Question

Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series:

Quarter	Seasonal Index
Q1	71.7
Q2	84.7
Q3	107.1

Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4.


Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below:

	Coefficients
Intercept	2,215
Time	75.9

What is the trend projection of the series for period 43? (please round your answer to 1 decimal place)

5 points

Question 28

Suppose the following are the seasonal indices for the first three quarters of the year for a quarterly series:

Quarter	Seasonal Index
Q1	70.7
Q2	89.8
Q3	105.9

Remember that the seasonal indices should average 100 so you should be able to infer the seasonal index for Q4.


Furthermore, suppose that the estimated coeffcients from a regression of the deseasonalized series on Time are given below:

	Coefficients
Intercept	2,922
Time	66.1

What is the forecast for period 111, if period 111 is a Q1? (please round your answer to 1 decimal place)

Answer 1

27) Since the seasonal index should average to 100 and we are given indices for Q1, Q2, and Q3. hence seasonal index for Q4 can be calculated using the following calculations

So, the seasonal index for Q4 = 136.5

The estimated coefficients from a regression of the deseasonalized series on Time are given, Thus the regression equation will be following using intercept and slope coefficient of the time period,

Y = 2215 + 75.9t where t is the period

What is the trend projection of the series for period 43? Use the linear regression calculated previously to extrapolate out into the future.

Y = 2215 + 75.9*43 = 5478.7

Since the slope is positive we will see trend increasing in the positive direction.

28) Since the seasonal index should average to 100and we are given indices for Q1, Q2, and Q3. hence seasonal index for Q4 can be calculated using the following calculations

So, the seasonal index for Q4 = 133.6

The estimated coefficients from a regression of the deseasonalized series on Time are given below:

	Coefficients
Intercept	2,922
Time	66.1

What is the forecast for period 111, if the period 111 is a Q1?

First, we calculate the trend projection for period 111 using the coefficients of the regression equation

Y = 2922 + 66.1*t = 2922+66.1*111 = 10259.1

Multiply the linear forecast you made by the seasonal factors to get a seasonalized forecast.

Since period 111 is in Q1 and seasonal index of Q1 is 70.7 or 0.707

Thus seasonalized forecast for period 111 = 10259.1*0.707 = 7253.184

Please like the solution if it helped you. thank you.