Math Is Fun Forum

Alive

Member

Registered: 2010-08-14

Posts: 92

Urgent Assignment Help Needed!

Hi, I need step by step in the questions for an assignment. I don't want you guys to do it  but I need to understand what to do. Really appreciate it if you give the method to do these!

First of all this is a Core Assignment (Correlation and regression)
We are to select numerical bivariate data (eg from the web) where you think there is probably a correlation. It must be real. Example; Global temperature vs time in years.

Part 1, I know how to do.. But when it comes to Part 2, I'm not really sure.. I know how to get the least squares regression line but making predictions for interpolation and interpolation?? I don't know how to do..? What predictions??? Don't know Residuals either.. 
For Part 3, do we transform this graph? For example make a graph with y to x squared, and then make one for y to the log ? And make predictions which I again don't know how to?
Please guys this is Really urgent and no time left. Please answer directly, Thanks!

Last edited by Alive (2011-04-03 21:41:09)

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All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi Alive;

I know how to get the least squares regression line but making predictions for interpolation and interpolation?? I don't know how to do..? What predictions???

If you know how to get a regression line then you know the hard part.
Predictions are values for points you do not already have. Interpolation is for between points you have and extrapolation is for past points you have.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Which values? I still don't get it. Please give an example.

Also please help explaining what to do for the rest.. Like residuals, transformation. Thanks

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi Alive;

What would be a lot easier is if I could see your data. You know the data you are trying to correlate. Then I could just do the problem which is a heck of a lot easier than explaining terms that have whole books written about them. In one post no less.

Here is the data and regression model for the temperature for 6 months.

The question is what was the temperature in June ( 6th  month ) this is interpolation. What is the temperature going to be in August ( 8th month ) that is extrapolation.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Okay I'm changing my data... It actually won't work... Cause it's got no relation really.. I'm changing it to this:

Year - CO2 (ppm)
1975 331
1976 332
1977 334
1978 335
1979 337
1980 339
1981 340
1982 341
1983 343
1984 344
1985 346
1986 347
1987 349
1988 351
1989 353
1990 354
1991 355
1992 356
1993 357
1994 359
1995 361
1996 363
1997 364
1998 367
1999 369

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi Alive;

Sorry for the delay but chores came up!

Okay I will look at that data but do you understand and can you do my question at the bottom of post #4. Or do you need help there?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Then there's no interpolation left for my data? So I should make spaces between them?

New Data gathered:

Year - CO2 (ppm)
1965 320
1966 321
1967 322
1968 323
1969 324
1970 326
1971 326
1972 327
1973 330
1974 330
1975 331
1976 332
1977 334
1978 335
1979 337
1981 340
1983 343
1985 346
1987 349
1989 353
1991 355
1993 357
1995 361
1997 364
1999 369

Could you please explain the rest as well, residuals and transformations, Thanks.

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi;

This its the linear regression model.

What this correlation says is that the c ( CO2 ) is very well explained by the y ( years ). The closer you get to 1 the better the correlation.

These are the residuals

The points in the graph below are the scatterplot. The line is the linear fit. The graph shows that a linear fit is a good one.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Could you please check if you did the linear regression right? Cause it looks a little different from my calculation.
My one comes up as:
y = -2484.326+1.4261551x
The teacher wants us to put the residuals in the y axis and leave the x axis like it is for question  (years..) for question 1b), did I not understand this correctly because in the questions it doesn't state to do this.. it only states it in 2c)

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi Alive;

Hold on, I only have data from 1975 on. It did not copy correctly. Please wait I will do it again.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

I put the data into the calculator and pressed linear regression, I guess I must have done it wrong somehow. Coming back to what the teacher said, should we plot the y value as the residuals or the original data? Original data makes more sense...

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi;

I am getting this for the linear refression

Please check yours again.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Thanks, it now comes up as  y = 1.4216915x -2475.611
And so the residuals will be different now??

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

The residuals are the differences between the CO2 that is given and the CO2 that is computed by the regression formula.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Example:
Do we just put in 320 to the regression formula:
y = 1.4216915 (320) - 2475.611
for each one of them?

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Nope the year goes into the function. You should not always label all variables as x and y.
That confuses things. That equation is  CO2 = 1.4216915 (year) - 2475.611

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Thanks, could you please quickly guide me through all the other questions as well as time is running out, Thanks for the help till now though

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Urgent Assignment Help Needed!

hi Alive,

Is it the transformations you want to do now?

see http://en.wikipedia.org/wiki/Data_transformation_(statistics)

Your data from post #5 doesn't need transforming as it has such a good, linear correlation as it is, which makes for a bit of a problem.  Sorry.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

Hi Alive;

I have to agree, with data that fits that well I would not not use a logarithmic fit. What else do you need?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Quadratic transformations?????
I changed my data because I thought it needed to be straight as possible... Fail...
Now what? Get new data or something? *A.s.a.p help please?*

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Urgent Assignment Help Needed!

What is a quadratic transformation? I have heard of log transform. They used to have log graph paper for that.

I do not think you should change your data.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Urgent Assignment Help Needed!

On the Wiki page they have an example using area of country and population where a log transform works nicely.

Changing the data?  In view of the time pressure why not:

(i) keep what you have already done.

(ii) Explain why it has proved unsuitable for transforming. (credit for that surely)

(iii) Quickly get new data where a log transform is useful.

(iv) submit this as well.

Afterall.  If the purpose of the assignment is to show what you can do and understand, then this approach hits all the targets.

Bob

Last edited by Bob (2011-04-06 22:47:36)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Okay,

http://img849.imageshack.us/img849/6446/cci0704201100001.jpg

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

Alive

Member

Registered: 2010-08-14

Posts: 92

Re: Urgent Assignment Help Needed!

Can you guys please find me some new data? I don't know how to find them... And I haven't come so far anyway, so I guess doing it altogether will be the best option........... Please find me data that has 25 data in it please and can transform easily!

---

All things can be forgiven if we can progress.
Yusuf Islam (formerly known as Cat Stevens)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Urgent Assignment Help Needed!

http://www.mongabay.com/igapo/world_statistics_by_area.htm

I haven't checked that the log transform will be useful but with so much data here you can select some so it is.  eg.  Pick a few small countries and a few large.

That way you get the bunched and wide scatter effect.

Bob

ps.  It copies straight into Excel so it must have the right field separators!  then you can delete whole columns to isolate what you want.

pps.  You want countries that still give a good correlation so you'll need to select carefully.  Make up some common factor to explain why you've just included those ones.  eg.  they have similar population growth or they're on the same continent or if you're really stuck for a reason 'they are meeting to consider a co-operation pact'

Last edited by Bob (2011-04-06 23:10:15)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob