Find the MSE for question (b) The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The following figures provide a time series of the cost per unit for the firm's leading product over the past eight years.### Data Table| Year | Cost/Unit ($) ||------|---------------|| 1 | 20.00 || 2 | 24.50 || 3 | 28.20 || 4 | 27.50 || 5 | 26.60 || 6 | 30.00 || 7 | 31.00 || 8 | 36.00 |### Instruction(a) Choose the correct time series plot.### Time Series Plots- **Plot (i):** The line graph shows a general upward trend. It starts at around $20 and increases to $36 over eight years, with a slight dip between years 3 and 5.- **Plot (ii):** This plot shows an overall increasing trend with a more significant dip between years 3 and 5.- **Plot (iii):** This graph incorrectly shows a downward trend where costs start high and decrease over time.- **Plot (iv):** This plot also incorrectly shows a decrease in costs, not aligning with the data.### AnalysisBased on the data provided in the table, Plot (i) correctly represents the time series with an overall increasing trend in manufacturing costs per unit over eight years, allowing for a minor fluctuation. **Developing Three-Month and Four-Month Moving Averages for a Time Series**Below is a table showing the sales data, along with three-month and four-month moving averages computed for the series:| Month | Sales | 3 Month Moving Average | 4 Month Moving Average ||-------|-------|------------------------|-------------------------|| 1 | 9.6 | | || 2 | 9.4 | | || 3 | 9.2 | | || 4 | 9.7 | 9.40 | || 5 | 9.8 | 9.43 | 9.48 || 6 | 9.9 | 9.57 | 9.53 || 7 | 9.7 | 9.80 | 9.65 || 8 | 10.6 | 9.80 | 9.78 || 9 | 9.9 | 10.07 | 10.00 || 10 | 9.6 | 10.07 | 10.03 || 11 | 9.7 | 10.03 | 9.95 || 12 | 9.5 | 9.73 | 9.95 |The table contains check marks next to each calculated moving average value, indicating their correctness.**Mean Square Errors (MSE):**- **3-Month Moving Average MSE:** 0.170- **4-Month Moving Average MSE:** 0.229There are error messages (x) indicating that the entered MSE values may be incorrect.When calculating moving averages:- **Three-Month Moving Average:** The average of sales over a period of three consecutive months.- **Four-Month Moving Average:** The average of sales over a period of four consecutive months.**Instructions:**Enter the Mean Square Errors for the three-month and four-month moving average forecasts. If needed, round your answers to three decimal digits.

First, we find the error and squared errors Month Sales 3MMA E E^2 1 9.6 2 9.4 3 9.2 4 9.7 9.4 0.3 0.09 5 9.8 9.43 0.37 0.1369 6 9.9 9.57 0.33 0.1089 7 9.7 9.8 -0.1 0.01 8 10.6 9.8 0.8 0.64 9 9.9 10.07 -0.17 0.0289 10 9.6 10.07 -0.47 0.2209 11 9.7 10.03 -0.33 0.1089 12 9.5 9.73 -0.23 0.0529The MSE for the 3 month moving average forecasts is MSE=∑E212=0.1553 So the required MSE is 0.1533.Proceeding in a similar manner for a 4-month moving average Month Sales 4MMA E E^2 1 9.6 2 9.4 3 9.2 4 9.7 5 9.8 9.48 0.32 0.1024 6 9.9 9.53 0.37 0.1369 7 9.7 9.65 0.05 0.0025 8 10.6 9.78 0.82 0.6724 9 9.9 10 -0.1 0.01 10 9.6 10.03 -0.43 0.1849 11 9.7 9.95 -0.25 0.0625 12 9.5 9.95 -0.45 0.2025 The MSE for the 4 month moving average forecasts is MSE=∑E212=0.17176 So the required MSE is 0.17176.