Question 1

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

Accepted Answer

The Paasche price index is a weighted average of prices, where the consumption quantities in the year of interest are used as weights.

Question 2

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

A recent base period ensures that the price index is reflective of current market conditions and not heavily skewed by outdated technology, outdated consumer habits or preferences, or other factors that may have changed over time. A more recent base period provides a better representation of the current economy and market trends.

Question 3

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 of each other, so the test is only valid if the yields in one block have no influence on the yields in any other block. This assumption is true in this scenario since the agronomist planted the three varieties of seeds on each of the five different patches of fields, which are likely to be geographically separated and have different soil compositions, weather conditions, and other factors that can affect the crop yield. Therefore, we can assume that the crop yields in one block are independent of the crop yields in any other block.

Question 4

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

Accepted Answer

The Paasche price index uses current consumption quantities as weights, which can be hard to obtain because they may change frequently and can be difficult to measure accurately.

Question 5

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 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
A) 
B) 
C) 
D)

Accepted Answer

According to Cook's distance statistic, an observation i is influential if its Cook's distance value Dᵢ is greater than the threshold value of Fᵥ₁ᵥ₂/ (n – k – 1 + Fᵥ₁ᵥ₂). Therefore, for a 0.50 level of significance (α = 0.50), the threshold value for Cook's distance is Fᵥ₁ᵥ₂/ (n – k – 1 + Fᵥ₁ᵥ₂) / 2, which means that an observation is influential if its Cook's distance exceeds this value.

None of the answer choices provide the values for v₁, v₂, or n, so we cannot calculate the threshold value of Cook's distance or isolate the specific condition under which an observation is considered influential.

Therefore, the best choice would be B, as it does not provide any condition that is definitive enough to determine whether an observation is influential.

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

Accepted Answer

The Laspeyres price index is indeed a form of weighted aggregate price index, where the weights are determined by the base period quantities.

Question 9

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

Accepted Answer

In an unweighted aggregate price index, each commodity is given equal importance regardless of its price. Therefore, more expensive commodities have a larger impact on the overall index even if they are a small portion of the overall consumption. This can result in an inaccurate reflection of actual price changes for the majority of consumers who consume cheaper goods.

Question 10

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 A)hᵢ < 2(k + 1)/n. B)hᵢ > 2(k + 1)/n. C)hᵢ < n(k + 1)/2. D)hᵢ > n(k + 1)/2.

Accepted Answer

The answer of Using the hat matrix elements hᵢ to...

Question 11

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 12

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 A)|tᵢ| < tn₋k₋₁. B)|tᵢ| > tn₋k₋₁. C)|tᵢ| < tn₋k₋₂. D)|tᵢ| > tn₋k₋₂.

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 13

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 Laspeyres price index is based on the consumption pattern of the initial period, which may differ from the current period, leading to inaccuracies in reflecting the current consumption cost.

Question 14

Which of the following is used to determine observations that have influential effect on the fitted model? A)Durbin Watson statistic B)Variance inflationary factor C)The C_p statistic D)Cook's distance statistic

Accepted Answer

Cook's distance statistic is used to identify observations that have a significant effect on the fitted model. It measures the change in the parameter estimates when a particular observation is omitted from the model. A large value of Cook's distance indicates that the corresponding observation has a strong influence on the model.

Question 15

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 16

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.

Question 17

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

It is important to consider all three measures before deciding to remove an observation from the regression analysis. When consistent results are obtained from all three measures, it is more likely that the observation is truly influential and should be removed.

Question 18

Which of the following is not used to determine observations that have influential effect on the fitted model? A)The hat matrix elements hᵢ B)The studentized deleted residuals tᵢ C)The C_p statistic D)Cook's distance statistic

Accepted Answer

The C_p statistic is not commonly used to determine influential observations in a fitted model. The other options (hat matrix elements, studentized deleted residuals, Cook's distance statistic) are commonly used in regression diagnostics to identify influential points.

Question 19

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 helps in eliminating the impact of sudden fluctuations in prices on the index, making it more reliable for comparison over time.

Question 20

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 account for differences in the magnitude of prices per unit, but they do not account for differences in the consumption levels of the items in the market basket.

Quiz 19: Questions that Involve Online Topics

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

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

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

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

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

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

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

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 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.

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 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.

Which of the following is 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.

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

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.

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

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

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.