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Navigate to Store 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

Generate Key

Follow the screenshots below to generate the key

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Now type pagespeed in the search box and you will get PageSpeed Insights API

You will get create project option click on it,

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Now click on Enable as shown in the image.

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After that you will get an option to "Create Credential" click on it and then you will get your API Key for pagespeed.