Question 1

For a price index, it is preferable to select the base period in a period of economic stability.

Accepted Answer

Selecting a base period in a period of economic stability ensures that the prices used as the basis for the index are not subject to extreme fluctuations or distortions. This provides a more accurate representation of price movements over time.

Question 2

The more expensive commodities are overly influential in an unweighted aggregate price index.

Accepted Answer

In an unweighted aggregate price index, each individual commodity is given equal importance regardless of its price. This means that more expensive commodities will have a greater impact on the overall index, which can lead to an inaccurate representation of price movements for everyday goods and services.

Question 3

Only when all three of the hat matrix elements hᵢ, the Studentized deleted residuals tᵢ and the Cook's distance statistic Dᵢ reveal consistent result should an observation be removed from the regression analysis.

Accepted Answer

When all three elements, hᵢ, tᵢ, and Dᵢ, consistently indicate that an observation should be removed, it is safer to do so in order to avoid biased results.

Question 4

The Laspeyres price index has the disadvantage that the consumption pattern in the initial period might be quite different from that in the current period and, hence, does not reflect accurately the current consumption cost.

Accepted Answer

The statement is true. The Laspeyres price index uses the consumption pattern from an initial period as a base, and if the consumption pattern changes over time, it may not accurately reflect the current cost of consumption.

Question 5

Using the Studentized residuals tᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting tn₋k₋₂ denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xᵢ is an influential point if

Accepted Answer

According to the definition of influential point, an observation is considered influential if it significantly affects the estimates or predictions of the regression model. In multiple regression, one way to identify influential points is to use the Studentized residuals, which are the residuals divided by their estimated standard errors.

The Studentized residuals follow a t-distribution with n-k-1 degrees of freedom, where n is the sample size and k is the number of independent variables in the regression model. Therefore, we can compare the absolute value of each Studentized residual to a critical value from the t-distribution to determine if the point is influential.

The upper critical value of a two-tail t test with a 0.10 level of significance and n-k-1 degrees of freedom is denoted tn₋k₋₂. So, an observation Xᵢ is considered influential if |tᵢ| > tn₋k₋₂, which is choice D. Therefore, the correct answer is D.

Question 6

Using the Cook's distance statistic Dᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting Fᵥ₁ᵥ₂ denote the critical value of an F distribution with v₁ and v₂ degrees of freedom at a 0.50 level of significance, Xᵢ is an influential point if

Accepted Answer

Cook's distance measures the influence of each observation on the regression coefficients, and points with high Cook's distance are considered to be influential. The critical value for Cook's distance depends on the number of independent variables and the sample size, and can be approximated by an F distribution. Specifically, an observation is considered influential if its Cook's distance is greater than the critical value of an F distribution with k+1 and n-k-1 degrees of freedom at a 0.5 level of significance. Therefore, the correct choice is B, since Dᵢ > Fk₊₁,n₋k₋₁ indicates that observation i is influential. Choices A, C, and D are incorrect, either because they use the wrong F distribution or because they have the wrong sign.

Question 7

The changes in the price of the least consumed commodities are overly influential in a weighted aggregate price index.

Accepted Answer

The answer of The changes in the price of the...

Question 8

The Paasche price index uses the consumption quantities in the year of interest as the weights.

Accepted Answer

The Paasche price index uses the consumption quantities in the year of interest as the weights.

Question 9

Using the hat matrix elements hᵢ to determine influential points in a multiple regression model with k independent variable and n observations, Xᵢ is an influential point if

Accepted Answer

An observation is considered influential if its hat value hᵢ is greater than 2(k + 1)/n, where k is the number of independent variables and n is the number of observations.

Question 10

The Laspeyres price index is a form of weighted aggregate price index.

Accepted Answer

The Laspeyres price index is a type of weighted aggregate price index that keeps the base period weights constant. It is commonly used to determine inflation rates by calculating the percentage change in the average price of a fixed basket of goods and services between two periods.

Question 11

Unweighted aggregate price indices account for differences in the magnitude of prices per unit and differences in the consumption levels of the items in the market basket.

Accepted Answer

Unweighted aggregate price indices do not account for differences in the consumption levels of the items in the market basket. They simply reflect the average price changes of all the items in the basket without taking into account how much of each item is consumed. Weighted aggregate price indices are used to account for differences in consumption levels by assigning weights to each item in the basket based on its importance in the overall consumption pattern.

Question 12

The Paasche price index reflects more accurately the consumption cost at a point in time because it uses the consumption quantities in the initial year as the base.

Accepted Answer

The answer of The Paasche price index reflects more accurately...

Question 13

The Paasche price index is a form of unweighted aggregate price index.

Accepted Answer

The answer of The Paasche price index is a form...

Question 14

The Paasche price index has the disadvantage that current consumption quantities are usually hard to obtain.

Accepted Answer

The Paasche price index requires current consumption quantities which may be difficult to obtain. This is because it is based on the current prices of a specific basket of goods and services that may not be accurately reflected in official consumption data.

Question 15

The base period should be recent so that a price index is not severely affected by change in technology, and consumer attitudes and habits.

Accepted Answer

Using a recent base period ensures that a price index accurately reflects current market conditions and consumer behavior, without being heavily influenced by outdated technologies or outdated consumer habits. This helps to ensure the accuracy and relevance of the index.

Question 16

Which of the following is not used to determine observations that have influential effect on the fitted model?

Accepted Answer

Cp statistic is used for comparing different models and selecting the best one, it is not used to determine observations that have influential effect on the fitted model. The hat matrix elements hᵢ, studentized deleted residuals tᵢ and Cook's distance statistic are used to identify influential observations in the model.

Question 17

A simple price index tracks the price of a group of commodities at a given period of time to the price paid for that group of commodities at a particular point of time in the past.

Accepted Answer

The answer of A simple price index tracks the price...

Question 18

Which of the following is used to determine observations that have influential effect on the fitted model?

Accepted Answer

Cook's distance statistic is specifically used to determine influential observations in a fitted model. Durbin Watson statistic tests for autocorrelation, variance inflationary factor tests for multicollinearity, and the Cp statistic is used for model selection.

Question 19

TABLE 12-2
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows. 
-Referring to Table 12-2, the Friedman rank test is valid only if the 5 blocks are independent so that the yields in one block have no influence on the yields in any other block.

Accepted Answer

The Friedman rank test assumes that the blocks are independent so that the yields in one block have no effect on the yields in any other block. Therefore, the given statement is true.

Question 20

The Laspeyres price index uses the initial consumption quantities as the weights.

Accepted Answer

The Laspeyres price index uses the initial consumption quantities as the weights.

Quiz 19: Questions that Involve Online Topics

For a price index, it is preferable to select the base period in a period of economic stability.

The more expensive commodities are overly influential in an unweighted aggregate price index.

Only when all three of the hat matrix elements hᵢ, the Studentized deleted residuals tᵢ and the Cook's distance statistic Dᵢ reveal consistent result should an observation be removed from the regression analysis.

The Laspeyres price index has the disadvantage that the consumption pattern in the initial period might be quite different from that in the current period and, hence, does not reflect accurately the current consumption cost.

Using the Studentized residuals tᵢ to determine influential points in a multiple regression model with k independent variable and n observations and letting tn₋k₋₂ denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xᵢ is an influential point if

The changes in the price of the least consumed commodities are overly influential in a weighted aggregate price index.

The Paasche price index uses the consumption quantities in the year of interest as the weights.

Using the hat matrix elements hᵢ to determine influential points in a multiple regression model with k independent variable and n observations, Xᵢ is an influential point if

The Laspeyres price index is a form of weighted aggregate price index.

Unweighted aggregate price indices account for differences in the magnitude of prices per unit and differences in the consumption levels of the items in the market basket.

The Paasche price index reflects more accurately the consumption cost at a point in time because it uses the consumption quantities in the initial year as the base.

The Paasche price index is a form of unweighted aggregate price index.

The Paasche price index has the disadvantage that current consumption quantities are usually hard to obtain.

The base period should be recent so that a price index is not severely affected by change in technology, and consumer attitudes and habits.

Which of the following is not used to determine observations that have influential effect on the fitted model?

A simple price index tracks the price of a group of commodities at a given period of time to the price paid for that group of commodities at a particular point of time in the past.

Which of the following is used to determine observations that have influential effect on the fitted model?

The Laspeyres price index uses the initial consumption quantities as the weights.