Managerial Economics 7th Edition By Keat - Test Bank

Managerial Economics 7th Edition By Keat – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

Managerial Economics, 7e (Keat)

Chapter 5  Demand Estimation and Forecasting (Appendices 5A and 5B)

 

Multiple-Choice Questions

 

1) Regression analysis can best be described as

1. A) a statistical technique for estimating the best relationship between one variable and a set of other selected variables.
2. B) a statistical technique for determining the true values of variables.
3. C) a statistical technique for creating functional relationships among variables.
4. D) None of the above

Answer:  A

Diff: 2

 

2) If a regression coefficient passes the t-test, it means that

1. A) the regression equation is valid.
2. B) the regression coefficient is significantly different from zero.
3. C) the regression coefficient can be used for forecasting.
4. D) the regression coefficient should be included in the regression equation.

Answer:  B

Diff: 2

 

3) The coefficient of a linear regression equation indicates

1. A) the change in the dependent variable relative to a unit change in the independent variable.
2. B) the change in the independent variable relative to a unit change in the dependent variable.
3. C) the percentage change in the dependent variable relative to a unit change in the independent variable.
4. D) the percentage change in the independent variable relative to a unit change in the dependent variable.

Answer:  A

Diff: 2

 

4) Which of the following is a test of the statistical significance of the entire regression equation?

1. A) t-test
2. B) R2
3. C) F-test
4. D) Durbin-Watson test

Answer:  C

Diff: 1

 

 

5) Which of the following is a test of the statistical significance of a particular regression coefficient?

1. A) t-test
2. B) R2
3. C) F-test
4. D) Durbin-Watson test

Answer:  A

Diff: 2

6) Which of the following is a measure of the explanatory power of the regression model?

1. A) t-test
2. B) R2
3. C) F-test
4. D) Durbin-Watson test

Answer:  B

Diff: 1

 

7) R2 is a statistical measure which

1. A) determines how important one variable is in explaining the value of another variable.
2. B) tests the true value of a variable.
3. C) determines how well an equation can estimate the relationship between one variable and a set of other variables.
4. D) All of the above

Answer:  C

Diff: 1

 

8) When the R2 of a regression equation is very high, it indicates that

1. A) all the coefficients are statistically significant.
2. B) the intercept term has no economic meaning.
3. C) a high proportion of the variation in the dependent variable can be accounted for by the variation in the independent variables.
4. D) there is a good chance of serial correlation and so the equation must be discarded.

Answer:  C

Diff: 1

 

9) Which of the following indicators will always improve when more variables are added to a regression equation?

1. A) the magnitudes of the coefficients
2. B) the t-test
3. C) R2
4. D) the standard errors of the coefficients

Answer:  C

Diff: 1

 

 

10) Which indicator shows how well a regression line fits through the scatter of data points?

1. A) F-test
2. B) R2
3. C) t-test
4. D) Durbin-Watson test

Answer:  B

Diff: 1

11) When a regression coefficient is significant at the .05 level, it means that

1. A) there is only a five percent chance that there will be an error in a forecast.
2. B) there is 95 percent chance that the regression coefficient is the true population coefficient.
3. C) there is a five percent chance or less that the estimated coefficient is zero.
4. D) there is a five percent chance or less that the regression coefficient is not the true population coefficient.

Answer:  C

Diff: 2

 

12) The t-test is a statistical measure which

1. A) tests the true value of a variable.
2. B) tests the statistical significance of a regression coefficient.
3. C) tests the statistical significance of a regression equation.
4. D) None of the above

Answer:  B

Diff: 2

 

13) The t-statistic is computed by

1. A) dividing the regression coefficient by the standard error of the estimate.
2. B) dividing the regression coefficient by the standard error of the coefficient.
3. C) dividing the standard error of the coefficient by the regression coefficient.
4. D) dividing the R2by the F-statistic.

Answer:  B

Diff: 2

 

14) A one-tail test of significance would be used to determine whether

1. A) demand for a good is price elastic.
2. B) two goods are substitutes for each other in supply.
3. C) two goods are unrelated to each other in demand.
4. D) supply of a good is price inelastic.

Answer:  B

Diff: 2

 

 

15) The F-test is used to determine if

1. A) a regression coefficient is significant.
2. B) multicollinearity exists.
3. C) a regression equation significantly accounts for the variation in the value of a dependent variable.
4. D) an identification problem is present.

Answer:  C

Diff: 2

Answer the following question(s) based on the following regression equation (Standard errors in parentheses, n = 150):

 

QD = 1000 – 50PA + 10PB + .05I, (20) (7) (.04)

 

where QD = quantity demanded of good A, PA = price of good A, PB = price of a competing good B, and I = per capita income.

 

16) Using the “rule of 2,” which of the following variables can be deemed statistically significant?

1. A) PA
2. B) PB
3. C) I
4. D) All of the above
5. E) None of the above

Answer:  A

Diff: 3

 

17) For which of the following variables should a “two tail” t-test be applied?

1. A) PA
2. B) I
3. C) PB
4. D) Should be applied for all.

Answer:  B

Diff: 3

 

18) For the regression equation Q = 100 – 10X + 0.25X2, which of the following statements is true?

1. A) X2is the more important variable because it is positive.
2. B) When X decreases by one unit, Q decreases by 10 units.
3. C) When X increases by 10 units, Q decreases by 1 unit.
4. D) The change in Q associated with a one unit increase in X depends on the initial level of X.

Answer:  D

Diff: 3

 

 

19) When using regression analysis for forecasting, the confidence interval indicates

2. A) the degree of confidence that one has in the equation’s R2.
3. B) the range in which the value of the dependent variable is expected to lie with a given degree of probability.
4. C) the degree of confidence that one has in the regression coefficients.
5. D) the range in which the actual outcome of a forecast is going to lie.

Answer:  B

Diff: 2

 

20) The use of a dummy variable in regression analysis indicates

1. A) that a researcher does not really know what to include in the equation.
2. B) that a categorical variable is expected to have an impact on a dependent variable.
3. C) that insufficient data is available for the analysis.
4. D) the use of hypothetical data.

Answer:  B

Diff: 2

21) In using regression analysis to estimate demand, which of the following problems is most directly a result of insufficient data?

1. A) the identification problem
2. B) the problem of a low R2
3. C) the problem of high standard errors
4. D) the problem of insignificant F-statistics

Answer:  A

Diff: 3

 

22) Which of the following is most likely to indicate a statistically significant regression coefficient?

1. A) |t| > R2
2. B) R2> .90
3. C) |t| > 2
4. D) |t| > 4

Answer:  C

Diff: 3

 

23) The F-test is used in forecasting to

1. A) establish confidence intervals for testing regression coefficients.
2. B) examine the degree of multicollinearity among independent variables.
3. C) determine how well a regression equation can account for dependent variable values.
4. D) determine whether an identification problem exists.

Answer:  C

Diff: 2

 

 

Answer the following questions on the basis of the following regression equation. (Standard errors in parentheses, n = 200.)

 

Q = -6,500 – 100PA + 50PB + .3I + .2A; R2 =.12, (2,500) (50) (30) (.1) (.08)

 

where Q is the quantity demanded of good A; PA = $10, price of good A; PB = $8, price of good B; I = $12,000, per capita income; and A = $20,000, monthly advertising expenditures.

 

24) Which of the variables does not pass the t-test at the .05 level of significance?

1. A) PA
2. B) PB
3. C) A
4. D) I
5. E) All the variables pass the t-test.

Answer:  B

Diff: 3

 

25) As a researcher, which aspect of the results would be of greatest concern?

1. A) the negative value of the constant (i.e., -6,500)
2. B) the relatively low impact of the competitor’s price
3. C) the fact that not all of the variables are statistically significant
4. D) the poor fit of the regression line

Answer:  D

Diff: 3

26) As the manager of good A, which of the following would be of greatest concern (based on the regression results above)?

1. A) None of the factors below would be of concern.
2. B) an impending recession
3. C) pressure on you by your salespersons to lower the price so that they can boost their sales
4. D) a price reduction by the makers of good B

Answer:  C

Diff: 3

 

27) Which of the following cannot be determined on the basis of the above regression results?

1. A) the degree of price elasticity of good B
2. B) whether or not good A is “normal”
3. C) the degree of competition between A and B
4. D) All of the above can be determined.

Answer:  A

Diff: 3

 

 

28) In the estimation of demand, the “identification problem” refers to

1. A) the problem of selecting the proper level of significance.
2. B) the problem of deciding whether to use time series or cross-sectional data.
3. C) the problem of separating out the effects of price on the quantity demanded when supply cannot be held constant.
4. D) the problem of having insufficient variation in prices.

Answer:  C

Diff: 3

 

29) Which of the following refers to a relatively high correlation among the independent variables of a regression equation?

1. A) autocorrelation
2. B) the identification problem
3. C) statistically insignificant regression coefficients
4. D) multicollinearity

Answer:  D

Diff: 2

 

30) The problem of autocorrelation refers to

1. A) independent variables in a regression equation whose values are closely related to each other.
2. B) insufficient data to estimate regression coefficient values.
3. C) regression coefficient values which are not significantly different from zero.
4. D) regression equation variables which exhibit a similar pattern in their values over a number of time periods.

Answer:  D

Diff: 2

31) A dummy variable is also called

1. A) an approximate variable.
2. B) a discrete variable.
3. C) a zero-sum variable.
4. D) an improper variable.

Answer:  B

Diff: 1

 

32) A manager will have the least confidence in an explanatory variable that

1. A) does not pass the F-test.
2. B) is expressed as a dummy variable.
3. C) does not pass the t-test.
4. D) constitutes only a small part of R2.

Answer:  C

Diff: 2

 

 

33) From a management policy perspective, which regression result is the most useful?

1. A) a regression equation that passes the F-test
2. B) a regression equation whose explanatory variables all pass the t-test
3. C) a regression equation that has the highest R2
4. D) a regression equation that has the least number of dummy variables

Answer:  B

Diff: 3

 

34) The fact that a person with a forceful and persuasive personality but not necessarily the greatest amount of knowledge and judgment can exercise a disproportionate amount of influence is a major drawback of

1. A) the Delphi method of forecasting.
2. B) the market research method.
3. C) opinion polling.
4. D) the jury of executive opinion approach.

Answer:  D

Diff: 2

 

35) The forecasting technique, which predicts technological trends and is carried out by a sequential series of written questions and answers is

1. A) the Delphi method.
2. B) the market research method.
3. C) opinion polling.
4. D) the jury of executive opinion approach.

Answer:  A

Diff: 2

 

36) Average weekly claims for unemployment insurance, money supply and the index of stock prices are all examples of

1. A) leading indicators.
2. B) coincident indicators.
3. C) lagging indicators.
4. D) None of the above

Answer:  A

Diff: 1

37) One of the series included among the lagging indicators is

1. A) the change in sensitive material prices.
2. B) the index of industrial production.
3. C) employees on non-agricultural payrolls.
4. D) average duration of unemployment.

Answer:  D

Diff: 3

 

 

38) Which of the following is not one of the leading indicators?

1. A) index of consumer expectations, U. of Michigan
2. B) change in consumer price index for services
3. C) vendor performance, slower deliveries diffusion index
4. D) manufacturers’ new orders, nondefense capital goods

Answer:  B

Diff: 2

 

39) Which of the following is a leading economic indicator?

1. A) average hours, manufacturing
2. B) money supply M2
3. C) stock prices, 500 common stocks
4. D) All of the above

Answer:  D

Diff: 2

 

40) The method of forecasting with leading indicators can be criticized for

1. A) occasionally forecasting a recession when none ensues.
2. B) forecasting the direction of the economy but not the size of the change in economic activity.
3. C) frequent revisions of data after original publication.
4. D) All of the above

Answer:  D

Diff: 2

 

41) A general rule of thumb is that if, after a period of increases, the leading indicator index sustains ________ consecutive declines, a recession (or at least a slowing of the economy) will follow.

1. A) three
2. B) four
3. C) five
4. D) six

Answer:  A

Diff: 1

 

42) The forecasting technique which involves the use of the least squares statistical method to examine trends, and takes into account seasonal and cyclical fluctuations, is known as

1. A) compound growth rate projection.
2. B) the Delphi method.
3. C) time series projection.
4. D) exponential smoothing projection.

Answer:  C

Diff: 1

 

43) Quantitative forecasting that projects past data without explaining the reasons for future trends is called

1. A) scientific forecasting.
2. B) dumb forecasting.
3. C) empirical forecasting.
4. D) naïve forecasting.

Answer:  D

Diff: 1

 

44) Which of the following is not a drawback of forecasting using the compound growth rate method?

1. A) only considers first and last observations
2. B) considers only equal absolute changes
3. C) disregards fluctuations between the original and terminal observations
4. D) does not consider any trends in the data

Answer:  B

Diff: 2

 

45) Charting observations on a semi-logarithmic graph will help the analyst to ascertain whether

1. A) absolute changes from period to period are constant.
2. B) whether percentage changes from period to period are constant.
3. C) whether percentage changes from period to period are declining.
4. D) Both B and C

Answer:  D

Diff: 3

 

46) A major problem in projecting with a trend line is that

1. A) only straight-line projections can be accommodated.
2. B) it is valid only if the trend is upward.
3. C) it will not forecast turning points in activity.
4. D) it is a very complex method of forecasting.

Answer:  C

Diff: 3

 

47) Which of the following is the exponential trend equation to forecast sales (S)?

1. A) S = a + b(t)
2. B) S = a + bt
3. C) S = a + b(t) + c(t)2
4. D) None of the above

Answer:  B

Diff: 3

 

 

48) Among the advantages of the ________ technique of forecasting are ease of calculation, relatively little requirement for analytical skills, and the ability to provide the analyst with information regarding the statistical significance of results and the size of statistical errors.

1. A) least-squares trend analysis
2. B) compound growth rate
3. C) visual trend-fitting
4. D) expert opinion

Answer:  A

Diff: 3

49) Among the advantages of the least-squares trend analysis techniques is

1. A) the ease of calculation.
2. B) relatively little analytical skill required.
3. C) its ability to provide information regarding the statistical significance of the results.
4. D) All of the above

Answer:  D

Diff: 2

 

50) The forecasting method that involves using an average of past observations to predict the future (if the forecaster feels that the future is a reflection of some average of past results) is the

1. A) moving average method.
2. B) econometric forecasting method.
3. C) exponential smoothing method.
4. D) Both A and B
5. E) Both A and C

Answer:  E

Diff: 2

 

51) An explanatory forecasting technique in which the analyst must select independent variables that help determine the dependent variable is called

1. A) exponential smoothing.
2. B) regression analysis.
3. C) trend analysis.
4. D) moving average method.

Answer:  B

Diff: 1

 

52) When the more recent observations are more relevant to the estimate of the next period than previous observations, the naïve forecasting method to employ is

1. A) exponential smoothing.
2. B) compound growth rate.
3. C) trend analysis.
4. D) moving averages.

Answer:  A

Diff: 3

 

 

53) Which of the following is a Leading Economic Indicator?

1. A) commercial and industrial loans outstanding
2. B) industrial production
3. C) average weekly duration of unemployment
4. D) None of the above

Answer:  D

Diff: 1

 

54) Which of the following is a Lagging Economic Indicator?

1. A) change in average labor costs in manufacturing
2. B) M2measure of the money supply
3. C) industrial production
4. D) None of the above

Answer:  A

Diff: 1

55) The Delphi method is a

1. A) smoothing technique in forecasting.
2. B) consensual forecast based on expert opinions.
3. C) compound growth approach to forecasting.
4. D) naïve forecasting approach.

Answer:  B

Diff: 1

 

56) The Trend Projection approach to forecasting is represented by

1. A) time-series regressions.
2. B) exponential smoothing.
3. C) opinion polls.
4. D) All of the above

Answer:  D

Diff: 2

 

 

Analytical Questions

 

The following questions refer to this regression equation, (standard errors in parentheses.)

 

Q = 8,400 – 10 P + 5 A + 4 Px + 0.05 I, (1,732) (2.29) (1.36) (1.75) 0.15)

 

R2 = 0.65

N = 120

F = 35.25

Standard error of estimate = 34.3

Q = Quantity demanded

P = Price = 1,000

A = Advertising expenditures, in thousands = 40

PX = price of competitor’s good = 800

I = average monthly income = 4,000

 

1) Calculate the elasticity for each variable and briefly comment on what information this gives you in each case.

Answer:  Based on the above figures, Q = 2,000

(Own) Price elasticity = -10(1,000/2,000) = -5. Demand is elastic at this price.

Advertising elasticity = 5(40/2,000) = 0.1. A 1% increase in advertising expenditure will lead to a 0.1% increase in sales.

Cross-price elasticity = 4(800/2,000) = 1.6. Because the cross-price elasticity is positive, the goods are considered substitutes. A 1% increase in the competitor’s price is expected to produce a 1.6% increase in the firm’s sales.

Income elasticity = 0.05(4,000/2,000) = 0.1. The good is most likely a normal good because the income elasticity is greater than zero and also a necessity because the income elasticity is less than one. This good is not likely to be particularly responsive to income changes.

2) Calculate t-statistics for each variable and explain what this tells you.

Answer:  Price: -10/2.29 = -4.37

Advertising: 5/1.36 = 3.86

Competitor’s price: 4/1.75 = 2.29

Income: 0.05/1.5 = 0.33

All variables are statistically significant with the exception of income. Thus we can conclude that the other variables do have an impact on the quantity demanded of this good.

 

3) How is the R2 value calculated, and what information does this give you?

Answer:  R2 = RSS/TSS = 1 – (ESS/TSS), where TSS = sum of squared deviations of the sample values of Y from their mean, RSS = sum of squared deviations of the estimated values from their mean, and ESS = sum of the squared deviations of the sample values from their estimated values. The R2 value tells you what percentage of the variation in the dependent variable is explained by variation in the independent variables, or the “goodness of fit” of the equation. In this case, 65% of the variation in quantity demanded is explained by variation in the independent variables.

 

 

4) How would you evaluate the quality of this equation overall? Do you have any concerns? Explain.

Answer:  The overall equation is significant, as shown by the F-test. The R2 value is reasonably high. One variable is not significant (might be desirable to re-estimate the equation without it, although the inclusion of irrelevant variables does not affect the properties of the OLS model). The sample size is sufficiently large. There are no significant concerns. {Other answers are possible.}

 

5) When would you use a one-tailed rather than a two-tailed t-test when checking significance levels?

Answer:  You would use a one-tailed test when the sign of the variable is important. That is, if you only want to know if the independent variable has a statistically significant effect on the dependent variable, a two-tailed test should be used. If direction of effect is important, then a one-tailed test should be used.

 

6) Should this firm be concerned if macroeconomic forecasters predict a recession? Explain.

Answer:  Based on income elasticity from this equation (0.1), no. The good is income inelastic, so a recession should not cause a significant decrease in sales. Note also that income is not statistically significant in this equation, making it even less of a concern.

 

7) The firm is considering changing its price to $900. Predict the quantity demanded at that price, all other things equal and provide a 95% confidence interval on your estimate. (In doing this, explain the value of t-critical you will use in developing your 95% confidence interval.)

Answer:  At a price of $900, the point estimate of quantity demanded is 3,000. With a sample size of 120, the degree of freedom is 115. Critical t values for 100 and 125 are 1.984 and 1.979 respectively, therefore a best guess of t-critical for this model is tcritical = 1.981. Given this, the 95% CI is given by BG ± tcritical × SEE or 2,932 to 3,068.

8) What is multicollinearity? In general, how would you know if you had a problem with multicollinearity, and how could you correct it?

Answer:  Multicollinearity occurs when the independent variables are correlated. One indication of multicollinearity is that the equation will pass the F-test, but individual variables will not have significant t values. Multicollinearity can sometimes be corrected by omitting some of the correlated variables or by choosing proxy variable.

 

9) How could a manager use the information contained in this regression equation?

Answer:  Many answers are possible. A manager might note that demand is elastic, and thus that sales might respond to a price decrease. Likewise, sales should respond to increases in advertising. Sales are less likely to be impacted by income changes. The equation could be used to forecast expected sales based on changes in one or more of the variables. The equation could be used to help in coordinating production plans or with other parts of the firm.

 

 

10) Why is the identification problem more likely with time-series estimates of demand?

Answer:  Identification problems occur when it is possible that both demand and supply are shifting. Thus a series of observations is not identifying points along a single demand curve; it is identifying a series of equilibrium points that may or may not be along a single curve. This is most likely to be a problem in time series estimation of demand curves, simply because over any reasonably long time period it is quite likely that both supply and demand will change somewhat.

 

11) Use the equation

 

Qd = 5,000 – 15P + 50A + 3Px – 4I, (2,117) (2.7) (15) (2) (3)

 

where Qd = Quantity Demanded, P = Good Price, A = Advertising Expenditures, Px = Price of a Competitive Good, A = Advertising Expenditures, I = Average Monthly Income, and the Standard Errors of the Regression Coefficients are shown in Parentheses.

 

Calculate the t-statistics for each variable and explain what inferences can be drawn from them. If R2 of this equation is 0.25, what inference can be drawn from it?

Answer:

P = 15/2.7 = 5.55, and Good Price is a very significant determinant of demand for the good.

A = 50/15 = 3.33, and Advertising Expenditures also are a significant determinant of demand.

Px = 3/2 = 1.50, and Price of a Competitive Good is not a significant determinant of demand.

I = 4/3 = 1.33, and Average Monthly Income also is not a significant determinant of demand.

R2 = 0.25 collectively explain one quarter of the variation in quantity demanded.

 

12) What are the key steps for analyzing Demand functions based on Regression results?

Answer:  Check signs and magnitudes; compute elasticity coefficients; determine statistical significance.

 

13) Explain the difference between Cross-Section and Time-Series Regression Analysis.

Answer:  Cross-section analysis examines the relationships between given values of a dependent variable and one or more independent variables at one moment in time (for one time period only).

14) The demand equation for the Widget Company has been estimated to be:

 

Q = 20,000 + 10 I – 50P + 20 PC

 

where Q = monthly number of widgets sold, I = average monthly income, P = price of widgets, and PC = average price of competing goods.

 

1. If next month’s income is forecast to be 2,000, the price of competing goods is forecast to be $20, and the price of widgets will be set at $30, forecast sales.
2. What will sales be if the price is dropped to $20?

Answer:

900. The forecast for sales is 38,900.
901. The forecast for sales will be 39,400.

 

15) Based on annual data from 2000-2010, the Gadget Company estimates that sales are growing according to a linear trend:

 

Q = 50,000 + 200t

 

where t is time and t = 0 in 2000.

 

2013. Forecast sales for 2013.
2014. Do you see any problems with this forecasting method?

Answer:

1. 52,600
2. The equation is based on data from 2000-2010. The further away from the final year, the less likely the equation is to be correct, as more factors may alter the trend seen in the data. A further issue is that the model is based on only 11 observed values.

 

16) If $1,000 is placed in an account earning 8% annually on January 1, 1999, how much would be in this account on January 1, 2013?

Answer:  $2,937

 

17) You are given the following straight-line trend equation: Sales = 1,275 + 89.3t, where 1990 represents t = 1. Project sales for 2000.

Answer:  2,257.3

 

18) The following are the sales achieved by Jensen Fabrics during the last 7 years:

 

2007       $116,000

2008         124,000

2009         127,000

2010         146,000

2011         155,000

2012         154,000

2013         162,000

 

Using the compound growth rate calculation, what would be your estimate for sales in 2014?

Answer:  $171,200 (growth rate is 5.7%)

 

19) The following are the actual sales for the last six periods:

 

                   Period              Sales

1                    750

2                    820

3                    600

4                    850

5                    900

6                    700

 

Using a 3-month moving average, what would be your prediction for period 7?

Answer:  817

 

20) The following are the actual sales for the last six periods:

 

                   Period              Sales

1                    750

2                    820

3                    600

4                    850

5                    900

6                    700

 

If the exponential smoothing forecasting method is used, and the smoothing factor is .6, what will be the forecast for period 7?

Answer:  761

 

21) What are the prerequisites of a good forecast?

Answer:  A forecast must be consistent with all aspects (parts) of a business. A forecast should be based on knowledge of the relevant past, unless underlying conditions change or there is no past to consider. A forecast must consider the economic and political environment in which businesses operate. A forecast must provide information in a timely manner.

 

22) What are the four different characteristics that data exhibit when undertaking time-series forecasts?

Answer:  Trend; Cyclical Fluctuations; Seasonal Variation; Irregular Movements

 

23) Explain the difference between the Moving Average and Exponential Smoothing approaches to forecasting.

Answer:  The Moving Average approach assigns equal weights to each time period from which data are obtained, and drops the oldest time period when a new time period is added in calculating the average value.

 

The Exponential Smoothing approach assigns different weights to each time period from which data are drawn, with the smallest weight given the oldest time period and the greatest weight to the most recent period (all the weights are fractional, usually employing a geometric progression, and must add up to one).