I tried to restore my 13 inch 2011 MacBook Air to factory default and now I can to restore it. What can I do to restore if I do not have a backup. I was doing this so that I could sell it.

If you intend to sell our Mac, please follow the following recommendations: What to do before you sell, give away, or trade in your Mac - Apple Support

If you've not erased and installed a new system, or do not have backup

to external storage drive of its content, learn how to use Time Machine.

• How to back up your Mac with Time Machine - Apple Support

https://support.apple.com/kb/HT201250

• Backup disks you can use with Time Machine - Apple Support

https://support.apple.com/en-us/HT202784

• How to reinstall macOS - Apple Support

https://support.apple.com/en-us/HT204904

To have Mac's 'Time Machine' utility make backup on external HDD

via USB; figure hours for a first backup. Nothing rushed will do that.

After backups, then erase Mac; per instructions given in article.

A basic erase and install uses details found in macOS Recovery

helps to become familiar with those. Do backups, beforehand..

• About macOS Recovery on Intel-based Mac computers - Apple Support

https://support.apple.com/en-us/HT201314

To leave the Mac in an as-new state; where a new user/owner

can start up Mac, so they'd enter personal information afresh.

Then Mac would start up like new computer; w/ no old clutter.

• What to do before you sell, give away, or trade in your Mac - Apple Support

There are several steps to ready a Mac toward what fate awaits.