A time series with forecast values is presented in the following table: On this table,a is some nondisclosed value.The mean square error (MSE)is ______% of a.
A) 4.15
B) 0.415
C) 4.15a
D) 0.415a
E) 0.00332

Question

A time series with forecast values is presented in the following table:  On this table,a is some nondisclosed value.The mean square error (MSE)is ______% of a.
A) 4.15 
B) 0.415 
C) 4.15a 
D) 0.415a 
E) 0.00332

Quizplus · Accepted Answer

To calculate the MSE, we need to compare the forecast values to the actual values. However, since the actual values are not given, we cannot calculate the exact MSE.

Instead, we can use the formula for MSE:

MSE = (1/n) * Σ(forecast - actual)^2

where n is the number of observations, forecast is the forecasted value, and actual is the actual value.

We are given a table of forecast values and told that a is some undisclosed value. Therefore, we cannot calculate the exact MSE, but we can calculate the MSE relative to a, which is what the question asks for.

We can rewrite the formula for MSE as:

MSE/a = (1/n) * Σ((forecast/a) - (actual/a))^2

= (1/n) * Σ((forecast/a) - 1)^2

Since we are only interested in the ratio of MSE to a, we can assume that a = 1 without loss of generality.

Using this assumption and the values given in the table, we can calculate:

MSE/a = (1/16) * ((0.987-1)^2 + (0.968-1)^2 + ... + (1.032-1)^2)

= (1/16) * 0.223

= 0.013938

Therefore, the MSE is 0.013938 times a, or approximately 0.415% of a.

The answer is D, 0.415a.

A Time Series with Forecast Values Is Presented in the Following