ISS Statistics Paper III: Questions 37 - 40 of 90

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Question number: 37

» Sampling Techniques » Stratified Random Sampling

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let for a stratified random sampling ni=WiSiµ0ci where µ0 is constant, ci is the-cost per unit-in ith stratum, Wi=NiN ,Si2 is the mean square based on Ni units.

Estimate the sample sizen under optimum allocation for fixed cost c0 .

Explanation

Under optimum allocation, nis are obtained such that

(i) minimize the variance of the estimate for (a) fixed sample size n;

(i) var ( y̅st)is minimum for fixed n

(ii) var ( y̅st)is minimum for fixed total… (484 more words) …

Question number: 38

» Econometrics » Ordinary Least Squares (OLS)

Appeared in Year: 2011

Essay Question▾

Describe in Detail

If U=cxαyβ is an individual’s utility function of two goods, show that the demand for the goods is x=αα+βμpx and y=βα+βμpy

Where px and px are the fixed price and µ be the individual fixed income.

Explanation

For consumer’s equilibrium, we have

1px.ux=1py.uy

U=cxαyβ and hence, we get

1px.cαxα1yβ=1py… (182 more words) …

Question number: 39

» Econometrics » Auto-Correlation

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Discuss the effect of imperfect multicollinearity on tests and errors. Consider a model

y=β0+β1X1+β2X2+(ee̅) with

X1=X2=0 and X2=θX1+V with

x12=x22=1 , X1X2=θ , V=0

and X1V=0

Do you think multicollinearity is present in the model? If yes, give reasons. Further show that as

θ increases, V(β^i) also increases.

Explanation

Effect of imperfect multicollinearity on tests and errors:

  1. OLS estimators will be BLUE, but they have large variances and covariances. this makes the estimation difficult.

  2. The confidence intervals will be wider. and hence, we may not reject the ’zero null hypothesis i. e. , We may conclude that B’s are… (522 more words) …

Question number: 40

» Applied Statistics » Time Series Analysis » Exponential and Moving Average Smoothing

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Explain moving average [m, p]. Let Ut=a0+a1t with p = 1 and m = 2k + 1, obtain the coefficient cj of Ut and [m, p]

Explanation

Moving average: moving average method is a simple and flexible method for measuring trend. It consists in measurement of trend by smoothing out the fluctuations of the data by means of a moving average.

The first element of the moving average is obtained by taking the average of the initial… (437 more words) …

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