A company has developed a linear trend regression model based on 16 quarters of data.The independent variable is the measure of time (t = 1 thru 16 where quarter 1 is winter quarter,2 is spring,etc.).The company has also developed seasonal indexes for each quarter as follows: The linear trend forecast equation is: = 120 + 56t. Given this information,what is the seasonally adjusted forecast for period 19?
A)1,064
B)1,184
C)828.80
D)986.7

Question

A company has developed a linear trend regression model based on 16 quarters of data.The independent variable is the measure of time (t = 1 thru 16 where quarter 1 is winter quarter,2 is spring,etc.).The company has also developed seasonal indexes for each quarter as follows:  The linear trend forecast equation is:  = 120 + 56t. Given this information,what is the seasonally adjusted forecast for period 19?
A)1,064 
B)1,184 
C)828.80 
D)986.7

Quizplus · Accepted Answer

Since the question asks for the seasonally adjusted forecast, we need to take into account the seasonal indexes provided. To adjust the forecast for the 19th period (which corresponds to the winter quarter of year 5), we need to multiply the linear regression forecast (which is 120 + 56t) by the seasonal index for the winter quarter (which is 0.74). Therefore, the seasonally adjusted forecast for period 19 is:

Seasonally adjusted forecast = (120 + 56t) x Winter seasonal index
= (120 + 56(19)) x 0.74
= 828.80

So the answer is C, 828.80.

A Company Has Developed a Linear Trend Regression Model Based