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Sam Belsky
12-07-2011, 05:11 PM
The variables x and y in the data below are related by a linear relationship.
a) Assuming that the standard deviation σi for data point n yi is given σi = sqrt(yi), fit the data to a straight line y = a + bx minimizing Chi-square (i.e. compute a and b).
b) Plot the fitted curve against the data.
c) Compute the variances of a and b (σa and σb).
d. Compute the Chi-squared of the fit. Is the fit good (you will have to do a Chi-squared test to determine this).
e) Find 95% confidence intervals for a,b. You can assume that they are distributed as Gaussians with means and standard deviations equal to the value you computed in a) and c).

x y x y
1.00 7.73 26.00 50.88
2.00 10.90 27.00 63.07
3.00 12.80 28.00 57.16
4.00 14.82 29.00 57.81
5.00 16.64 30.00 65.97
6.00 17.45 31.00 67.09
7.00 21.19 32.00 71.40
8.00 22.68 33.00 67.18
9.00 21.51 34.00 65.18
10.00 30.95 35.00 88.18
11.00 28.25 36.00 71.06
12.00 33.74 37.00 69.78
13.00 33.28 38.00 77.76
14.00 33.67 39.00 85.66
15.00 40.91 40.00 95.09
16.00 40.68 41.00 89.63
17.00 36.90 42.00 84.48
18.00 36.90 43.00 84.46
19.00 45.17 44.00 95.83
20.00 46.16 45.00 88.68
21.00 48.01 46.00 91.02
22.00 48.27 47.00 95.01
23.00 48.23 48.00 96.37
24.00 47.63 49.00 102.59
25.00 60.33 50.00 118.61

Outlier
12-07-2011, 05:31 PM
Search keywords on Wikipedia.

Mean Joe
12-07-2011, 06:40 PM
You can do this problem in Excel, or R. Rather than by hand calculations.

12-07-2011, 07:47 PM
Search keywords on Wikipedia.

I get annoyed sometimes cause it'd be so easy to google or search on wiki and you'd find the answer. Yet so many ppl want us to hold their hands and get the answer for them.

Outlier
12-08-2011, 11:40 AM
I get annoyed sometimes cause it'd be so easy to google or search on wiki and you'd find the answer. Yet so many ppl want us to hold their hands and get the answer for them.
This forum is not very indulgent, and it probably shouldn't be. With the Net, anybody can bone up on any subject in a big hurry, at least to the extent that they can ask intelligent questions.

I've seen only one guy dump a homework problem [it was circuit design] on a forum, I gave him some rules of thumb, and he actually followed through and came up with one of a very few circuit implementations that met the specs. Probably most people just search for a more indulgent info source.

noetsi
12-08-2011, 02:07 PM
In fairness (even assuming that people know how to search for this on the net) if you don't know much about statistics much of the material available there can be confusing. Lots of sites assume a greater knowledge of basic statistics (and thus do little explaining) then many new people begin.

Even after years of working with statistics I find lots of commentary on statistics on the net confusing or contradictory.

BGM
12-08-2011, 02:21 PM
The dilemma here is that:

If we want to be short, we can only directly type the solution which is no good.

If we want to really help OP to understand all of the related concepts, the post is going to be very long.

So IMHO TS may not be a very efficient way to learn many elementary stuffs quickly.

I do not mean that TS not welcome new poster like OP but at least you need to have some background. Otherwise seeking help verbally/face-to-face from your professors/TA will be much more efficient.

Also I believe that all of the formulae required to solve the problems are listed in (a chapter) of the textbook. If OP understand the concepts behind, you just need to be brave enough to try to apply to your problem.

TheEcologist
12-08-2011, 02:42 PM
Some people here are very patient and indulgent to franky quite disrespectful posts like this and that is their right. I generally will not reply to such posts.

If you don't even have the common human decency or to indicate 1) what you have done or 2) indicate what points you have problems with or even 3) to say "thank you in advance" or something similar but just copy paste your homework here then you show absolutely no respect to the people you expect to help you for free (and even if you pay people you should show some respect). The OP has not shown any curtousy and just expects the awsers to be handed to him.

You don't have to completely apply to these (http://www.talkstats.com/showthread.php/14960-Forum-Guidelines-Smart-posting-behavior-pays-off) but some level of common decency should be expected.

That said I commend BGM for his almost ZEN-like patience.

Outlier
12-08-2011, 02:44 PM
if you don't know much about statistics
Then I'd say this person is in over his head.
That's another thing about forums. I have had electricians complain that, for a simple question, I gave a complicated answer.
Which I did.
That is because it is easy to ask questions but sometimes the answer is not easy.

E.g., What is time? J. Barbour says there is no such thing.

12-08-2011, 02:48 PM
I agree that while it IS possible that the OPs do not have the statistics background and may require a slower intro to this, it is not always the case. Furthermore, I think what more specifically annoys me is the apparent lack of effort.

Take this post for example. All they've done is post the question. No work that's been done, nor requested hints. It's like they just want us to solve it for them.

Then again, the same issues are posted under the forum guidelines. We can't help if they ignore them.

noetsi
12-08-2011, 03:05 PM
My solution would be to put it into a regression software which will generate all this information. But I am puzzled by something. It talks about a linear relationship (which I commonly associate with OLS although I know it applies to other methods). But then it talks about minimizing chi square which is commonly associated with other methods (notably logistic regression or SEM).

spunky
12-08-2011, 03:18 PM
That said I commend BGM for his almost ZEN-like patience.

i have always been in awe of BGM because, oh god, his/her command of statistical theory is superb... it far exceeds mine and that of a lot of people i know.... plus the elegance of his/her solutions... OH GOD, THE ELEGANCE!!! and, to top that, (s)he's been given the gift of infinite patience that we dont all posses....

TheEcologist
12-08-2011, 03:35 PM
i have always been in awe of BGM because, oh god, his/her command of statistical theory is superb... it far exceeds mine and that of a lot of people i know.... plus the elegance of his/her solutions... OH GOD, THE ELEGANCE!!! and, to top that, (s)he's been given the gift of infinite patience that we dont all posses....

I know! Its like he (or she) is some kind of stats Jedi master.

BGM
12-09-2011, 02:05 AM
Sometimes I "know" OP meet some kind of "bottleneck" which a short hint will do.

However some OP maybe just completely lost; and if I try to understand what OP lacking, I need to have quite a number of question and answers (I learn like that). So sometimes will make the post quite long.

I try to strike a balance but it is difficult as I said above. Thanks for the comment. My patience must be finite as I also avoided to reply in some posts. :P

P.S. I am a male :)