Question 1

The regression output produced by MINITAB for times series set of data is shown below: The regression equation is $\mathrm { C } 1 = 33.6 + 0.709 \mathrm { C } 2$

$$s = 3.283 \quad R - s q = 53.1 \% \quad R - s q ( a d j ) = 49.7 \%$$
Analysis of Variance
$\begin{array} { l l c r c r r r } \text { SOURCE } & \text { DF } & & \text { SS } & \text { MS } & \text { F } & p & \ \text { Regression } & & 1 & & 170.83 & 170.83 & 15.85 & 0.001 \ \text { Error } & 14 & & 150.92 & 10.78 & & & \ \text { Total } & 15 & & 321.75 & & & & \end{array}$
Durbin-Watson statistic $= 1.94$ Test for positive autocorrelation using a 0.05 significance level.
Test statistic = ____________________
Critical Value = ____________________
Conclusion: ____________________
Interpretation: __________________________________________________

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Question 2

When exponential smoothing is used in fitting a curve to a time series,the approach is slightly different from its application to forecasting.Compare the appropriate formulas and point out how they differ.

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Question 3

Gashol (a mixture of gasoline and methyl alcohol)sales in Iowa City have been recorded over the past 10 months as shown below:
 $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Manth } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { June } & \text { Juy } & \text { Aug } & \text { Sep } & \text { Oct } \
\hline \text { Sales } & 75 & 72 & 81 & 92 & 90 & 105 & 112 & 107 & 110 & 93 \
\hline
\end{array}$$
-Compute the four month centered moving average.

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Question 4

If a company's inventory costs were $3.5 million in 1995 (base period)and $5.95 million in 2002,what is the index number for 2002?
What does it mean?

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Question 5

In determining seasonal indexes for the months of the year,a statistician finds the total of the "unadjusted" seasonal indexes is 1150 instead of 1200.What correction must be made to arrive at the adjusted seasonal indexes?

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Question 6

How do the MAD and MSE criteria differ in their approach to evaluating the fit of an estimation equation to a time series?

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Question 7

What is the purpose of using the moving average?

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Question 8

Distinguish between the four components of a time series.Define each component.

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Question 9

Overtime
The quarterly overtime hours (in 1000s)recorded in a large steel mill are shown below. $$\begin{array} { | c | c | c | } 
\hline \text { Year } & \text { Quarter } & \text { Overtime Hours } \
\hline 1995 & 1 & 32 \
& 2 & 15 \
& 3 & 21 \
& 4 & 28 \
1996 & 1 & 35 \
& 2 & 16 \
& 3 & 27 \
& 4 & 29 \
1997 & 1 & 36 \
& 2 & 21 \
& 3 & 25 \
& 4 & 37 \
1998 & 1 & 41 \
& 2 & 29 \
& 3 & 31 \
& 4 & 40 \
\hline
\end{array}$$ Using the regression technique,the linear trend line $\hat{y}$= 21.675 + .854t was computed.
-What do the seasonal indexes tell us?

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The quarterly overtime hours (in 1000s)recorded in...

Question 10

Gashol (a mixture of gasoline and methyl alcohol)sales in Iowa City have been recorded over the past 10 months as shown below:
 $$\begin{array} { | c | c | c | c | c | c | c | c | c | c | c | } 
\hline \text { Manth } & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { June } & \text { Juy } & \text { Aug } & \text { Sep } & \text { Oct } \
\hline \text { Sales } & 75 & 72 & 81 & 92 & 90 & 105 & 112 & 107 & 110 & 93 \
\hline
\end{array}$$ 
-Compute the exponentially smoothed sales with $\alpha$ = 0.4 and $\alpha$ = 0.8 .

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Question 11

In the classical time series model,the time series is made up of (T),(C),(S),and (I)components What do these initials indicate?

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Question 12

Why do we examine time series?

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Question 13

Overtime
The quarterly overtime hours (in 1000s)recorded in a large steel mill are shown below. $$\begin{array} { | c | c | c | } 
\hline \text { Year } & \text { Quarter } & \text { Overtime Hours } \
\hline 1995 & 1 & 32 \
& 2 & 15 \
& 3 & 21 \
& 4 & 28 \
1996 & 1 & 35 \
& 2 & 16 \
& 3 & 27 \
& 4 & 29 \
1997 & 1 & 36 \
& 2 & 21 \
& 3 & 25 \
& 4 & 37 \
1998 & 1 & 41 \
& 2 & 29 \
& 3 & 31 \
& 4 & 40 \
\hline
\end{array}$$ Using the regression technique,the linear trend line 
$\hat{y}$= 21.675 + .854t was computed.
-Calculate the seasonal indexes based on the regression trend line.

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The quarterly overtime hours (in 1000s)recorded in...

Question 14

According to the chapter,regression models based on time series data are especially susceptible to autocorrelation.Why?

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Question 15

In determining monthly seasonal indexes for electrical consumption,the sum of the 12 means for electrical consumption as a percentage of the moving average is 1193.To get the seasonal indexes,each monthly mean is to be multiplied by ________________________.

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Question 16

Identify the following equation: $\mathrm { E } _ { \mathrm { t } } = \alpha \cdot \mathrm { y } _ { \mathrm { t } } + ( 1 - \alpha ) \cdot \mathrm { E } _ { \mathrm { t } - 1 }$ .

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Question 17

The following seasonal indexes and linear trend were computed from five year quarterly sales data.
Trend line is $$\hat { y } = 500 + 30 t , ( t = 1,2,3 , \ldots .20 )$$ $$\begin{array} { | c | c } 
\hline \text { Quarter } & \text { Sea50nal Index } \
\hline 1 & 1.4 \
\hline 2 & 1.2 \
\hline 3 & 0.9 \
\hline 4 & 0.5 \
\hline
\end{array}$$ Forecast the sales for the next four quarters

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Question 18

Table $$\begin{array}{l}
\begin{array} { | l | c | c | c | c | c | c | c | } 
\hline e _ { t } - e _ { t - 1 } & 5 & - 8 & 3 & 2 & 4 & 6 & - 9 \
\hline e _ { t } & 3 & - 5 & - 2 & - 0.4 & 3 & 10 & 0.3 \
\hline
\end{array}\\
\begin{array} { | l | c | c | c | c | c | c | c | } 
\hline e _ { t } - e _ { t - 1 } & 16 & 18 & 21 & - 4 & - 2 & 10 & 13 \
\hline e _ { t } & - 20 & - 8 & 15 & 19 & - 8 & - 6 & - 1 \
\hline
\end{array}
\end{array}$$
-At the 0.01 significance level with n = 15,k = 2,test the hypothesis that there is positive autocorrelation present.What is the appropriate conclusion?

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\begin{array} { | l | c...

Question 19

The means of the quarterly cost as a percentage of moving average are 151.5,77.5,67.3,and 110.6.Prepare the seasonal index for each quarter.

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Question 20

In determining weekly seasonal indexes for electrical consumption,the sum of the 52 means for electrical consumption as a percentage of the moving average is 5193.To get the seasonal indexes,each monthly mean is to be multiplied by ____________________________________.

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Quiz 18: Models for Time Series and Forecasting