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A construction company builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $298,000 in the first year of operation to $1,079,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 Year 2 Year 3 20 37 75 95 131 175 O 500 450 1 (a) Construct a time series plot. 400 2 330 3 4 8 245 21 quarter 3 forecast quarter 4 forecast 150 326 43 400 400+ 350+ 300 300 300 250 250 250 250 200 My www ~ L 200 200 200 150 150 150 150 100 100- 100- 30 50 30 12341234123412341234 12341234123412341234 12341234123412341234 12341234123412341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter Year Quarter Year/Quarter Year Quarter s[ $[ $ $ Year 4 Year 5 92 176 277 445 197 384 77 181 500 450 What type of pattern exists in the data? The time series plot shows both a linear trend and seasonal effects. O The time series plot shows only seasonal effects. O The time series plot shows only a linear trend. O The time series plot shows neither a linear trend nor seasonal effects. 350 Based only on the seasonal effects in the data, compute estimates of quarterly sales (in $1,000s) for year 6. quarter 1 forecast thousand quarter 2 forecast thousand thousand thousand 500 450 400 350 300 100 50 500 O (b) Use the following dummy variables to develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects in the data. x₂-1 if quarter 1, 0 otherwise; x₂-1 if quarter 2, 0 otherwise; x₂-1 if quarter 3, 0 otherwise. 9- 450 Ⓡ Activate Windows Go to Settings to activate Windows

A construction company builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $298,000 in the first year of operation to $1,079,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 Year 2 Year 3 20 37 75 95 131 175 O 500 450 1 (a) Construct a time series plot. 400 2 330 3 4 8 245 21 quarter 3 forecast quarter 4 forecast 150 326 43 400 400+ 350+ 300 300 300 250 250 250 250 200 My www ~ L 200 200 200 150 150 150 150 100 100- 100- 30 50 30 12341234123412341234 12341234123412341234 12341234123412341234 12341234123412341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter Year Quarter Year/Quarter Year Quarter s[ $[ $ $ Year 4 Year 5 92 176 277 445 197 384 77 181 500 450 What type of pattern exists in the data? The time series plot shows both a linear trend and seasonal effects. O The time series plot shows only seasonal effects. O The time series plot shows only a linear trend. O The time series plot shows neither a linear trend nor seasonal effects. 350 Based only on the seasonal effects in the data, compute estimates of quarterly sales (in $1,000s) for year 6. quarter 1 forecast thousand quarter 2 forecast thousand thousand thousand 500 450 400 350 300 100 50 500 O (b) Use the following dummy variables to develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects in the data. x₂-1 if quarter 1, 0 otherwise; x₂-1 if quarter 2, 0 otherwise; x₂-1 if quarter 3, 0 otherwise. 9- 450 Ⓡ Activate Windows Go to Settings to activate Windows

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(c) Let t = 1 refer to the observation in quarter 1 of year 1; t = 2 refer to the observation in quarter 2 of year 1; ... and t = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and t, develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects and any linear trend in the time series. (Round your numerical values to one decimal place.) Ŷ₂ = Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales (in $1,000s) for year 6. (Round your answers to the nearest thousand dollars.) quarter 1 forecast $ thousand quarter 2 forecast $ quarter 3 forecast $ quarter 4 forecast $ thousand thousand thousand
Transcribed Image Text:(c) Let t = 1 refer to the observation in quarter 1 of year 1; t = 2 refer to the observation in quarter 2 of year 1; ... and t = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables defined in part (b) and t, develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects and any linear trend in the time series. (Round your numerical values to one decimal place.) Ŷ₂ = Based upon the seasonal effects in the data and linear trend, compute estimates of quarterly sales (in $1,000s) for year 6. (Round your answers to the nearest thousand dollars.) quarter 1 forecast $ thousand quarter 2 forecast $ quarter 3 forecast $ quarter 4 forecast $ thousand thousand thousand
A construction company builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $298,000 in the first year of operation to $1,079,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 O 500 450 400 350 (a) Construct a time series plot. 200 1 2 150 3 300+ 250- 100 4 50 20 95 175 Year 2 quarter 2 forecast quarter 3 forecast quarter 4 forecast 37 131 245 21 Year 3 75 150 326 500- 450 400- 350 300 250 200 Mm WW NU 150- 100- 50 0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 3 Year 4 Year 5 Year/Quarter Year 1 Year 2 Year 1 Year 2 Year 4 Year 5 Year 3 Year/Quarter 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 43 Year 4 92 197 384 thousand thousand 77 thousand thousand Year 5 176 277 445 181 500 450 400+ 350 300- 250- 200- What type of pattern exists in the data? The time series plot shows both a linear trend and seasonal effects. O The time series plot shows only seasonal effects. O The time series plot shows only a linear trend. O The time series plot shows neither a linear trend nor seasonal effects. 150- 100- 50 Based only on the seasonal effects in the data, compute estimates of quarterly sales (in $1,000s) for year 6. quarter 1 forecast $ $ $ $ 0 500- 450 400- 350 300- 250- 200- 150- 100 50 0 (b) Use the following dummy variables to develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects in the data. x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise. ŷ= Ⓡ✓ 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year/Quarter Ⓡ Activate Windows Go to Settings to activate Windows.
Transcribed Image Text:A construction company builds permanent docks and seawalls along the southern shore of Long Island, New York. Although the firm has been in business only five years, revenue has increased from $298,000 in the first year of operation to $1,079,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 O 500 450 400 350 (a) Construct a time series plot. 200 1 2 150 3 300+ 250- 100 4 50 20 95 175 Year 2 quarter 2 forecast quarter 3 forecast quarter 4 forecast 37 131 245 21 Year 3 75 150 326 500- 450 400- 350 300 250 200 Mm WW NU 150- 100- 50 0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 3 Year 4 Year 5 Year/Quarter Year 1 Year 2 Year 1 Year 2 Year 4 Year 5 Year 3 Year/Quarter 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 43 Year 4 92 197 384 thousand thousand 77 thousand thousand Year 5 176 277 445 181 500 450 400+ 350 300- 250- 200- What type of pattern exists in the data? The time series plot shows both a linear trend and seasonal effects. O The time series plot shows only seasonal effects. O The time series plot shows only a linear trend. O The time series plot shows neither a linear trend nor seasonal effects. 150- 100- 50 Based only on the seasonal effects in the data, compute estimates of quarterly sales (in $1,000s) for year 6. quarter 1 forecast $ $ $ $ 0 500- 450 400- 350 300- 250- 200- 150- 100 50 0 (b) Use the following dummy variables to develop an estimated regression equation for the time series data (in $1,000s) to account for seasonal effects in the data. x₁ = 1 if quarter 1, 0 otherwise; x₂ = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise. ŷ= Ⓡ✓ 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 5 Year 1 Year 2 Year 3 Year 4 Year/Quarter Ⓡ Activate Windows Go to Settings to activate Windows.
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