The compound that will not form a yellow precipitate on heating with an alkaline solution of iodine is:

The reaction described is the Iodoform test. A positive test (formation of a yellow precipitate of $CHI_3$) is given by compounds containing either a methyl ketone group ($CH_3-C=O$) or a methyl carbinol group ($CH_3-CH(OH)-$) attached to at least one hydrogen atom or alkyl/aryl group.

1. Ethanol ($CH_3CH_2OH$): Contains the $CH_3-CH(OH)-$ group. (Positive test).
2. Propan-2-ol ($CH_3CH(OH)CH_3$): Contains the $CH_3-CH(OH)-$ group. (Positive test).
3. Butan-2-ol ($CH_3CH_2CH(OH)CH_3$): Contains the $CH_3-CH(OH)-$ group. (Positive test).
4. Methanol ($CH_3OH$): Does not contain the requisite $CH_3-CH(OH)-$ group. Therefore, it does not give a yellow precipitate with alkaline iodine.