ISS (Statistical Services) Statistics Paper III: Questions 38  42 of 96
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Question number: 38
» Econometrics » Ordinary Least Squares (OLS)
Appeared in Year: 2011
Describe in Detail
If is an individual’s utility function of two goods, show that the demand for the goods is and
Where and are the fixed price and µ be the individual fixed income.
Explanation
For consumer’s equilibrium, we have
and hence, we get
→
→
→
→
→
→
→ ………………. (i)
since, µ the individual income is fixed, we have
→
→
Substituting the value of in (i),
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
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
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.