ISS (Statistical Services) Statistics Paper III: Questions 39 - 44 of 96

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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

with

and with

, ,

and

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

increases, 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 not significantly different from zero

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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 with p = 1 and m = 2k + 1, obtain the coefficient of 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 fixed subset of the number series i. e. the first averag

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Question number: 41

» Applied Statistics » Index Numbers » Price Relatives and Quantity or Volume Relatives

Appeared in Year: 2010

Short Answer Question▾

Write in Short

Discuss briefly the steps involved in the construction of cost of living index number.

Question number: 42

» Applied Statistics » Time Series Analysis » Economic Time Series & Components

Appeared in Year: 2010

Short Answer Question▾

Write in Short

Discuss the ratio to trend method for separating the seasonal component in a time series.

Question number: 43

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Explain aligned sample and unaligned systematic sampling method

Explanation

Systematic sampling in two dimensions:

The linear systematic sampling can be extended for two dimensions populations. here it is assumed that the n m k l population units are arranged in the form of ml rows, each containing nk units and a systematic sampling of m n units is selected. There are two procedures adopted to draw a sample of size mn.

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Question number: 44

» Sampling Techniques » Simple Random Sampling and Systematic Sampling

Appeared in Year: 2010

Essay Question▾

Describe in Detail

Explain the concepts of linear and circular systematic sampling giving suitable illustrations.

Further, show that for linear systematic sampling, sample mean is an unbiased estimator for population mean.

Explanation

Let us suppose that N sampling units are serially numbered from 1 to N in some order and a sample of size n is to be drawn in such a way that N is expressible as a product of two integers n and k.

N = nk → k = Where k, usually called the sampling interval. k is taken as the integer nearest to

Linear systematic sampling:

To draw a sample of

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