A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q1 + 0.5Q3 + 8Q4 + 3t With t in quarters and the origin is December 2010 and Q1 is the indicator variable for March, Q3 is the indicator variable for September and Q4 is the indicator variable for December. Which of the following statements is correct?

A) The overall general movement of number of surfboards sold by this company is positive because the coefficients of the indicator variables are positive. B) The overall general movement of number of surfboards sold by this company is positive because the intercept is positive. C) The overall general movement of number of surfboards sold by this company is positive because the coefficient of time t is positive. D) None of these choices are correct. A) The overall general movement of number of surfboards sold by this company is positive because the coefficients of the indicator variables are positive. B) The overall general movement of number of surfboards sold by this company is positive because the intercept is positive. C) The overall general movement of number of surfboards sold by this company is positive because the coefficient of time t is positive. D) None of these choices are correct. C

A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q1 + 0.5Q3 + 8Q4 + 3t With t in quarters, the origin is December 2010 and Q1 is the indicator variable for March, Q3 is the indicator variable for September and Q4 is the indicator variable for December. Which of the following is the correct value of the estimate for the number of surfboards sold by this manufacturing company in March 2015?

A) 86 B) 90 C) 93 D) 51 A) 86 B) 90 C) 93 D) 51

Quarterly enrolments in a women's leadership program for three years are shown below. \[\begin{array} { | c | c c | } \hline \text { Year } & \text { Quarter } & \text { Enrolment } \\ \hline 2014 & 1 & 26 \\ & 2 & 29 \\ & 3 & 33 \\ & 4 & 18 \\ 2015 & 1 & 27 \\ & 2 & 25 \\ & 3 & 36 \\ & 4 & 21 \\ 2016 & 1 & 32 \\ & 2 & 36 \\ & 3 & 39 \\ & 4 & 30 \\ \hline \end{array}\] Compute the four-quarter centred moving averages.

The answer of Quarterly enrolments in a women's leadership program...

The results of a quadratic model fit to time-series data were ŷt = 7.5 F1F1F1S1F1F1F10 0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

A) 289.5. B) 285.5. C) 236.1. D) 232.5. A) 289.5. B) 285.5. C) 236.1. D) 232.5.

Exam 17: Time-Series Analysis and Forecasting

The quarterly earnings of a large microcomputer company have been recorded for the years 2012-2015. These data (in millions of dollars) are shown in the accompanying table. Year Quarter 2012 2013 2014 2015 1 60 65 68 74 2 75 83 85 90 3 93 98 102 106 4 62 69 71 75 Using an appropriate moving average, measure the quarterly variation by computing the seasonal (quarterly) indexes.

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Question 1

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$\begin{array}{|c|cccc|}\hline \begin{array}{c}\text { Time } \\\text { period }\end{array} & y & \begin{array}{c}\text { Four-quarter } \\\text { moving average }\end{array} & \begin{array}{c}\text { Four-quarter centred } \\\text { moving average }\end{array} & \begin{array}{c}\text { Ratio } \\y^{\prime} \text { MA }\end{array} \\\hline 1 & 60 & - & - & - \\2 & 75 & 72.50 & - & - \\3 & 93 & 73.75 & 73.125 & 1.272 \\4 & 62 & 75.75 & 74.750 & 0.829 \\5 & 65 & 77.00 & 76.375 & 0.851 \\6 & 83 & 78.75 & 77.875 & 1.066 \\7 & 98 & 79.50 & 79.125 & 1.239\\8 & 69 & 80.00 & 79.750 & 0.865 \\9 & 68 & 81.00 & 80.500 & 0.845 \\10 & 85 & 81.50 & 81.250 & 1.046 \\11 & 102 & 83.00 & 82.250 & 1.240 \\12 & 71 & 84.25 & 83.625 & 0.849 \\13 & 74 & 85.25 & 84.750 & 0.873 \\14 & 90 & 86.25 & 85.750 & 1.050 \\15 & 106 & - & - & - \\16 & 75 & & - & - \\\hline\end{array}$ $\begin{array} { | c | c c c c | c | } \hline \text { Year } & \text { Quarter 1 } & \text { Quarter 2 } & \text { Quarter 3 } & \text { Quarter 4 } & \text { Total } \\\hline 2012 & - & - & 1.272 & 0.829 & \\2013 & 0.851 & 1.066 & 1.239 & 0.865 & \\2014 & 0.845 & 1.046 & 1.240 & 0.849 & \\2015 & 0.873 & 1.050 & - & - & \\\hline \text { Average } & 0.856 & 1.054 & 1.250 & 0.848 & 4.008 \\\text { Seasonal index } & 0.854 & 1.052 & 1.248 & 0.846 & 4.000 \\\hline\end{array}$

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

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Question 2

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B

A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters and the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following statements is correct?

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Question 3

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C

We calculate the three-period moving averages for a time series for all time periods except the:

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Question 4

Annual production (in millions) of computer chips in a large electronics company was recorded, as shown below. Year t Production 2006 1 26 2007 2 23 2008 3 21 2009 4 25 2010 5 32 2011 6 38 2012 7 43 2013 8 36 2014 9 29 2015 10 25 a. Calculate the percentage of trend for each time period. b. Plot the percentage of trend. c. Describe the cyclical effect (if there is one).

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Question 5

A time series regression equation for a surfboard manufacturing company in Australia is given below: Y = 35 + 4Q₁ + 0.5Q₃ + 8Q₄ + 3t With t in quarters, the origin is December 2010 and Q₁ is the indicator variable for March, Q₃ is the indicator variable for September and Q₄ is the indicator variable for December. Which of the following is the correct value of the estimate for the number of surfboards sold by this manufacturing company in March 2015?

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Question 6

Two forecasting models were used to predict the future values of a time series. These are shown in the following table, together with the actual values. Forecast Value Actual Value Model 1 Model 2 8.2 7.7 7.6 7.8 8.5 8.2 7.0 8.5 7.6 9.6 9.0 10.3 Compute MAD and SSE for each model to determine which was more accurate.

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Question 7

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:

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Question 8

Quarterly enrolments in a women's leadership program for three years are shown below. Year Quarter Enrolment 2014 1 26 2 29 3 33 4 18 2015 1 27 2 25 3 36 4 21 2016 1 32 2 36 3 39 4 30 Compute the four-quarter centred moving averages.

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Question 9

The most commonly used measures of forecast accuracy are the:

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Question 10

The number of pairs of sunglasses sold each quarter in a beachside drugstore were recorded for the years 2013-2016. These data are shown in the following table. Year Quarter 2013 2014 2015 2016 1 82 84 85 90 2 72 71 70 74 3 65 66 67 71 4 53 54 56 58 a. Develop a regression model, using indicator variables to represent quarters. b. Forecast the quarterly earnings for the years 2017 and 2018.

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Question 11

The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hours 2013 1 20 2 30 3 28 4 20 2014 1 24 2 34 3 28 4 21 1 28 2015 2 38 3 31 4 26 1 30 2016 2 41 3 35 4 28 a. Use the regression technique to calculate the linear trend line. b. Calculate the seasonal indexes based on the regression trend line in part (a). c. What do the seasonal indexes tell us?

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Question 12

The results of a quadratic model fit to time-series data were ŷt = 7.5  0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

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Question 13

Any variable that is measured over time in sequential order is called a time series.

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Question 14

Seasonal variations will be present in a deseasonalised time series.

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Question 15

The level of construction employment in Sydney is lowest during the winter. A model designed to forecast construction employment in Sydney should use:

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Question 16

The Pyramids of Giza are one of the most visited monuments in Egypt. The number of visitors per quarter has been recorded (in thousands) as shown in the accompanying table: Year Quarter 1995 1996 1997 1998 Winter 210 215 218 220 Spring 260 275 282 290 Summer 480 490 505 525 Autumn 250 255 265 270 a. Plot the time series. b. Discuss why exponential smoothing is not recommended as a forecasting method in this case. c. Calculate the four-quarter centred moving averages. d. Use the moving averages computed in (c) to calculate the seasonal (quarterly) indexes. e. Use the seasonal indexes computed in (d) to deseasonalise the original time-series data, and plot the deseasonalised time series. f. Use regression analysis to develop the trend line. g. Use the seasonal indexes calculated in (d) and the linear trend calculated in (f) to forecast the number of visitors in the next four quarters and describe the seasonal fluctuations in the number of visitors.

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Question 17

The trend equation for annual sales data (in millions of dollars) is $\ddot{\mathbf{p}}_{t}= 65 + 2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

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Question 18

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: ŷt = 135 + 4.8t  1.3_{_Q1} 1.7Q₂ + 1.5Q₃ where: Q_i = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.

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Question 19

The term $b _ { 1 }$ in the equation $\ddot { y } _ { 2 } = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 }$ , where ?t represents the predicted value of y at time t, is:

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Question 20

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

We calculate the three-period moving averages for a time series for all time periods except the:

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:

Quarterly enrolments in a women's leadership program for three years are shown below. Year Quarter Enrolment 2014 1 26 2 29 3 33 4 18 2015 1 27 2 25 3 36 4 21 2016 1 32 2 36 3 39 4 30 Compute the four-quarter centred moving averages.

The most commonly used measures of forecast accuracy are the:

The results of a quadratic model fit to time-series data were ŷt = 7.5  0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

Any variable that is measured over time in sequential order is called a time series.

Seasonal variations will be present in a deseasonalised time series.

The level of construction employment in Sydney is lowest during the winter. A model designed to forecast construction employment in Sydney should use:

The trend equation for annual sales data (in millions of dollars) is $\ddot{\mathbf{p}}_{t}= 65 + 2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: ŷt = 135 + 4.8t  1.3_{_Q1} 1.7Q₂ + 1.5Q₃ where: Q_i = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.

The term $b _ { 1 }$ in the equation $\ddot { y } _ { 2 } = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 }$ , where ?t represents the predicted value of y at time t, is:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Index Numbers

Filters

Exam 17: Time-Series Analysis and Forecasting

The high level of airline ticket sales that travel agencies experience during summer is an example of which component of a time series?

We calculate the three-period moving averages for a time series for all time periods except the:

In determining monthly seasonal indexes, the first step is to construct a centred moving average with a period of:

Quarterly enrolments in a women's leadership program for three years are shown below. Year Quarter Enrolment 2014 1 26 2 29 3 33 4 18 2015 1 27 2 25 3 36 4 21 2016 1 32 2 36 3 39 4 30 Compute the four-quarter centred moving averages.

The most commonly used measures of forecast accuracy are the:

The results of a quadratic model fit to time-series data were ŷt = 7.5  0.2t + 2.8t2, where t = 1 for 2002. The forecast value for 2011 is:

Any variable that is measured over time in sequential order is called a time series.

Seasonal variations will be present in a deseasonalised time series.

The level of construction employment in Sydney is lowest during the winter. A model designed to forecast construction employment in Sydney should use:

The trend equation for annual sales data (in millions of dollars) is p¨t=65+2.5t\ddot{\mathbf{p}}_{t}= 65 + 2.5 tp¨​t​=65+2.5t , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: ŷt = 135 + 4.8t  1.3Q1  1.7Q2 + 1.5Q3 where: Qi = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.

The term b1b _ { 1 }b1​ in the equation y¨2=b0+b1t+b2Q1+b3Q2+b4Q3\ddot { y } _ { 2 } = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 }y¨​2​=b0​+b1​t+b2​Q1​+b3​Q2​+b4​Q3​ , where ?t represents the predicted value of y at time t, is:

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference and Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Index Numbers

Filters

The trend equation for annual sales data (in millions of dollars) is $\ddot{\mathbf{p}}_{t}= 65 + 2.5 t$ , where t = 1 for 2000. The monthly seasonal index for December is 0.97. The forecast sales for December of 2009 is:

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: ŷt = 135 + 4.8t  1.3_{_Q1} 1.7Q₂ + 1.5Q₃ where: Q_i = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.

The term $b _ { 1 }$ in the equation $\ddot { y } _ { 2 } = b _ { 0 } + b _ { 1 } t + b _ { 2 } Q _ { 1 } + b _ { 3 } Q _ { 2 } + b _ { 4 } Q _ { 3 }$ , where ?t represents the predicted value of y at time t, is: