Question $7$ options:

An insurance company is assessing property premiums in Melbourne suburbs for content and building insurance. The company is considering the following criteria:

Postal code

Age of the property

Lockable garage

Locks and security systems in the property

The company has hired a master student from Deakin to do the assessment. The student has been trained to use aggregation functions and decided to use such functions to assess the criteria. The student has used a large database of properties in Melbourne. Using fitting functions in R they found the weights for the following three models:

a$.$ WAM, w$=<0\mathrm{.}1,0\mathrm{.}3,0\mathrm{.}2,0\mathrm{.}4>,$ RMSE$=9\%,$ AAE$=82\%,$ Pearson CC $=92\%$; SCC$=87\%$;

b$.$ WPM$,$ p$=2,$ w$=<0\mathrm{.}3,0\mathrm{.}1,0\mathrm{.}1,0\mathrm{.}5>,$ RMSE$=7\%,$ AAE$=6\mathrm{.}5\%,$ Pearson CC$=92\%,$ SCC$=88\%$;

c$.$ OWA, w$=<0\mathrm{.}2,0\mathrm{.}3,0\mathrm{.}1,0\mathrm{.}4>,$ RMSE$=8\mathrm{.}2\%,$ AAE$=7\mathrm{.}2\%,$ Pearson CC$=90\%,$ SCC$=86\%.$

$(1)$ Which is the best performing model? Please type $"$a$","$b$"$ or $"$c$".$

$(2)$ Which is the most important of the fourth criteria for the best performing model? Please type $"$A$","$B$","$C$"$ or $"$D$".$

$(3)$ Is criterium C more important than either criterium D or criterium A$?$ Please type "Yes" or $"$No$".$

$(4)$ Does the model tend to high or low values? Please type "high" or "low".