I had been just doing a bit of testing with YSlow and it is saying:

Grade F on Compress components with gzip: You will find 10 plain text components that needs to be sent compressed

I understand that Apache 1.3 uses mod_gzip while Apache 2.x uses mod_deflate, so the simplest means to fix remedy this is by using mod_deflate with an Apache 2 server.

However, I have checked with two hosting that is shared companies and something company and they have all in all me they don't support mod_deflate.

I understand that some older browsers have trouble accepting gzipped / deflated content, and I am not recommending it's enabled automatically, but what are the disadvantages to make mod_deflate available? Could it be just extra strain on the server's processors?

Also, what are the options? I saw that if you work with a Content management systems like Wordpress you may choose to use a caching wordpress plugin which may serve out gzipped cached versions from the pages initially produced via PHP.

Compression takes CPU time. Maybe the webhost made the decision they are concerned much more about CPU than network traffic. Maybe they provide it having a more costly package. MAybe they just did not add it. Only your webhost knows.

When utilizing PHP you should check whether your PHP setup has zlib support enabled. If that's the situation you should use ob_start("ob_gzhandler"); in code make it possible for an output buffer that will compress your computer data or set zlib.output_compression inside your php configuration for example by utilizing php_flag zlib.outout_compression on inside your .htaccessfile.