ISS (Statistical Services) Statistics Paper III: Questions 39  44 of 96
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Question number: 39
» Econometrics » AutoCorrelation
Appeared in Year: 2011
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:

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

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
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
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
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
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
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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