Final answer:
To answer the student's question about mean square errors, you should calculate the moving averages, find the deviations, square them, and then compute the mean of these squares. Round appropriately and use tools like a calculator or computer program for assistance.
Step-by-step explanation:
The question involves analyzing data, calculating mean square errors, and perhaps writing a linear equation. To calculate the mean square error (MSE) for the three-month and four-month moving average forecasts, you must follow these steps:
Firstly, calculate the moving averages for three months and four months respectively.
Secondly, compare these averages with the actual data to find the deviations for each period.
Then, square these deviations to get the square errors.
Finally, calculate the mean of these square errors to obtain the MSE for each forecast.
Round your answers to three decimal digits as required. Remember that using a calculator or a suitable computer program can greatly facilitate this computation. Keep in mind that graphical methods can be used to verify these calculations; however, there is always some uncertainty when extracting data from graphs.
Concerning the other parts of the question that mention standard error and distribution, the standard error of the sample mean is a measure of the amount of variability in the sample mean from sample to sample. The distribution of the sample mean would typically be a normal distribution, especially if the sample size is large, due to the Central Limit Theorem.