Who Dares To Opt For Statistics Paper
 

Plz Confirm ur nominations if u ve opted for Stats/are willing to opt/having statistics background......Purpose of this data base is to share knowledge and expereinces on this paper. Word [I]Dare[/I] is used b/c attempting this paper needs self confidence in addition to stock of technical knowledge.

Stats is one of my optional paper,no doubt I attempted stats paper in CA Foundation n in B.Com but It will b my first expereince to take this paper in CSS.

Paper is more technical except Q from sampling, Regression Analysis, MCQs and genral question on the application of stats in other fields.

It will be of great use if any body who previously attempted stats in CSS shares his tips and illustrates some concepts. Plz don't hesitate to quote ur marks obtained in stats so as to help new comers in their decision.

Some precious notes on Statistics Regression Analysis

________________________________________
A Simple Regression Example
In this lesson, we show how to apply regression analysis to some fictitious data, and we show how to interpret the results of our analysis.
Note: Regression computations are usually handled by a software package or a graphing calculator. For this example, however, we will do the computations "manually", since the gory details have educational value.
Problem Statement
Last year, five randomly selected students took a math aptitude test before they began their statistics course. The Statistics Department has three questions.
 What linear regression equation best predicts statistics performance, based on math aptitude scores?
 If a student made an 80 on the aptitude test, what grade would we expect her to make in statistics?
 How well does the regression equation fit the data?
How to Find the Regression Equation
In the table below, the xi column shows scores on the aptitude test. Similarly, the yi column shows statistics grades. The last two rows show sums and mean scores that we will use to conduct the regression analysis.
Student xi yi (xi - x) (yi - y) (xi - x)2 (yi - y)2 (xi - x)(yi - y)
1 95 85 17 8 289 64 136
2 85 95 7 18 49 324 126
3 80 70 2 -7 4 49 -14
4 70 65 -8 -12 64 144 96
5 60 70 -18 -7 324 49 126
Sum 390 385 730 630 470
Mean 78 77

The regression equation is a linear equation of the form: ŷ = b0 + b1x . To conduct a regression analysis, we need to solve for b0 and b1. Computations are shown below.
b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2]
b1 = 470/730 = 0.644 b0 = y - b1 * x
b0 = 77 - (0.644)(78) = 26.768
Therefore, the regression equation is: ŷ = 26.768 + 0.644x .
How to Use the Regression Equation
Once you have the regression equation, using it is a snap. Choose a value for the independent variable (x), perform the computation, and you have an estimated value (ŷ) for the dependent variable.
In our example, the independent variable is the student's score on the aptitude test. The dependent variable is the student's statistics grade. If a student made an 80 on the aptitude test, the estimated statistics grade would be:
ŷ = 26.768 + 0.644x = 26.768 + 0.644 * 80 = 26.768 + 51.52 = 78.288
Warning: When you use a regression equation, do not use values for the independent variable that are outside the range of values used to create the equation. That is called extrapolation, and it can produce unreasonable estimates.
In this example, the aptitude test scores used to create the regression equation ranged from 60 to 95. Therefore, only use values inside that range to estimate statistics grades. Using values outside that range (less than 60 or greater than 95) is problematic.
How to Find the Coefficient of Determination
Whenever you use a regression equation, you should ask how well the equation fits the data. One way to assess fit is to check the coefficient of determination, which can be computed from the following formula.
R2 = { ( 1 / N ) * Σ [ (xi - x) * (yi - y) ] / (σx * σy ) }2
where N is the number of observations used to fit the model, Σ is the summation symbol, xi is the x value for observation i, x is the mean x value, yi is the y value for observation i, y is the mean y value, σx is the standard deviation of x, and σy is the standard deviation of y. Computations for the sample problem of this lesson are shown below.
σx = sqrt [ Σ ( xi - x )2 / N ]
σx = sqrt( 730/5 ) = sqrt(146) = 12.083 σy = sqrt [ Σ ( yi - y )2 / N ]
σy = sqrt( 630/5 ) = sqrt(126) = 11.225
R2 = { ( 1 / N ) * Σ [ (xi - x) * (yi - y) ] / (σx * σy ) }2
R2 = [ ( 1/5 ) * 470 / ( 12.083 * 11.225 ) ]2 = ( 94 / 135.632 )2 = ( 0.693 )2 = 0.48
A coefficient of determination equal to 0.48 indicates that about 48% of the variation in statistics grades (the dependent variable) can be explained by the relationship to math aptitude scores (the independent variable). This would be considered a good fit to the data, in the sense that it would substantially improve an educator's ability to predict student performance in statistics class.

Student..xi...........yi.......... (xi - x)... (yi - y)... (xi - x)2......(yi - y)2.......(xi - x)(yi - y)..
1........... 95......... 85......... 17......... 8........... 289............64................136..........
2........... 85......... 95......... 7........... 18......... 49..............324...............126..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
3........... 80......... 70......... 2........... -7.......... 4................49...............-14......................................................
4........... 70......... 65......... -8.......... -12........ 64.............144...............96........................................................................................................................................................................................................................................................................................................................................................
5........... 60......... 70......... -18........ -7.......... 324............49..............126..................................................
Sum...... ............. 390....... 385....... ............. 730...........630..............70.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Mean..... 78...........77

[B][U]Some fundamental concepts [/U][/B]
Statistical data analysis can be subdivided into descriptive statistics and inferential statistics. Descriptive statistics is concerned with exploring and describing a sample of data, whereas inferential statistics uses statistics from a sample of data to make general statements about the whole population. Note that the word ``data'' is plural and a single element of data is called a ``datum'', so avoid saying things like ``the data has been ''.
Descriptive statistics is concerned with exploring, visualising, and summarizing data sampled from a population but without fitting any probability models to the data. This kind of Exploratory Data Analysis (EDA) is used to explore sample data in the initial stages of data analysis. Since no probability models are involved, it can not be used to test hypotheses or to make testable out-of-sample predictions about the whole population. Nevertheless, it is a very important preliminary part of analysis that can reveal many interesting features in the sample data.
Inferential statistics is the next stage in data analysis and involves the identification of a suitable probability model. The model is then fitted to the data to obtain an optimal estimation of the model's parameters. The model then undergoes evaluation by testing either predictions or hypotheses of the model. Models based on a unique sample of data can be used to infer generalities about features of the whole population.
Much of climate analysis is still at the descriptive stage, and this often misleads climate researchers into thinking that statistical results are not as testable or as useful as physical ideas. This is not the case and statistical thinking and model-based inference can be exploited to much greater benefit to make sense of the complex climate system.

Plz contribute ur valued material on this subject

Its very risky subject ......risk may be rewarding or it may convert in punishment

Really???
 

Assalam-o-alaikum:
how are u? i hav recently started preparing for CSS and making my mind for Stat. as i hav done B.com, i feel confident about it. as u said,

[QUOTE=Raz]Its very risky subject ......risk may be rewarding or it may convert in punishment[/QUOTE]

i want to know how its risky plz. well about marks in stats i dont remember exactly but were around 80s. thanx for your contribution in the end.
Plz keep on sharing,
Allah Hafiz

Probability
 

[U][B]Why Probability?[/B][/U]

In the real world, we often don’t know whether a given proposition is true or false.
Probability theory gives us a way to reason about propositions whose truth is uncertain.
Useful in weighing evidence, diagnosing problems, and analyzing situations whose exact details are unknown.

[B][U]Random Variables[/U][/B]

A random variable V is a variable whose value is unknown, or that depends on the situation.
E.g., the number of students in class today
Whether it will rain tonight (Boolean variable)
Let the domain of V be dom[V]={v1,…,vn}
The proposition V=vi may be uncertain, and be assigned a probability.


[B][U]Experiments[/U][/B]

A (stochastic) experiment is a process by which a given random variable gets assigned a specific value.
The sample space S of the experiment is the domain of the random variable.
The outcome of the experiment is the specific value of the random variable that is selected.


[B][U]Events[/U][/B]

An event E is a set of possible outcomes
That is, E  S = dom[V].
We say that event E occurs when VE.
Note that VE is the (uncertain) proposition that the actual outcome will be one of the outcomes in the set E.


[B][U]Probability[/U][/B]

The probability p = Pr[E]  [0,1] of an event E is a real number representing our degree of certainty that E will occur.
If Pr[E] = 1, then E is absolutely certain to occur,
thus VE is true.
If Pr[E] = 0, then E is absolutely certain not to occur,
thus VE is false.
If Pr[E] = ½, then we are completely uncertain about whether E will occur; that is,
VE and VE are considered equally likely.
What about other cases?

[B]Four Definitions of Probability[/B]


Several alternative definitions of probability are commonly encountered:
Frequentist, Bayesian, Laplacian, Axiomatic
They have different strengths & weaknesses.
Fortunately, they coincide and work well with each other in most cases.


[B][U]Probability: Frequentist Definition[/U][/B]

The probability of an event E is the limit, as n→∞, of the fraction of times that VE in n repetitions of the same experiment.
Problems:
Only well-defined for experiments that are infinitely repeatable (at least in principle).
Can never be measured exactly in finite time!
Advantage: Objective, mathematical def’n.

[B][U]Probability: Bayesian Definition[/U][/B]

Suppose a rational entity R is offered a choice between two rewards:
Winning $1 if event E occurs.
Receiving p dollars (where p[0,1]) unconditionally.
If R is indifferent between these two rewards, then we say R’s probability for E is p.
Problem: Subjective definition, depends on the reasoner R, and his knowledge & rationality.


[B][U]Probability: Laplacian Definition[/U][/B]

First, assume that all outcomes in the sample space are equally likely
This term still needs to be defined.
Then, the probability of event E, Pr[E] = |E|/|S|. Very simple!
Problems: Still needs a definition for equally likely, and depends on existence of a finite sample space with all equally likely outcomes.

[B][U]Probability: Axiomatic Definition[/U][/B]

Let p be any function p:S→[0,1], such that:
0 ≤ p(s) ≤ 1 for all outcomes sS.
∑ p(s) = 1.
Such a p is called a probability distribution.
Then, the probability of any event ES is just:

Advantage: Totally mathematically well-defined.
Problem: Leaves operational def’n unspecified.

right mr.raz is...... opting for statistics may b a risky venture as we may b tempted to go 4 statistics on the basis that we ve studied it in bcom etc....although helpful but we study only certain applications in bcom ca etc as compared to css paper.....

Courage to undertake stats undertaken: evil
 

Hi there,
Im nu to forum and i have stats as optional course. I studied it durin my MBA. Plz tell me of ur approach to the subject i.e u wanta capitalize on numerical part of the paper or theoretical or both. Im sound at numerics but lag prominently behind in theory. Also plz tell which book u r using 4 stats. Im currently chewing on Lind,Markel & Mason, my MBA text book 4 stats.

am appearing for 2011 Statistics Exam.