" something, then they have to have told you what constitutes a sufficient "proof" in your context (perhaps just by example).

As far as I can tell, what you've said (that the output is increasing by approximately equal amounts, and that the graph looks like a straight line through the origin) is probably all you need. The fact that you are using a graphing calculator suggests that you might have been taught some specific ways to use it for this, but not necessarily.

Given that the problem is essentially multiple-choice, one way to "prove" your choice would be to pick a point and find a relationship of each of the three types (if possible) that fits that point, and show that they are very different at the other points. But really, graphing should be enough.

 

[HallsofIvy]

The graph does look pretty linear to me! I would start by finding A and B so that the first and last pairs satisfy y= Ax+ B. The first pair is (0, 0) and (3, 8.9) so 0= A(0)+ B, B= 0, and 8.9= A(3)+ 0 so A= 8.9/3= 2.97 (to two decimal places).

Now, check the other pairs, (.5, 1.4), (1, 3.2), (1.5, 4.6), (2, 5.8), and (2.5, 7.6).
2.97(.5)= 1.485 which differs from 1.4 by 0,085.
2.97(1)= 2,97 which differs from 3.2 by 0.23.
2.97(1.5)= 4.455 which differs from 4.6 by 0.145,
2.97(2)= 5.94 which differs from 5.8 by 0.14.
2.97(2.5)= 7.425 which differs from 7.6 by 0.175.


Now, the most common way to measure "error" of a data set is the "root mean square". Add the squares of those errors (including the first and last which have error 0) and divide by 8 to get the "mean" squares then take the square root.