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 mo $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 }$ t to the data. Write the prediction equation. b. Use the prediction equation to obtain forecasts for the next two months. c. Find 95% forecast intervals for the next two months.

The answer of Consider the monthly time series shown in...

(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. \[\begin{array} { l l } \hline \text { Year } & \text { Sales } \\ \hline 1980 & 1.740 \\ 1981 & 1.444 \\ 1982 & 0.896 \\ 1983 & 1.289 \\ 1984 & 1.455 \\ 1985 & 4.882 \\ \hline \end{array}\] -The _______ is what remains of a time series value after the secular, cyclical, and seasonal components have been removed.

A) exponential effect B) additive effect C) residual effect D) error effect A) exponential effect B) additive effect C) residual effect D) error effect

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

A) We expect the mean volume of wheat harvested to increase 2000 bushels from one year to the next. B) We expect the volume of wheat harvested to increase 2000 bushels for each additional corporate member. C) We expect the volume of wheat harvested to be 2000 bushels in any given year. D) We expect to harvest 2000 bushels of wheat in 2005. A) We expect the mean volume of wheat harvested to increase 2000 bushels from one year to the next. B) We expect the volume of wheat harvested to increase 2000 bushels for each additional corporate member. C) We expect the volume of wheat harvested to be 2000 bushels in any given year. D) We expect to harvest 2000 bushels of wheat in 2005.

(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. \[\begin{array} { l c c } \hline & \text { Wheat Harvested by Coop. Member } \\ \text { Year } & \text { Time } & ( \mathrm { y } , \text { in thousands of bushels) } \\ \hline 1991 & 1 & 75 \\ 1992 & 2 & 78 \\ 1993 & 3 & 82 \\ 1994 & 4 & 82 \\ 1995 & 5 & 84 \\ 1996 & 6 & 85 \\ 1997 & 7 & 87 \\ 1998 & 8 & 91 \\ 1999 & 9 & 92 \\ 2000 & 10 & 92 \\ 2001 & 11 & 93 \\ 2002 & 12 & 96 \\ 2003 & 13 & 101 \\ 2004 & 14 & 102 \\ \hline \end{array}\] -A forecast was obtained for the year 2005 and the corresponding 95% prediction interval was found to be (103, 107). Interpret this interval.

A) We are 95% confident that the volume of wheat harvested in 2005 will be between 103,000 and 107,000 bushels. B) We are 95% confident that the mean volume of wheat harvested in all years will be between 103,000 and 107,000 bushels. C) We expect the volume of wheat harvested to increase between 103,000 and 107,000 bushels from one year to the next. D) We are 95% confident that the 2005 harvest will be between 103,000 and 107,000 bushels larger than the harvest in 2004. A) We are 95% confident that the volume of wheat harvested in 2005 will be between 103,000 and 107,000 bushels. B) We are 95% confident that the mean volume of wheat harvested in all years will be between 103,000 and 107,000 bushels. C) We expect the volume of wheat harvested to increase between 103,000 and 107,000 bushels from one year to the next. D) We are 95% confident that the 2005 harvest will be between 103,000 and 107,000 bushels larger than the harvest in 2004.

(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 the exponential smoothing technique to the data from 1980 to 1985, forecast the number of Chevrolet passenger cars to be sold to U.S. and Canadian dealers in 1986 using $w = 0.7$

A) 4.882 million cars B) 3.427 million cars C) 3.834 million cars D) 2.448 million cars A) 4.882 million cars B) 3.427 million cars C) 3.834 million cars D) 2.448 million cars

The printout below shows a regression analysis for a time series that included 20 observations. Regression Analysis: C2 versus C1 The regression equation is $\mathrm { C } 2 = 1.20 + 0.0362 \mathrm { C } 1$ $\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm { T } & \mathrm { P } \\ \text { Constant } & 1.19947 & 0.08471 & 14.16 & 0.000 \\ \mathrm { C } 1 & 0.036241 & 0.007072 & 5.12 & 0.000 \\\end{array}$ $\begin{array} { lll} \mathrm {~S} = 0.182361 & \mathrm { R } - \mathrm { Sq } = 59.3 \% \quad \mathrm { R } - \mathrm { Sq } ( \text { adj } ) = 57.1 \% \end{array}$ Analysis of Variance $\begin{array}{lcrrrr} \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 1 & 0.87340 & 0.87340 & 26.26 & 0.000 \\ \text { Residual Error } & 18 & 0.59860 & 0.03326 & & \\ \text { Total } & 19 & 1.47200 & & & \end{array}$ Locate the Durbin-Watson d-statistic and test the null hypothesis that there is no autocorrelation of residuals. Use $\alpha = 0.10$.

@#LAT-DLM&; The rejection region is @#LAT-DLM& or

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

Smaller values of the trend smoothing constant v assign more weight to the most recent trend of the series and less to past trends.

(True/False)

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Question 41

Consider the table below which displays the price of a commodity for six consecutive years. Year Price (dollars) 1 250 2 255 3 253 4 255 5 259 6 261 a. Use the Holt model to forecast values for Years 7-10 using $\mathrm { w } = 0.6$ and $\mathrm { v } = 0.5$ . b. Calculate the forecast errors for Years 7-10 if the actual values in those years are 263, 267, 269, 268 respectively. c. Calculate MAD, MAPE, and RMSE, using the forecast errors for Years 7-10.

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Question 42

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 mo $\mathrm { E } \left( \mathrm { Y } _ { \mathrm { t } } \right) = \beta _ { 0 } + \beta _ { 1 }$ t to the data. Write the prediction equation. b. Use the prediction equation to obtain forecasts for the next two months. c. Find 95% forecast intervals for the next two months.

(Essay)

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Question 43

The tendency of a series of values to increase or decrease over a long period of time is known as the _______ of a time series.

(Multiple Choice)

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Question 44

The least squares model is an excellent choice for forecasting time series since it works particularly well outside the region of known observations.

(True/False)

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Question 45

(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 $\mathrm { n } = 40 \mathrm { years }$ were used in the analysis. $\hat { y } _ { t } = 7.81 + 0.91 x _ { 1 t } + 0.57 x _ { 2 t } \quad s = 1.29 \quad \text { Durbin-Watson } d = 2.09$ -Is there evidence of positive autocorrelation of residuals in the consumption model presented above? Test using $\alpha = 0.10$ .

(Multiple Choice)

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Question 46

(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 -The _______ is what remains of a time series value after the secular, cyclical, and seasonal components have been removed.

(Multiple Choice)

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Question 47

We plot time series residuals against observed values of Y to determine whether a cyclical component is apparent.

(True/False)

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Question 48

(Situation L) A farmer's marketing cooperative recorded the volume of wheat harvested by its members from 1991-2004. 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 -Suppose the least squares regression equation is $\hat { y } _ { t } = 75 + 2 t$ Interpret the estimate of $\beta _ { 1 }$ in terms of the problem.

(Multiple Choice)

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Question 49

The Laspeyres index uses the purchase quantities of the period as weights.

(True/False)

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Question 50

(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. Wheat Harvested by Coop. Member Year Time (, 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 -A forecast was obtained for the year 2005 and the corresponding 95% prediction interval was found to be (103, 107). Interpret this interval.

(Multiple Choice)

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Question 51

The straight-line regression model accounts for both the secular trend and the cyclical effect in a time series.

(True/False)

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Question 52

(Situation G) The number of industrial and construction failures in the United States by the type of firm for the years 1985-1996 is given in the table. Year Commercial Service Construction Manufacturing and Mining Retail Trade Wholesale Trade 1985 1637 2262 1645 4799 1089 1986 1331 1770 1360 4139 1028 1987 1041 1463 1122 3406 887 1988 773 1204 1013 2889 740 1989 930 1378 1165 3183 908 1990 1594 2355 1599 4910 1284 1991 2366 3614 2223 6882 1709 1992 3840 4872 3683 9730 2783 1993 8627 5247 4433 11,429 3598 1994 12,787 6936 5759 13,787 4882 1995 16,647 7004 5662 13,501 4835 1996 20,911 7035 5641 13,509 4808 -Using 1985 as the base period and using just construction failures, calculate the simple index for 1992.

(Multiple Choice)

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Question 53

(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 $E \left( Y _ { t } \right) = \beta _ { 0 } + \beta _ { 1 } t$ , where $y =$ monthly close of the DJIA and $t =$ month $( 1,2,3 , \ldots , 40 )$ . The regression results appear below: $\hat { y } = 88 + 0.25 t \quad R ^ { 2 } = 0.37 \quad \text { MSE } = 144 \quad F = 4.25 \quad \text { Durbin-Watson } \mathrm { d } = 0.96$ -What is the value of the test statistic for testing whether autocorrelation exists in the data?

(Multiple Choice)

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Question 54

Fourth-order autocorrelation in a quarterly time series may indicate seasonality.

(True/False)

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Question 55

(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 the exponential smoothing technique to the data from 1980 to 1985, forecast the number of Chevrolet passenger cars to be sold to U.S. and Canadian dealers in 1986 using $w = 0.7$

(Multiple Choice)

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Question 56

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 Use exponential smoothing with $w = 0.6$ to forecast the price of the commodity in years 11 and $12 .$

(Short Answer)

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Question 57

The printout below shows a regression analysis for a time series that included 20 observations. Regression Analysis: C2 versus C1 The regression equation is $\mathrm { C } 2 = 1.20 + 0.0362 \mathrm { C } 1$ Predictor Coef SE Coef Constant 1.19947 0.08471 14.16 0.000 1 0.036241 0.007072 5.12 0.000 =0.182361 -=59.3\%-( adj )=57.1\% Analysis of Variance Source DF SS MS F P Regression 1 0.87340 0.87340 26.26 0.000 Residual Error 18 0.59860 0.03326 Total 19 1.47200 Locate the Durbin-Watson d-statistic and test the null hypothesis that there is no autocorrelation of residuals. Use $\alpha = 0.10$ .

(Essay)

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Question 58

One of the major weaknesses of exponential smoothing is that it is not easily adapted to forecasting.

(True/False)

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Question 59

Which of the following statements about the Durbin-Watson d-statistic is true?

(Multiple Choice)

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Question 60

Smaller values of the trend smoothing constant v assign more weight to the most recent trend of the series and less to past trends.

The tendency of a series of values to increase or decrease over a long period of time is known as the _______ of a time series.

The least squares model is an excellent choice for forecasting time series since it works particularly well outside the region of known observations.

We plot time series residuals against observed values of Y to determine whether a cyclical component is apparent.

The Laspeyres index uses the purchase quantities of the period as weights.

The straight-line regression model accounts for both the secular trend and the cyclical effect in a time series.

Fourth-order autocorrelation in a quarterly time series may indicate seasonality.

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 Use exponential smoothing with $w = 0.6$ to forecast the price of the commodity in years 11 and $12 .$

One of the major weaknesses of exponential smoothing is that it is not easily adapted to forecasting.

Which of the following statements about the Durbin-Watson d-statistic is true?

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

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

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Nonparametric Statistics Available on CD

Filters

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

Smaller values of the trend smoothing constant v assign more weight to the most recent trend of the series and less to past trends.

The tendency of a series of values to increase or decrease over a long period of time is known as the _______ of a time series.

The least squares model is an excellent choice for forecasting time series since it works particularly well outside the region of known observations.

We plot time series residuals against observed values of Y to determine whether a cyclical component is apparent.

The Laspeyres index uses the purchase quantities of the period as weights.

The straight-line regression model accounts for both the secular trend and the cyclical effect in a time series.

Fourth-order autocorrelation in a quarterly time series may indicate seasonality.

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 Use exponential smoothing with w=0.6w = 0.6w=0.6 to forecast the price of the commodity in years 11 and 12.12 .12.

One of the major weaknesses of exponential smoothing is that it is not easily adapted to forecasting.

Which of the following statements about the Durbin-Watson d-statistic is true?

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

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

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Nonparametric Statistics Available on CD

Filters

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 Use exponential smoothing with $w = 0.6$ to forecast the price of the commodity in years 11 and $12 .$