Consider the following time series data: Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy: a. Mean absolute error b. Mean squared error c. Mean absolute percentage error d. What is the forecast for week 7?

Question

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Answer 1

Textbook Question

Chapter 5, Problem 1P

Consider the following time series data:

Chapter 5, Problem 1P, Consider the following time series data:

Using the naïve method (most recent value) as the forecast

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for week 7?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

(a)

Expert Solution

To determine

Find the value of mean absolute error.

Answer to Problem 1P

The mean absolute error is 4.4.

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

(b)

Expert Solution

To determine

Obtain the mean squared error.

Answer to Problem 1P

The mean squared error is 20.8.

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

(c)

Expert Solution

To determine

Find the mean absolute percentage error.

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38

MAPE=∑i=k+1n|yiei|100n−k=159.385=31.88

Thus, the mean absolute percentage error is 31.88.

(d)

Expert Solution

To determine

Obtain the forecast for week 7.

Answer to Problem 1P

The forecast for week 7 is 14.

Explanation of Solution

The forecast for week 7 is obtained as given below:

y^7=y6=14

Thus, the forecast for week 7 is 14.

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Answer 2

Textbook Question

Chapter 5, Problem 1P

Consider the following time series data:

Chapter 5, Problem 1P, Consider the following time series data:

Using the naïve method (most recent value) as the forecast

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for week 7?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

(a)

Expert Solution

To determine

Find the value of mean absolute error.

Answer to Problem 1P

The mean absolute error is 4.4.

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

(b)

Expert Solution

To determine

Obtain the mean squared error.

Answer to Problem 1P

The mean squared error is 20.8.

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

(c)

Expert Solution

To determine

Find the mean absolute percentage error.

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38

MAPE=∑i=k+1n|yiei|100n−k=159.385=31.88

Thus, the mean absolute percentage error is 31.88.

(d)

Expert Solution

To determine

Obtain the forecast for week 7.

Answer to Problem 1P

The forecast for week 7 is 14.

Explanation of Solution

The forecast for week 7 is obtained as given below:

y^7=y6=14

Thus, the forecast for week 7 is 14.

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Answer 3

Textbook Question

Chapter 5, Problem 1P

Consider the following time series data:

Chapter 5, Problem 1P, Consider the following time series data:

Using the naïve method (most recent value) as the forecast

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for week 7?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

(a)

Expert Solution

To determine

Find the value of mean absolute error.

Answer to Problem 1P

The mean absolute error is 4.4.

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

(b)

Expert Solution

To determine

Obtain the mean squared error.

Answer to Problem 1P

The mean squared error is 20.8.

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

(c)

Expert Solution

To determine

Find the mean absolute percentage error.

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38

MAPE=∑i=k+1n|yiei|100n−k=159.385=31.88

Thus, the mean absolute percentage error is 31.88.

(d)

Expert Solution

To determine

Obtain the forecast for week 7.

Answer to Problem 1P

The forecast for week 7 is 14.

Explanation of Solution

The forecast for week 7 is obtained as given below:

y^7=y6=14

Thus, the forecast for week 7 is 14.

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Answer 4

Textbook Question

Chapter 5, Problem 1P

Consider the following time series data:

Chapter 5, Problem 1P, Consider the following time series data:

Using the naïve method (most recent value) as the forecast

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

a. Mean absolute error
b. Mean squared error
c. Mean absolute percentage error
d. What is the forecast for week 7?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

(a)

Expert Solution

To determine

Find the value of mean absolute error.

Answer to Problem 1P

The mean absolute error is 4.4.

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

(b)

Expert Solution

To determine

Obtain the mean squared error.

Answer to Problem 1P

The mean squared error is 20.8.

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

(c)

Expert Solution

To determine

Find the mean absolute percentage error.

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38

MAPE=∑i=k+1n|yiei|100n−k=159.385=31.88

Thus, the mean absolute percentage error is 31.88.

(d)

Expert Solution

To determine

Obtain the forecast for week 7.

Answer to Problem 1P

The forecast for week 7 is 14.

Explanation of Solution

The forecast for week 7 is obtained as given below:

y^7=y6=14

Thus, the forecast for week 7 is 14.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

Find the value of mean absolute error.

Answer to Problem 1P

The mean absolute error is 4.4.

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

(b)

Expert Solution

To determine

Obtain the mean squared error.

Answer to Problem 1P

The mean squared error is 20.8.

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

(c)

Expert Solution

To determine

Find the mean absolute percentage error.

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38

MAPE=∑i=k+1n|yiei|100n−k=159.385=31.88

Thus, the mean absolute percentage error is 31.88.

(d)

Expert Solution

To determine

Obtain the forecast for week 7.

Answer to Problem 1P

The forecast for week 7 is 14.

Explanation of Solution

The forecast for week 7 is obtained as given below:

y^7=y6=14

Thus, the forecast for week 7 is 14.

Answer 8

(a)

Expert Solution

To determine

Find the value of mean absolute error.

Answer to Problem 1P

The mean absolute error is 4.4.

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Find the value of mean absolute error.

Answer 13

Answer to Problem 1P

The mean absolute error is 4.4.

Answer 14

Explanation of Solution

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error
1	18
2	13	18	−5	5
3	16	13	3	3
4	11	16	−5	5
5	17	11	6	6
6	14	17	−3	3
			Total	22

MAE=∑|er|n−k=225=4.4

Thus, the mean absolute error is 4.4.

Answer 15

(b)

Expert Solution

To determine

Obtain the mean squared error.

Answer to Problem 1P

The mean squared error is 20.8.

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Obtain the mean squared error.

Answer 20

Answer to Problem 1P

The mean squared error is 20.8.

Answer 21

Explanation of Solution

The mean squared error is obtained as given below:

Absolute Value of Forecast Error	Squared Forecast Error
5	25
3	9
5	25
6	36
3	9
22	104

MSE=∑|er|2n−k=1045=20.8

Thus, the mean squared error is 20.8.

Answer 22

(c)

Expert Solution

To determine

Find the mean absolute percentage error.

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38

MAPE=∑i=k+1n|yiei|100n−k=159.385=31.88

Thus, the mean absolute percentage error is 31.88.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Find the mean absolute percentage error.

Answer 27

Answer to Problem 1P

The mean absolute percentage error is 31.88.

Answer 28

Explanation of Solution

The mean absolute percentage error is obtained is given below:

Week	Time Series Value (yi)	Forecast	Forecast Error ei	Percentage Error yiei	Absolute percentage Error \|yiei\|
1	18
2	13	18	−5	−38.46	38.46
3	16	13	3	18.75	18.75
4	11	16	−5	−45.45	45.45
5	17	11	6	35.29	35.29
6	14	17	−3	−21.43	21.43
			Total	−51.30	159.38