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firm has been in business only five years, revenue has increased from $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. O Sales ($1,000s) Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 20 37 92 176 100 202 Sales ($1,000s) 2 (a) Construct a time series plot. 500- 450- 3 400 350 300- 250- 200- 150- 100- 50 0 500 450 400- 350- 300- 250 200- 150- 100 50- 0- 500 450- 400 350 300- 250 200- 150- 0 100- 50 175 13 136 245 26 75 155 326 48 384 82 1234 1 2 3 4 1 23412341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 282 1 2 3 4 1 2341 2 3 4 1 2341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 12341234123412341234 Year 1 Year 2 Year 3 Year 4 Year 5 445 181

firm has been in business only five years, revenue has increased from $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. O Sales ($1,000s) Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 20 37 92 176 100 202 Sales ($1,000s) 2 (a) Construct a time series plot. 500- 450- 3 400 350 300- 250- 200- 150- 100- 50 0 500 450 400- 350- 300- 250 200- 150- 100 50- 0- 500 450- 400 350 300- 250 200- 150- 0 100- 50 175 13 136 245 26 75 155 326 48 384 82 1234 1 2 3 4 1 23412341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 282 1 2 3 4 1 2341 2 3 4 1 2341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 12341234123412341234 Year 1 Year 2 Year 3 Year 4 Year 5 445 181

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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(b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data (in $1,000s). Qrt1 = 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3 = 1 if quarter 3, 0 otherwise. Ŷ₁ = 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 quarter 3 forecast thousand quarter 4 forecast thousand $ $ $ (c) Let t = 1 refer to the observation in Quarter 1 of Year 1; t = 2 to 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 equation to account for seasonal effects and any linear trend in the time series. (Round your numerical values to one decimal place.) Ŷ: 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 $ thousand quarter 3 forecast $ thousand quarter 4 forecast $ thousand
Transcribed Image Text:(b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data (in $1,000s). Qrt1 = 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3 = 1 if quarter 3, 0 otherwise. Ŷ₁ = 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 quarter 3 forecast thousand quarter 4 forecast thousand $ $ $ (c) Let t = 1 refer to the observation in Quarter 1 of Year 1; t = 2 to 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 equation to account for seasonal effects and any linear trend in the time series. (Round your numerical values to one decimal place.) Ŷ: 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 $ thousand quarter 3 forecast $ thousand quarter 4 forecast $ thousand
South Shore Construction 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 $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. O 8 Sales ($1,000s) Sales ($1,000s) Quarter Year 1 Year 2 Year 3 Year 3 37 75 Sales ($1,00 (a) Construct a time series plot. 500T 450- 500 450 1 2 3 400 350- 300+ 250 200+ 150- 100 50 50- 0 4 400 350- 300+ 250 200- 150+ 100- 0 50 5001 450 400 350 300+ 250 200- 150- 100 50 0 500- 450- 400- 350+ 300+ 250 200 150- 100+ 20 of 100 175 13 1 2 3 4 Year 1 1 2 3 4 Year 1 136 245 26 155 326 48 M Year 3 Year/Quarter Year Year 4 Year 5 4 92 202 384 1 2 3 41 2 3 4 1 2 341234 Year 2 Year 4 Year 5 82 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 2 Year 4 Year 5 Year 3 Year/Quarter 282 1 2 3 4 1 2 341 2 3 4 1 2 341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 176 445 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 The time series plot shows only seasonal effects. O The time series plot shows only a linear trend. 181 @ n What type of pattern exists in the data? O The time series plot shows neither a linear trend nor seasonal effects. O The time series plot shows both a linear trend and seasonal effects. (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data (in $1,000s). Qrt1= 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3= 1 if quarter 3, 0 otherwise.
Transcribed Image Text:South Shore Construction 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 $308,000 in the first year of operation to $1,084,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. O 8 Sales ($1,000s) Sales ($1,000s) Quarter Year 1 Year 2 Year 3 Year 3 37 75 Sales ($1,00 (a) Construct a time series plot. 500T 450- 500 450 1 2 3 400 350- 300+ 250 200+ 150- 100 50 50- 0 4 400 350- 300+ 250 200- 150+ 100- 0 50 5001 450 400 350 300+ 250 200- 150- 100 50 0 500- 450- 400- 350+ 300+ 250 200 150- 100+ 20 of 100 175 13 1 2 3 4 Year 1 1 2 3 4 Year 1 136 245 26 155 326 48 M Year 3 Year/Quarter Year Year 4 Year 5 4 92 202 384 1 2 3 41 2 3 4 1 2 341234 Year 2 Year 4 Year 5 82 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Year 2 Year 4 Year 5 Year 3 Year/Quarter 282 1 2 3 4 1 2 341 2 3 4 1 2 341234 Year 1 Year 2 Year 3 Year 4 Year 5 Year/Quarter 176 445 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 The time series plot shows only seasonal effects. O The time series plot shows only a linear trend. 181 @ n What type of pattern exists in the data? O The time series plot shows neither a linear trend nor seasonal effects. O The time series plot shows both a linear trend and seasonal effects. (b) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data (in $1,000s). Qrt1= 1 if quarter 1, 0 otherwise; Qrt2 = 1 if quarter 2, 0 otherwise; Qrt3= 1 if quarter 3, 0 otherwise.
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