Scenario Background

In the year $2400,$ the nation of Novaterra faces significant challenges in ensuring its national defense. The key to their defense strategy lies in the deployment of "Iron Man suits," technologically advanced exoskeletons that enhance soldiers' capabilities. The government needs to forecast the required number of these suits accurately to ensure national security without overspending. Your task is to assist the nation's leaders in making these critical decisions by applying operations management techniques.

Part $1$: Simple Regression Forecasting

The government has collected data on the number of Iron Man suits required over the past $10$ years. The data is shown below:

$\backslash$table$[[$Year$,$Number of Threats,Number of Suits Required$],[2390,50,500],[2391,55,550],[2392,53,530],[2393,60,600],[2394,62,620],[2395,58,580],[2396,65,650],[2397,67,700],[2398,70,750]]$

Question $1$: Using simple regression, develop a model to predict the number of Iron Man suits required based on the number of threats.

a$.$ Plot the data points and fit a simple linear regression line.

b$.$ Calculate the regression equation.

c$.$ Using your model, predict the number of Iron Man suits required if the number of threats in $2400$ is expected to be $80.$