DSE 2013 Paper Discussion

[kangkan]

Hi..wont Pr(β<=(1/1+r))=F(x=1/1+r)=[(1/1+r)-(1/2)/1/2]=(1-r)/(1+r) give us the fraction of poplation with B<1/1+r.....so wont 1-r/1+r be the fraction of population with B<1/1+r...? how do we translate this into into demand for x1 in period 1 for the individual?

[Granpa Simpson]

see its just like converting a probabilistic market demand in to form..and it can be converted..u can find it in any of Operation Research books..giving form to a probabilistic demand model..:)

[kangkan]

aarrgh...now i need to study operations reaserch :(

[Granpa Simpson]

this is the simplest case of such a conversion..many methods including simulations and markov chain transition matrices can be used but in this case u dont need them..!!!

[Granpa Simpson]

Beng more specific you can say that on an average the total market demand can be said to be equal to N*[(1-r)/(1+r)]..!!!

[neha:)]

How to do 12th and 13th one? ( series 01)

[neha:)]

Q. 12) A population is growing at the instantaneous growth rate of 1.5 per cent. The time taken (in years) for it to double is approximately
(a) log2/0.15
(b) log2/15
(c) log2/.015
(d) log2/1.5

Q.13) A linear regression model y =  a +bX + e is estimated using OLS. It turns out that the estimated B^ (B hat) equals zero. This implies that:
(a) R square is zero
(b) R square is one
(c) 0 < R square < 1
(d) In this case the R square is undefined

[Nupur]

1(1+1.5/100)^t=2
where t is the doubling time (which we have to find out!!)
(1.015)^t=2
Taking log on both sides, get:
t log(1.015)= log 2
=>t = (log2/log 1.015)~(log 2)/0.015 which is the answer (option c)!
(Note: It's natural log everywhere!)

[Granpa Simpson]

β=0, implies y=α,
in this case y=mean of y=α.
So clearly (Y-mean of Y)=TSS=0.
Now use R^2=ESS/TSS, so clearly since TSS=0, R^2 is undefined.
Note: Here ESS=[Y(hat)-Y(bar)]^2.

[Dreyfus]

@nupur..its instantaneous growth by the way....
I proceeded this way....

[neha:)]

Nupur, could you pls explain why you took log 1.015 = 0.015?

[Dreyfus]

@subhayu.....in the question the value of sample beta is given! There may be another sample from same population which could have different value for sample beta...den y r u taking R² as undefined ?
And R² can never be undefined as it takes value b/w 0 and 1...please help

[neha:)]

Thanku!

[Granpa Simpson]

When I was solving the problem even i was worried about the same that R^2 cannot be undefined..in any case ur right...will have to think about that......however in this link i found that R^2 can be undefined if values are constant..dont know about the validity of the fact..if you get to know anything about the solution plz let me know..dat would be of grt help Vaibhav..!!!

[Granpa Simpson]

http://www.talkstats.com/showthread.php/17050-Regression-line-slope-for-R-2-1

[kangkan]

Hi..if Beta=0,the Explained sum of squares will be zero. since ESS is B^2 sign(x^2).hennce ESS is zero

TSS need not nescessarliy be zero. hence R2 should be zero right?

[kangkan]

at shub..if we consider the series  Y=X^2,then we wud have ESS=0 ( since r=0,Beta will zero 0 and hence TSS will be zero)..but ESS obvviously not zero..so i guess it shud be just zero  :)

[Granpa Simpson]

I think kangkan's approach is the correct one...thanx kangkan..

[Granpa Simpson]

Yes ur absolutely correct since this a SRF so the ESS will be zero...thanx a lot..!!!

[Nupur]

Neha this is done using calculator. (ln 1.015= 0.0148). But its actually a problem because a simple calculator which is allowed in the exam doesn't have a log (ln) button! In that case we can eliminate options B and D because value of log 1.015 in denominator can't be greater than 1.015.( hope you know this is because log x < x for all x>o) But still we can't eliminate further b/w options a and c without access to a calculator with log button!

In any case Vaibhav's method is with us which doesn't need any calculator and is simple enough!
Vaibhav, could you please (for my concept clarity) tell me if my method is wrong?? Is it not for instantaneous growth?? Then why is the answer coming the same?