(Situation L) A farmer's marketing cooperative recorded the volume of wheat harvested by its members from 1991 The cooperative is interested in detecting the long-term trend of the amount of wheat harvested. The data collected is shown in the table. \[\begin{array} { l c c } \hline \text { Year } & \text { Time } & \begin{array} { c } \text { Wheat Harvested by Coop. Member } \\ \text { (y, in thousands of bushels) } \end{array} \\ \hline 1991 & 1 & 75 \\ 1992 & 2 & 78 \\ 1993 & 3 & 82 \\ 1994 & 4 & 82 \\ 1995 & 5 & 84 \\ 1996 & 6 & 85 \\ 1997 & 7 & 87 \\ 1998 & 8 & 91 \\ 1999 & 9 & 92 \\ 2000 & 10 & 92 \\ 2001 & 11 & 93 \\ 2002 & 12 & 96 \\ 2003 & 13 & 101 \\ 2004 & 14 & 102 \\ \hline \end{array}\] -Find the least squares prediction equation for the model $y _ { t } = \beta _ { 0 } + \beta _ { 1 } t + \varepsilon$.

A) $\hat { y } _ { t } = - 74.2 - 1.9165 \mathrm { t }$ B) $\hat { y } _ { \mathrm { t } } = 1.9165 - 74.2 \mathrm { t }$ C) $\hat { y } _ { t } = 74.2 - 1.9165 \mathrm { t }$ D) $\hat { y } _ { \mathrm { t } } = 74.2 + 1.9165 \mathrm { t }$ A) $\hat { y } _ { t } = - 74.2 - 1.9165 \mathrm { t }$ B) $\hat { y } _ { \mathrm { t } } = 1.9165 - 74.2 \mathrm { t }$ C) $\hat { y } _ { t } = 74.2 - 1.9165 \mathrm { t }$ D) $\hat { y } _ { \mathrm { t } } = 74.2 + 1.9165 \mathrm { t }$

Consider the actual values Y and forecast values F given in the table below. \[\begin{array} { | c | c | c | } \hline \text { Time Period } & \mathrm { Y } & \mathrm { F } \\ \hline 1 & 19.5 & 19.3 \\ \hline 2 & 21.5 & 20.9 \\ \hline 3 & 22.6 & 22.5 \\ \hline \end{array}\] Calculate the mean absolute deviation (MAD) of the forecasts.

A) 1.42 B) 0.90 C) 0.30 D) 0.37 A) 1.42 B) 0.90 C) 0.30 D) 0.37

Consider the monthly time series shown in the table. $\begin{array}{l|c|c} \hline {\text { Month }} & \mathrm{t} & \mathrm{Y} \\ \hline \text { January } & 1 & 185 \\ \hline \text { February } & 2 & 192 \\ \hline \text { March } & 3 & 189 \\ \hline \text { April } & 4 & 201 \\ \hline \text { May } & 5 & 195 \\ \hline \text { June } & 6 & 199 \\ \hline \text { July } & 7 & 206 \\ \hline \text { August } & 8 & 203 \\ \hline \text { September } & 9 & 208 \\ \hline \text { October } & 10 & 209 \\ \hline \text { November } & 11 & 218 \\ \hline \text { December } & 12 & 216 \\ \hline \end{array}$ a. Use the method of least squares to fit the model $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { t }$ to the data. Write the prediction equation. b. Construct a residual plot for the model. c. Is there evidence of a cyclical component? Explain.

a. @#LAT-DLM& b. @#IMG-DLM& c. No, ther

Consider the actual values Y and forecast values F given in the table below. \[\begin{array} { | c | c | c | } \hline \text { Time Period } & \mathrm { Y } & \mathrm { F } \\ \hline 1 & 19.5 & 19.3 \\ \hline 2 & 21.5 & 20.9 \\ \hline 3 & 22.6 & 22.5 \\ \hline \end{array}\] Calculate the root mean squared error (RMSE) of the forecasts.

A) 0.90 B) 0.30 C) 0.37 D) 1.42 A) 0.90 B) 0.30 C) 0.37 D) 1.42

Consider the actual values Y and forecast values F given in the table below. \[\begin{array} { | c | c | c | } \hline \text { Time Period } & \text { Y } & \text { F } \\ \hline 1 & 19.5 & 19.3 \\ \hline 2 & 21.5 & 20.9 \\ \hline 3 & 22.6 & 22.5 \\ \hline \end{array}\] Calculate the mean absolute percentage error (MAPE) of the forecasts.

A) 0.37 B) 0.30 C) 1.42 D) 0.90 A) 0.37 B) 0.30 C) 1.42 D) 0.90

(Situation K) Foreign Exchange rates, the values of foreign currency in U.S. dollars, are important to investors and international travelers. The table lists the monthly foreign exchange rates of the British pound (in U.S. dollars per pound) for a certain year. \[\begin{array} { l l } \underline {\text { Month }} & \underline { \text { Exchange Rate } } \\ \text { January } & 1.13 \\ \text { February } & 1.10 \\ \text { March } & 1.13 \\ \text { April } & 1.23 \\ \text { May } & 1.25 \\ \text { June } & 1.28 \\ \text { July } & 1.38 \\ \text { August } & 1.39 \\ \text { September } & 1.36 \\ \text { October } & 1.42 \\ \text { November } & 1.44 \\ \text { December } & 1.44 \end{array}\] -Consider the table below which displays the price of a commodity for six consecutive years. $\begin{array}{c|c} \hline \text { Year } & \text { Price } \\ \hline 1 & 250 \\ \hline 2 & 255 \\ \hline 3 & 253 \\ \hline 4 & 255 \\ \hline 5 & 259 \\ \hline 6 & 261 \\ \hline \end{array}$ a. $\text { Use the method of least squares to fit the model } E\left(Y_{t}\right)=\beta_{0}+\beta_{1} t \text { to the data. Write the }$ prediction equation. b. Calculate the residuals and construct a residual plot. c. Calculate the Durbin Watson d statistic.

The answer of (Situation K) Foreign Exchange rates, the values...

(Situation F) The sales (in thousands of dollars) of automobiles by the three largest American automakers from 1986 through 1992 are shown in the table below. \[\begin{array} { l r c r } \hline \text { Year } & \text { G.M. } & \text { Ford } & \text { Chrysler } \\ \hline 1986 & 8993 & 5810 & 1796 \\ 1987 & 7101 & 4328 & 1225 \\ 1988 & 6762 & 4313 & 1283 \\ 1989 & 6244 & 4255 & 1182 \\ 1990 & 7769 & 4934 & 1494 \\ 1991 & 8256 & 5585 & 2034 \\ 1992 & 9305 & 5551 & 2157 \\ \hline \end{array}\] -Using 1986 as the base year, find the simple composite index for 1990.

A) 85.53 B) 116.92 C) 65.81 D) 151.95 A) 85.53 B) 116.92 C) 65.81 D) 151.95

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. \[\begin{array} { l l } \hline \text { Year } & \text { Sales } \\ \hline 1980 & 1.740 \\ 1981 & 1.444 \\ 1982 & 0.896 \\ 1983 & 1.289 \\ 1984 & 1.455 \\ 1985 & 4.882 \\ \hline \end{array}\] -Using a smoothing constant of $\mathrm { w } = 0.70 ,$ 0.70, calculate the value of the exponentially smoothed series in 1985.

The first value of the exponentially smo

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. \[\begin{array} { c l } \hline \text { Year } & \text { Sales } \\ \hline 1980 & 1.740 \\ 1981 & 1.444 \\ 1982 & 0.896 \\ 1983 & 1.289 \\ 1984 & 1.455 \\ 1985 & 4.882 \\ \hline \end{array}\] -Using a smoothing constant of $\mathrm { w } = 0.80$ ate the value of the exponentially smoothed series in 1983.

A) 1.289 B) 1.340 C) 1.228 D) 1.235 A) 1.289 B) 1.340 C) 1.228 D) 1.235

Exam 14: Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year Sales 1980 1.740 1981 1.444 1982 0.896 1983 1.289 1984 1.455 1985 4.882 -Use the Holt forecasting model with trend to forecast the number of Chevrolet passenger cars sold to U.S. and Canadian dealers in 1990 using $\mathrm { w } = 0.4 \text { and } \mathrm { v } = 0.5$

(Multiple Choice)

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Question 21

(Situation O) Using data from the post-Korean war period, an economist modeled annual consumption, $y _ { t }$ , as a function of total labor income, $\mathrm { x } _ { 1 \mathrm { t } }$ , and total property income, $\mathrm { x } _ { 2 \mathrm { t } }$ , with the following results. Assume data for $\mathrm { n } = 40$ years were used in the analysis. $\hat { y } _ { t } = 7.81 + 0.91 x _ { 1 t } + 0.57 x _ { 2 t } \quad s = 1.29 \quad \text { Durbin-Watson } d = 2.09$ -For the situation above, give the rejection region for the Durbin-Watson test for autocorrelation of residuals. Use ? = 0.10.

(Multiple Choice)

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Question 22

The exponentially smoothed forecast takes into account both changes in trend and seasonality.

(True/False)

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Question 23

(Situation M) Fast food chains are closely watching what proposed legislation will do to consumption of "huge meals" in the United States. Researchers have accumulated statistics on the annual consumption of "huge for the past 25 years. The goal of the analysis is to use the past data to predict future consumption and then compare the predicted consumption to the actual consumption in those years. -Propose a straight-line model for the long-term trend of the time series. Do not include a seasonal component. Let $t =$ the year in which the data was collected $( t = 1,2 , \ldots , 25 )$ .

(Multiple Choice)

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Question 24

(Situation L) A farmer's marketing cooperative recorded the volume of wheat harvested by its members from 1991 The cooperative is interested in detecting the long-term trend of the amount of wheat harvested. The data collected is shown in the table. Year Time Wheat Harvested by Coop. Member (y, in thousands of bushels) 1991 1 75 1992 2 78 1993 3 82 1994 4 82 1995 5 84 1996 6 85 1997 7 87 1998 8 91 1999 9 92 2000 10 92 2001 11 93 2002 12 96 2003 13 101 2004 14 102 -Find the least squares prediction equation for the model $y _ { t } = \beta _ { 0 } + \beta _ { 1 } t + \varepsilon$ .

(Multiple Choice)

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Question 25

Consider the actual values Y and forecast values F given in the table below. Time Period 1 19.5 19.3 2 21.5 20.9 3 22.6 22.5 Calculate the mean absolute deviation (MAD) of the forecasts.

(Multiple Choice)

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Question 26

Consider the monthly time series shown in the table. Month January 1 185 February 2 192 March 3 189 April 4 201 May 5 195 June 6 199 July 7 206 August 8 203 September 9 208 October 10 209 November 11 218 December 12 216 a. Use the method of least squares to fit the model $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { t }$ to the data. Write the prediction equation. b. Construct a residual plot for the model. c. Is there evidence of a cyclical component? Explain.

(Essay)

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Question 27

The d-test requires that the residuals be normally distributed.

(True/False)

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Question 28

Consider the actual values Y and forecast values F given in the table below. Time Period 1 19.5 19.3 2 21.5 20.9 3 22.6 22.5 Calculate the root mean squared error (RMSE) of the forecasts.

(Multiple Choice)

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Question 29

The choice of exponential smoothing constant w has little or no effect on forecast values found using exponential smoothing.

(True/False)

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Question 30

Consider the actual values Y and forecast values F given in the table below. Time Period Y F 1 19.5 19.3 2 21.5 20.9 3 22.6 22.5 Calculate the mean absolute percentage error (MAPE) of the forecasts.

(Multiple Choice)

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Question 31

(Situation K) Foreign Exchange rates, the values of foreign currency in U.S. dollars, are important to investors and international travelers. The table lists the monthly foreign exchange rates of the British pound (in U.S. dollars per pound) for a certain year. January 1.13 February 1.10 March 1.13 April 1.23 May 1.25 June 1.28 July 1.38 August 1.39 September 1.36 October 1.42 November 1.44 December 1.44 -Consider the table below which displays the price of a commodity for six consecutive years. Year Price 1 250 2 255 3 253 4 255 5 259 6 261 a. $\text { Use the method of least squares to fit the model } E\left(Y_{t}\right)=\beta_{0}+\beta_{1} t \text { to the data. Write the }$ prediction equation. b. Calculate the residuals and construct a residual plot. c. Calculate the Durbin Watson d statistic.

(Essay)

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Question 32

The table below shows the price of a commodity for each of ten consecutive years. Year 1 2 3 4 5 6 7 8 9 10 Price \ 1.19 \ 1.22 \ 1.23 \ 1.45 \ 1.39 \ 1.42 \ 1.47 \ 1.55 \ 1.62 \ 1.65 a. Using Year 1 as the base period, calculate the simple index for the price of the commodity for each year. b. Plot the simple indexes for years 1-10. c. Use the simple index to interpret the trend in the price of the commodity.

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Question 33

(Situation F) The sales (in thousands of dollars) of automobiles by the three largest American automakers from 1986 through 1992 are shown in the table below. Year G.M. Ford Chrysler 1986 8993 5810 1796 1987 7101 4328 1225 1988 6762 4313 1283 1989 6244 4255 1182 1990 7769 4934 1494 1991 8256 5585 2034 1992 9305 5551 2157 -Using 1986 as the base year, find the simple composite index for 1990.

(Multiple Choice)

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Question 34

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year Sales 1980 1.740 1981 1.444 1982 0.896 1983 1.289 1984 1.455 1985 4.882 -Using a smoothing constant of $\mathrm { w } = 0.70 ,$ 0.70, calculate the value of the exponentially smoothed series in 1985.

(Essay)

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Question 35

(Situation J) The table lists the number (in millions) of Chevrolet passenger cars sold to dealers in the U.S. and Canada from 1980 to 1985. Year Sales 1980 1.740 1981 1.444 1982 0.896 1983 1.289 1984 1.455 1985 4.882 -Using a smoothing constant of $\mathrm { w } = 0.80$ ate the value of the exponentially smoothed series in 1983.

(Multiple Choice)

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Question 36

The table below shows the prices and quantities of three commodities for six consecutive years. $\quad$ $\quad$ $\quad$ $\quad$ $\text {Commodity A}$ $\quad$ $\quad$ $\text {Commodity B}$ $\quad$ $\text {Commodity C}$ Year Price Quantity Price Quantity Price Quantity 1 250 1200 121 3200 675 1800 2 255 1500 115 3500 700 1900 3 253 2700 128 2400 714 2100 4 255 1800 126 2800 721 2500 5 259 2100 129 2700 725 3100 6 261 2000 135 2500 734 3900 a. Compute the Laspeyres price index for the six-year period, using Year 1 as the base period. b. Compute the Paasche price index for the six-year period, using Year 1 as the base period. c. Plot the Laspeyres and Paasche indexes on the same graph. Comment on the differences.

(Essay)

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Question 37

Consider the monthly time series shown in the table. Month t January 1 185 February 2 192 March 3 189 April 4 201 May 5 195 June 6 199 July 7 206 August 8 203 September 9 208 October 10 209 November 11 218 December 12 216 a. Calculate the values in the exponentially smoothed series using w $w = 0.6$ b. Graph the time series and the exponentially smoothed series on the same graph.

(Essay)

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Question 38

(Situation N) An economist wishes to study the monthly trend in the Dow Jones Industrial Average (DJIA). Data collected over the past 40 months were used to fit the model $\mathrm { E } \left( \mathrm { Y } _ { t } \right) = \beta _ { 0 } + \beta _ { 1 } \mathrm { t }$ , where $y =$ monthly close of the DJIA and $t =$ month $( 1,2,3 , \ldots , 40 )$ . The regression results appear below: $\hat { y } = 88 + 0.25 t \quad R ^ { 2 } = 0.37 \quad \text { MSE } = 144 \quad F = 4.25 \quad \text { Durbin-Watson } d = 0.96$ -Use the value of the Durbin-Watson test statistic to make a statement about autocorrelation of residuals in the regression model above.

(Multiple Choice)

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Question 39

A(n) _______ is a number that measures the change in a variable over time relative to the value of the variable during a base period.

(Multiple Choice)

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Question 40

The exponentially smoothed forecast takes into account both changes in trend and seasonality.

Consider the actual values Y and forecast values F given in the table below. Time Period 1 19.5 19.3 2 21.5 20.9 3 22.6 22.5 Calculate the mean absolute deviation (MAD) of the forecasts.

The d-test requires that the residuals be normally distributed.

Consider the actual values Y and forecast values F given in the table below. Time Period 1 19.5 19.3 2 21.5 20.9 3 22.6 22.5 Calculate the root mean squared error (RMSE) of the forecasts.

The choice of exponential smoothing constant w has little or no effect on forecast values found using exponential smoothing.

Consider the actual values Y and forecast values F given in the table below. Time Period Y F 1 19.5 19.3 2 21.5 20.9 3 22.6 22.5 Calculate the mean absolute percentage error (MAPE) of the forecasts.

A(n) _______ is a number that measures the change in a variable over time relative to the value of the variable during a base period.

Statistics, Data, and Statistical Thinking

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Random Variables and Probability Distributions

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Inferences Based on a Single Sample: Estimation With Confidence Intervals

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Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

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