Q$3.$ Information, Information Gain Function, $\backslash$& Rank

The following data reports past observations on weather conditions and the decision to Play or not. We are interested in whether the weather conditions can be used to predict the Play or not decision. The excel version of the dataset is available for download on Canvas $\backslash (\backslash$rightarrow $\backslash )$ Assignment $1.$

$($Excel version: BANA$273\_2020\_$HW$1$Q$3)$

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Outloo

$\backslash [$

$\backslash$mathrm$\{$k$\}$

$\backslash ]$ & Temperature & Humidit

$\backslash [$

$\backslash$mathrm$\{$y$\}$

$\backslash ]$ & Windy & Play $\backslash \backslash$

$\backslash$hline sunny & hot & high & FALSE & no $\backslash \backslash$

$\backslash$hline sunny & hot & high & TRUE & no $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

overcas $\backslash \backslash$

$\backslash ($ t $\backslash )$

$\backslash$end$\{$tabular$\}$ & hot & high & FALSE & yes $\backslash \backslash$

$\backslash$hline rainy & mild & high & FALSE & yes $\backslash \backslash$

$\backslash$hline rainy & cool & normal & FALSE & yes $\backslash \backslash$

$\backslash$hline rainy & cool & normal & TRUE & no $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

overcas $\backslash \backslash$

t

$\backslash$end$\{$tabular$\}$ & cool & normal & TRUE & yes $\backslash \backslash$

$\backslash$hline sunny & mild & high & FALSE & no $\backslash \backslash$

$\backslash$hline sunny & cool & normal & FALSE & yes $\backslash \backslash$

$\backslash$hline rainy & mild & normal & FALSE & yes $\backslash \backslash$

$\backslash$hline sunny & mild & normal & TRUE & yes $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

overcas $\backslash \backslash$

t

$\backslash$end$\{$tabular$\}$ & mild & high & TRUE & yes $\backslash \backslash$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$l$\}$

overcas $\backslash \backslash$

t

$\backslash$end$\{$tabular$\}$ & hot & normal & FALSE & yes $\backslash \backslash$

$\backslash$hline rainy & mild & high & TRUE & no $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

a$.$ Based on the table, what is the entropy of "Play"?

b$.$ Create contingency tables given each of the following attributes:

$1)$ Temperature

$2)$ Humidity

$3)$ Windy

c$.$ Based on the contingency tables, calculate the information gain of each of the above $3$ attributes $($i$.$e$.,$ Temperature, Humidity, and Windy$)$

d$.$ Please rank the $3$ attributes from the most informative to the least informative for predicting Play