QUESTION 7- 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. Quarter Year 1 Year 2 Year 3 Year 4 Year 5
1 20 37 75 92 176
2 100 136 155 202 282
3 175 245 326 384 445
4 13 26 48 82
181

Let Period = 1 refer to the observation in quarter 1 of year 1; Period = 2 refer to the observation in quarter 2 of year 1; ... and Period = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables (Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise) and the variable Period, develop an equation to account for seasonal effects and any linear trend in the time series.

Based on the seasonal effects in the data and linear trend estimated above, compute estimates of quarterly sales for year 7.

Quarter Period (t) Revenue ($1,000s)
Qtr1 25
Qtr2 26
Qtr3 27
Qtr4 28

QUESTION 8-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.

Quarter Year 1 Year 2 Year 3 Year 4 Year 5
1 20 37 75 92 176
2 100 136 155 202 282
3 175 245 326 384 445
4 13 26 48 82
181

Let Period = 1 refer to the observation in quarter 1 of year 1; Period = 2 refer to the observation in quarter 2 of year 1; ... and Period = 20 refer to the observation in quarter 4 of year 5. Using the dummy variables (Qtr1 = 1 if quarter 1, 0 otherwise; Qtr2 = 1 if quarter 2, 0 otherwise; Qtr3 = 1 if quarter 3, 0 otherwise) and the variable Period, develop an equation to account for seasonal effects and any linear trend in the time series.

Estimate MSE using the model from #7.