Question 1

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

Accepted Answer

A)  The trend value ŷ. 
B)  The ratio of the time series divided by the predicted values. 
C)  The ratio of the time series divided by the moving average and the ratio of the time series divided by the predicted values. 
D)  The ratio of the time series divided by the moving average. 
A)  The trend value ŷ. 
B)  The ratio of the time series divided by the predicted values. 
C)  The ratio of the time series divided by the moving average and the ratio of the time series divided by the predicted values. 
D)  The ratio of the time series divided by the moving average.

Question 2

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called seasonal.

Accepted Answer

A) True 
 B)False

Question 3

The result of a quadratic model fit to time-series data was  $=8.5-0.25 t+2.5 t^{2}$ , where t = 1 for 1994. The forecast value for 2001 is 129.25.

Accepted Answer

A) True 
 B)False

Question 4

The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. $$\begin{array} { | c | c | c | } 
\hline \text { Year } & \text { Quarter } & \text { Overtime hours } \
\hline 2007 & 1 & 20 \
& 2 & 30 \
& 3 & 28 \
& 4 & 20 \
2008 & 1 & 24 \
& 2 & 34 \
& 3 & 28 \
& 4 & 21 \
2009 & 1 & 28 \
& 2 & 38 \
& 3 & 31 \
& 4 & 26 \
2010 & 1 & 30 \
& 2 & 41 \
& 3 & 35 \
& 4 & 28 \
\hline
\end{array}$$ 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?

Accepted Answer

a. ŷ_t = 23.2 + 0.668t. b. Use Excel to ca

Question 5

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

Accepted Answer

A)  lowest MAD and highest SSE. 
B)  highest MAD and lowest SSE. 
C)  lowest MAD and SSE. 
D)  highest MAD and SSE. 
A)  lowest MAD and highest SSE. 
B)  highest MAD and lowest SSE. 
C)  lowest MAD and SSE. 
D)  highest MAD and SSE.

Question 6

Which of the following are examples of seasons when measuring the seasonal component of a time series?

Accepted Answer

A)  Centuries 
B)  Decades 
C)  Quarters 
D)  None of these choices are correct. 
A)  Centuries 
B)  Decades 
C)  Quarters 
D)  None of these choices are correct.

Question 7

The term 'seasonal variation' may refer to the four traditional seasons, or to systematic patterns that occur during a quarter, a week, or even one day, but within 12 months.

Accepted Answer

A) True 
 B)False

Question 8

The table below shows the number of pizzas sold daily during a four-week period at King Pizza in Melbourne. $$\begin{array}{l}
\quad\quad\quad\quad\quad\quad\quad\quad\text { Week }\
\begin{array} { | l | r r r c | } \hline\text { Day } & 1 & 2 & 3 & 4 \\hline
\text { Sunday } & 253 & 234 & 248 & 232 \
\text { Monday } & 98 & 93 & 99 & 104 \
\text { Tuesday } & 106 & 88 & 87 & 115 \
\text { Wednesday } & 119 & 134 & 113 & 102 \
\text { Thursday } & 138 & 123 & 130 & 118 \
\text { Friday } & 201 & 215 & 218 & 205 \
\text { Saturday } & 327 & 399 & 415 & 390 \
\hline
\end{array}
\end{array}$$ a. Calculate the seasonal (daily) indexes, using a seven-day moving average.
b. Use regression analysis to find the linear trend line.
c. Calculate the seasonal (daily) indexes, using the trend line developed in (b).

Accepted Answer

a. @#IMG-DLM& @#IMG-DLM& b. @#IMG-DLM& 158.230 + 1.659t.
c.

Question 9

The stock market has a 5-day working week. If we wanted to measure the impact of the day of the week on stock market performance, we would need:

Accepted Answer

A)  seven indicator variables. 
B)  six indicator variables. 
C)  five indicator variables. 
D)  four indicator variables. 
A)  seven indicator variables. 
B)  six indicator variables. 
C)  five indicator variables. 
D)  four indicator variables.

Question 10

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

Accepted Answer

A) True 
 B)False

Question 11

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).

Accepted Answer

A) True 
 B)False

Question 12

Regression analysis with t = 1 to 40 was used to develop the following equation:  $=1500+5 t+1.5 Q_{1}+1.8 Q_{2}-3.0 Q_{3}$ ,
where: $Q _ { i }$ = 1, if quarter i (i = 1, 2, 3)
= 0, otherwise.
Forecast the next four quarters.

Accepted Answer

The answer of Regression analysis with t = 1 to...

Question 13

A company selling swimming goggles wants to analyze the company's Australian sales figures.
Time series forecasting with regression was used to generate Excel output to estimate trend of the time series of Swimming goggle sales (in thousands of dollars) where the origin is the March Quarter 2000. $\begin{array}{l}
\text { SUMMARV OUTPUT }\
\hline\text { Regression Stotitics }\
\begin{array}{lc}
\hline \text { Multiple R } & 0.37281 \
\text { R Square } & 0.13899 \
\text { Adjusted R } & \
\text { Square } & 0.12243 \
\text { StandardError } & 10.3925 \
\text { Observations } & 54\
\hline
\end{array}
\end{array}$

$\text { ANOVA }$
$\begin{array}{lccccc} 
\hline& & & & & \text { Sgnificance } \
& d f & S & M S & F & F \
\hline \text { Regression } & 1 & 906.5867925 & 906.59 & 8.39406 & 0.005497292 \
\text { Residual } & 52 & 5616.172467 & 108 & & \
\text { Total } & 53 & 6522.759259 & & & \\hline
\end{array}$

$\begin{array}{lcrrrrr}
\hline&& \text { Standard } & & && \text { Upper } \
&\text { Coefficients } & \text { Error } & \text { t Stat } & \text {p-value } & \text { Lower } 95 \%&  95 \%\
\hline\text { Intercept } & 12.237 & 2.789633876 & 4.3866 & 5.6 \mathrm{E}-05 & 6.639227133 & 17.8348469 \
\mathrm{t} & 0.26289 & 0.090738795 & 2.8973 & 0.0055 & 0.080812368 & 0.4449738 \\hline
\end{array}$ (a) Forecast goggles sales for each quarter of 2016.
(b) Are these good predictions? Explain.

Accepted Answer

(a) @#IMG-DLM& (b) No they are not good prediction

Question 14

a. Apply exponential smoothing with w = 0.1 and w = 0.8 to help detect the components of the following time series. $$\begin{array} { c c } 
\text { Period } t & y \mathrm { t } \
\hline 1 & 40 \
2 & 45 \
3 & 44 \
4 & 47 \
5 & 48 \
6 & 50 \
7 & 52 \
8 & 51 \
9 & 48 \
10 & 47
\end{array}$$ b. Draw the time series and the two sets of exponentially smoothed values. Does there appear to be a trend component in the time series?

Accepted Answer

a. @#IMG-DLM& b. @#IMG-DLM& There appear

Question 15

The actual and forecast values of a time series are shown below. $$\begin{array} { | c c | } 
\hline \text { Actual values } y _ { t } & \text { Forecast values } F _ { t } \
\hline 135 & 140 \
162 & 165 \
155 & 150 \
182 & 191 \
174 & 168 \
194 & 190 \
233 & 220 \
280 & 240 \
\hline
\end{array}$$ a. Calculate the mean absolute deviation (MAD).
b. Calculate the sum of squares for forecast error (SSE).

Accepted Answer

a. MAD = @#IMG-DLM&

Question 16

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

Accepted Answer

A)  Moving averages. 
B)  Exponential smoothing. 
C)  Mean absolute deviation. 
D)  Seasonal indexes. 
A)  Moving averages. 
B)  Exponential smoothing. 
C)  Mean absolute deviation. 
D)  Seasonal indexes.

Question 17

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

Accepted Answer

A) True 
 B)False

Question 18

Regression analysis with t = 1 to 80 was used to develop the following forecast equation:
$\hat{y}$t = 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.

Accepted Answer

\[\begin{array} { | c | c c c c c | } 
\

Question 19

To calculate the five-period moving average of a time series for a given time period, we average the value in that time period and the values in the four preceding periods.

Accepted Answer

A) True 
 B)False

Question 20

Of the four different components of a time series, cyclical variation is the one most likely to exhibit the long-term direction of the data.

Accepted Answer

A) True 
 B)False

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called seasonal.

The result of a quadratic model fit to time-series data was $The result of a quadratic model fit to time-series data was =8.5-0.25 t+2.5 t^{2} , where t = 1 for 1994. The forecast value for 2001 is 129.25.$ $=8.5-0.25 t+2.5 t^{2}$ , where t = 1 for 1994. The forecast value for 2001 is 129.25.

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

Which of the following are examples of seasons when measuring the seasonal component of a time series?

The term 'seasonal variation' may refer to the four traditional seasons, or to systematic patterns that occur during a quarter, a week, or even one day, but within 12 months.

The stock market has a 5-day working week. If we wanted to measure the impact of the day of the week on stock market performance, we would need:

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).

The actual and forecast values of a time series are shown below. Actual values Forecast values 135 140 162 165 155 150 182 191 174 168 194 190 233 220 280 240 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: $\hat{y}$ _t = 135 + 4.8t -1.3Q₁ -1.7Q₂ + 1.5Q₃ where: Q_i = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.

To calculate the five-period moving average of a time series for a given time period, we average the value in that time period and the values in the four preceding periods.

Of the four different components of a time series, cyclical variation is the one most likely to exhibit the long-term direction of the data.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Index Numbers

Decision Analysis

Filters

Exam 23: Time-Series Analysis and Forecasting

Which of the following best describes what may be used when measuring the seasonal and random variation of a time series with no cyclical effect?

The time-series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called seasonal.

The result of a quadratic model fit to time-series data was =8.5−0.25t+2.5t2=8.5-0.25 t+2.5 t^{2}=8.5−0.25t+2.5t2 , where t = 1 for 1994. The forecast value for 2001 is 129.25.

The mean absolute deviation (MAD) and the sum of squares for forecast error (SSE) are the most commonly used measures of forecast accuracy. The model that forecasts the data best will usually have the:

Which of the following are examples of seasons when measuring the seasonal component of a time series?

The term 'seasonal variation' may refer to the four traditional seasons, or to systematic patterns that occur during a quarter, a week, or even one day, but within 12 months.

The stock market has a 5-day working week. If we wanted to measure the impact of the day of the week on stock market performance, we would need:

The time-series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend.

In determining weekly seasonal indexes for natural gas consumption, the sum of the 52 means for gas consumption as a percentage of the moving average is 5195. To get the seasonal indexes, each monthly mean is to be multiplied by (5200 / 5195).

Regression analysis with t = 1 to 40 was used to develop the following equation: =1500+5t+1.5Q1+1.8Q2−3.0Q3=1500+5 t+1.5 Q_{1}+1.8 Q_{2}-3.0 Q_{3}=1500+5t+1.5Q1​+1.8Q2​−3.0Q3​ , where: QiQ _ { i }Qi​ = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four quarters.

The actual and forecast values of a time series are shown below. Actual values Forecast values 135 140 162 165 155 150 182 191 174 168 194 190 233 220 280 240 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

Which of the following methods is appropriate for forecasting a time series when the trend, cyclical and seasonal components of the series are not significant?

A time series can consist of four different components: long-term trend, cyclical variation, seasonal variation, and random variation.

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: y^\hat{y}y^​ t = 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.

To calculate the five-period moving average of a time series for a given time period, we average the value in that time period and the values in the four preceding periods.

Of the four different components of a time series, cyclical variation is the one most likely to exhibit the long-term direction of the data.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Index Numbers

Decision Analysis

Filters

The result of a quadratic model fit to time-series data was $The result of a quadratic model fit to time-series data was =8.5-0.25 t+2.5 t^{2} , where t = 1 for 1994. The forecast value for 2001 is 129.25.$ $=8.5-0.25 t+2.5 t^{2}$ , where t = 1 for 1994. The forecast value for 2001 is 129.25.

Regression analysis with t = 1 to 80 was used to develop the following forecast equation: $\hat{y}$ _t = 135 + 4.8t -1.3Q₁ -1.7Q₂ + 1.5Q₃ where: Q_i = 1, if quarter i (i = 1, 2, 3) = 0, otherwise. Forecast the next four values.