Question

the demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for this time series using the following simple linear trend equation: trt = 12 + 2t. What are the forecast errors for the 5th and 6th years?

Answer 1

Answer and explanation:

Given : The demand for a product for the last six years has been 15, 15, 17, 18, 20, and 19. The manager wants to predict the demand for this time series using the following simple linear trend equation : $tr_t = 12 + 2t$

To find : What are the forecast errors for the 5th and 6th years?

Solution :

Data : 15, 15, 17, 18, 20, and 19.

The simple linear trend equation is given as, $tr_t = 12 + 2t$

For t = 5 years

$tr_t = 12 + 2(5)$

$tr_t = 12 +10$

$tr_t = 22$

Observed $tr_t = 20$

Predicted $tr_t = 22$

Forecast error = Observed – Predicted = 20 – 22 = -2

Absolute forecast error = |-2| = 2 .

For t = 6 years

$tr_t = 12 + 2(6)$

$tr_t = 12 +12$

$tr_t = 24$

Observed $tr_t = 19$

Predicted $tr_t = 24$

Forecast error = Observed – Predicted = 19 – 24 = -5

Absolute forecast error = |-5| = 5.