Will subpages performance affects the overall SEO performance of the entire site?
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I have site issues on certain subpages which I am not focusing for SEO, e.g. "News". I was wondering does the issues of these subpages affect my overall SEO performance (those pages which I will like it to be rank, e.g. "Products" page)?
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It can do under certain circumstances, particularly if vulnerabilities are detected. If your news section had malware or if links from your news section were detected to HTTP resources (internal / external pages, images embedded from HTTP) that could cause problems (Google want everything on HTTPS now)
It would be unusual but there are certain circumstances where you could see wider impact(s). Another thing is, if the news section garnered your site a manual penalty, then quite often that could spread to all pages / keywords / rankings. Simply deleting the news section would be unlikely to restore performance instantly
If it were something like poor content or duplicate content, that would be more likely to just affect your news section without impacting your other pages (e.g: products) unless of course they shared the same issues
If the news section is riddled with technical errors it could bring the site health metrics for your overall domain slightly but in general the impact to the rest of the site should be non-radical
Hope that helps