Statistics and Econometrics Questions and Answers

Answer: B

A statistic is calculated from a sample.

In statistics, a parameter is a numerical characteristic of the whole population, such as the population mean, while a statistic is the corresponding measure computed from a sample, such as the sample mean. Statistics are used to estimate parameters and to test hypotheses about them.

Population and universe mean the same thing, and measures computed from them are parameters, not statistics. A hypothesis is a statement to be tested, not data from which a quantity is calculated.

Answer: B

Chain indices use \(\frac{\Sigma p_{n}}{\Sigma p_{n-1}} \times 100\).

In the chain base method, each year is compared with the year immediately before it, not with a fixed base year. The resulting link relatives, current-year prices over previous-year prices multiplied by 100, are then chained by successive multiplication to give a chain index, which keeps the comparison up to date.

The options with \(p_{0}\) in the denominator compare every year with a fixed base year 0, a fixed-base index (simple aggregative or price relative). The one with quantities \(q_{n}\) and \(q_{0}\) is a value index, not a chain index.

Answer: B

The most suitable average for qualitative measurements is the median.

Qualitative characteristics such as intelligence, honesty or beauty cannot be measured numerically, but people can be ranked by them. The median, the value of the middle item when items are arranged in order, needs only ranks, so it is the average used for such data.

The arithmetic and geometric means require actual numerical values. The correlation coefficient measures association between two variables and is not an average at all.

Answer: B

The Consumer Price Index is also known as the Cost of Living Index.

A Consumer Price Index measures changes in the retail prices of a fixed basket of goods and services bought by a particular class of consumers, such as industrial workers or agricultural labourers. Because it shows how much more those consumers must spend to keep the same standard of living, it is also called the cost of living index, and it is used to fix dearness allowances.

The Wholesale Price Index measures prices at the wholesale level and is a different index. 'Sensitive' and 'composite' are not names for the CPI.

Answer: C

The precision of OLS estimators is measured by their Standard errors.

An estimator's precision describes how tightly its sampling distribution clusters around the true parameter. The standard error is the estimated standard deviation of that sampling distribution: the smaller it is, the more precise the estimate, and it is what confidence intervals and t-tests are built on.

The mean of the sampling distribution concerns unbiasedness, not precision. The mode and the sign of an estimate say nothing about how much it would vary from sample to sample.

Answer: A

The statement that is not a classical assumption is Values taken by dependent variable Y is fixed in repeated sampling.

The classical linear regression model assumes that the explanatory variable X is fixed (non-stochastic) in repeated sampling. The dependent variable Y cannot be fixed: it contains the random error term, so its values vary from sample to sample.

The other three are standard assumptions: the model is linear in the parameters, the error term has zero mean, and the error term has constant variance (homoscedasticity), along with no autocorrelation and no exact multicollinearity.

Answer: A

The t value will be 0.

The t statistic for testing the hypothesis that the true coefficient equals a given value is

\[ t = \frac{\hat{\beta}_{2} - \beta_{2}}{se(\hat{\beta}_{2})} \]

If the estimate equals the hypothesised value, the numerator is zero, so t = 0 whatever the standard error. The estimate then gives no evidence at all against the null hypothesis.

A value of 1 would need the estimate to differ from the hypothesis by exactly one standard error, and the standard error itself is the denominator, not the value of t. The option of 30 has no basis in the formula.

Answer: C

The plausible approaches are (i), (ii) and (iii) only.

Taking logarithms of the variables often reduces heteroscedasticity, because it compresses the scale on which the error variance grows (i). Heteroscedasticity-consistent (White) standard errors keep the OLS estimates but correct the inference (ii). Generalised least squares, or weighted least squares when the form of the variance is known, transforms the model so that the errors become homoscedastic (iii).

Adding logged values of the variables as extra regressors (iv) changes the specification of the conditional mean but does nothing to the error variance, so it is not a remedy for heteroscedasticity. That rules out every option containing (iv).

Answer: C

A non-stationary time series has Both (A) and (B): a time-varying mean and a time-varying variance.

A (weakly) stationary series has a constant mean, a constant variance and an autocovariance that depends only on the lag between periods, not on time itself. A series is non-stationary when these properties fail. A random walk, for example, has a variance that grows with time, and a series with a trend has a mean that changes over time.

Options naming only the mean or only the variance are incomplete descriptions as the paper frames them, and a time-invariant mean and variance is the definition of a stationary series, not a non-stationary one.

Answer: B

When r = ±1 the two regression lines Coincide.

The angle between the regression line of Y on X and that of X on Y depends on the correlation coefficient. With perfect correlation, all points lie exactly on a straight line, so predicting Y from X and X from Y gives the same line: the two regression lines coincide.

When r = 0 the lines are perpendicular (one parallel to each axis), which is the trap in the first option. The lines always meet at the point of the means, so they are never parallel, and they are not indeterminate.