Do not get output for shell script using if and for

You need to double quote $result rather than single quote, otherwise it won't expand.

[ '$result' == 'yes' ] will never evaluate to true because it is trying to compare the literal $result to the literal yes.

Additionally, as Kusalananda points out; the == operator is for bash test constructs [[ while the = operator is for standard (POSIX) test constructs [.

Therefore, you should change that line to: [ "$result" = 'yes' ]

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Another good tool to know about is the set builtin and its -x switch which can be used to trace your scripts. If you add set -x to the top of your original script and run it you will see the following printed out:

+ read -e -i no -p 'Install? ' result
Install? yes
+ '[' '$result' == yes ']'

As you can see, it is trying to compare '$result' to 'yes'. When quoted correctly, you wouldn't see the variable $result but rather it's expansion like so:

+ read -e -i no -p 'Install? ' result
Install? yes
+ '[' yes == yes ']'
+ subs=('one' 'two')
+ declare -a subs
+ for sub in '"${subs[@]}"'
+ echo one
one
+ for sub in '"${subs[@]}"'
+ echo two
two

Whenever you are banging your head against the wall with a script you should turn on set -x and trace what it's doing and where it's going wrong.

Following @Jesse_b's answer.

Why do I need to double quote the variable?

The difference between single and double quotes:

Enclosing characters in single quotes preserves the literal value of each character within the quotes. A single quote may not occur between single quotes, even when preceded by a backslash.

Enclosing characters in double quotes preserves the literal value of all characters within the quotes, with the exception of $, `, \, and, when history expansion is enabled, !.

From man bash

You need to remember this well, it will save you the trouble of debugging for a while.