A construction company builds permanent docks and seawalls along the southern shore of Long Island, New...

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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 $318,000 in the first year of operation to $1,094,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 25 42 80 80 97 181 2 105 141 160 207 287 3 170 240 321 379 440 4 18 31 53 87 186 (a) Construct a time series plot. What type of pattern exists in the data? The time series plot shows both a linear trend and seasonal effects. The time series plot shows only seasonal effects. The time series plot shows neither a linear trend nor seasonal effects. The time series plot shows only a linear trend. (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. x = 1 if quarter 1, 0 otherwise; x2 = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise. = (c) Based on the model you developed in part (b), compute estimates of quarterly sales (in $1,000s) for year 6. quarter 1 forecast $ thousand quarter 2 forecast quarter 3 forecast $ thousand quarter 4 forecast $ $ thousand thousand (d) Lett 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.) (e) Based on the seasonal effects in the data and linear trend estimated in part (c), 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 quarter 4 forecast $ $ thousand thousand (f) Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer. The model in part (b) appears to be more effective since it has a higher MSE than the model in part (d). The model in part (b) appears to be more effective since it has a lower MSE than the model in part (d). The model in part (b) appears to be more effective since there is no linear trend visible in the data. The model in part (d) appears to be more effective since it has more variables than the model in part (b). The model in part (d) appears to be more effective since it has a lower MSE than the model in part (b). 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 $318,000 in the first year of operation to $1,094,000 in the most recent year. The following data show the quarterly sales revenue in thousands of dollars. Quarter Year 1 Year 2 Year 3 Year 4 Year 5 1 25 42 80 80 97 181 2 105 141 160 207 287 3 170 240 321 379 440 4 18 31 53 87 186 (a) Construct a time series plot. What type of pattern exists in the data? The time series plot shows both a linear trend and seasonal effects. The time series plot shows only seasonal effects. The time series plot shows neither a linear trend nor seasonal effects. The time series plot shows only a linear trend. (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. x = 1 if quarter 1, 0 otherwise; x2 = 1 if quarter 2, 0 otherwise; x3 = 1 if quarter 3, 0 otherwise. = (c) Based on the model you developed in part (b), compute estimates of quarterly sales (in $1,000s) for year 6. quarter 1 forecast $ thousand quarter 2 forecast quarter 3 forecast $ thousand quarter 4 forecast $ $ thousand thousand (d) Lett 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.) (e) Based on the seasonal effects in the data and linear trend estimated in part (c), 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 quarter 4 forecast $ $ thousand thousand (f) Is the model you developed in part (b) or the model you developed in part (d) more effective? Justify your answer. The model in part (b) appears to be more effective since it has a higher MSE than the model in part (d). The model in part (b) appears to be more effective since it has a lower MSE than the model in part (d). The model in part (b) appears to be more effective since there is no linear trend visible in the data. The model in part (d) appears to be more effective since it has more variables than the model in part (b). The model in part (d) appears to be more effective since it has a lower MSE than the model in part (b).