Answered: Quarter Year 1 Year 2 Year 3 1 4 6 7 2…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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Consider the following time series data.

Quarter	Year 1	Year 2	Year 3
1	4	6	7
2	0	1	4
3	3	5	6
4	5	7	8

(a)

Choose the correct time series plot.

(i)
(ii)
(iii)
(iv)

What type of pattern exists in the data?

(b)

Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300). If the constant is "1" it must be entered in the box. Do not round intermediate calculation.

ŷ = + Qtr1 + Qtr2 + Qtr3

(c)

Compute the quarterly forecasts for next year based on the model you developed in part (b).

If required, round your answers to three decimal places. Do not round intermediate calculation.

Year	Quarter	F_t
4	1
4	2
4	3
4	4

(d)

Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank (Example: -300).

ŷ = + Qtr1 + Qtr2 + Qtr3 + t

(e)

Compute the quarterly forecasts for next year based on the model you developed in part (d).

Do not round your interim computations and round your final answer to three decimal places.

Year	Quarter	Period	F_t
4	1	13
4	2	14
4	3	15
4	4	16

(f)

Calculate the MSE for the regression models developed in parts (b) and (d).

If required, round your intermediate calculations and final answer to three decimal places.

	Model developed in part (b)	Model developed in part (d)
MSE

Is the model you developed in part (b) or the model you developed in part (d) more effective?

The model developed in is more effective because it has the MSE

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