Navigate to System Configuration -> Excellence -> Page Speed -> Page Speed Setting
For page speed to work you need to generate the api key and put that in system configuration. Visit this link to generate the key https://developers.google.com/speed/docs/insights/v2/getting-started
Follow the screenshots below to generate the key
Now type pagespeed in the search box and you will get PageSpeed Insights API
You will get create project option click on it,
Now click on Enable as shown in the image.
After that you will get an option to "Create Credential" click on it and then you will get your API Key for pagespeed.