Step 1: Understand the term asked.
We must find the group that shows the $-\text{I}$ effect. A $-\text{I}$ group pulls the shared bonding electrons towards itself, that is, it withdraws electrons.
Step 2: Recall what causes a $-\text{I}$ effect.
Groups that contain electronegative atoms like oxygen, or that carry a positive charge, pull electrons away. They are electron withdrawing.
Step 3: Recall what causes a $+\text{I}$ effect.
Simple alkyl groups like methyl, ethyl, and propyl push electrons toward the rest of the molecule. They are electron donating, the opposite of what we want.
Step 4: Test the alkyl options.
Options 2, 3, and 4 are $\text{-CH}_3$, $\text{-C}_2\text{H}_5$, and $\text{-C}_3\text{H}_7$. These are all alkyl groups, so they show the $+\text{I}$ effect, not $-\text{I}$. So none of these is the answer.
Step 5: Test the ester option.
The group $-\text{COOR}$ has a carbon joined to two oxygen atoms. Oxygen is very electronegative, so this group strongly pulls electrons away through the bonds. That is a clear $-\text{I}$ effect.
Step 6: Pick the answer.
Only $-\text{COOR}$ withdraws electrons, so it is the $-\text{I}$ group. This is option 1.
\[ \boxed{-\text{COOR}} \]