Part $2$: Multiple Regression Forecasting

Realizing the need for more sophisticated forecasting, the government decides to incorporate multiple factors that might influence the required number of Iron Man suits. They have identified the following six variables:

Number of Threats $(T)$

Technology Advancement Index $($TAI$)$

Defense Budget $($DB$)$

Political Stability Index $($PSI$)$

International Support Level $($ISL$)$

Population Density in Urban Areas $($PDUA$)$

Historical data for these variables over the past $10$ years is provided below:

$\backslash$table$[[$Year$,\backslash$table$[[$Number of$],[$Threats $($T$)]],\backslash$table$[[$Technology$],[$Advancement$],[$Index $($TAL$)]],\backslash$table$[[$Defense Budget$],[($DB$,$ trillion$],[$credits$)]],\backslash$table$[[$Political Stability$],[$Index $($PSI$)]],\backslash$table$[[$International$],[$Support Level$],[($ISL$)]],\backslash$table$[[$Population$],[$Density in Urban$],[$Areas $($PDUA$,],[$people$/\frac{?}{k{m}^2})]],\backslash$table$[[$Number of Suits$],[$Required$]]],[2390,50,85,1\mathrm{.}0,70,50,100,500],[2391,55,86,1\mathrm{.}1,72,52,102,550],[2392,53,87,1\mathrm{.}05,71,51,101,530],[2393,60,88,1\mathrm{.}2,73,53,103,600],[2394,62,89,1\mathrm{.}25,74,54,104,620],[2395,58,90,1\mathrm{.}15,72,52,102,580],[2396,65,91,1\mathrm{.}3,75,55,105,650],[2397,67,92,1\mathrm{.}35,76,56,106,670],[2398,70,93,1\mathrm{.}4,77,58,107,700],[2399,75,94,1\mathrm{.}5,78,60,108,750]]$

Question $2$: Develop a multiple regression model to predict the number of Iron Man suits required. Using your model, predict the number of suits needed for $2400,$ given the following expected values:

Number of Threats $(T)$:$80$

Technology Advancement Index $($TAI$)$: $95$

Defense Budget $($DB$)$: $1\mathrm{.}2$ trillion credits

Political Stability Index $($PSI$)$: $75$

International Support Level $($ISL$.)$: $65$

Population Density in Urban Areas $($PDUA$)$ : $110$