First you are going to have to wait about 6-10 months to get credit for your backlinks:
- Creation Date: 22-oct-2016 (new website sandbox)
Match Words according to Google: (Google makes them bold in the results)
- dog
- dog toy
- dog toys
- dog's toy
- dogs
- dogtoys
- pet
- pet toys
- toy
- toys
Here are the factor correlations for page 1 for the search "dog toys"
Strong Correlation: Tune pages for exact matches in web page li tags with a value of at least 2
Strong Correlation: Tune pages for matches in web page HTML source with a value of at least 889
Strong Correlation: Tune pages for matches in web page BODY tag with a value of at least 792
Strong Correlation: Tune pages for matches in web page A tag hrefs with a value of at least 364
Strong Correlation: Tune pages for matches in Google result URL with a value of at least 4
Strong Correlation: Tune pages for directories in Google result URL path with a value of at least 3
Strong Correlation: Tune pages for exact matches in web page A tags with a value of at least 2
Strong Correlation: Tune pages for matches in Google result URL path with a value of at least 3
Strong Correlation: Tune pages for matches in web page A tags with a value of at least 152
Strong Correlation: Tune pages for internal links in web page HTML source with a value of at least 353
Strong Correlation: Tune pages for matches in web page name attributes with a value of at least 1
Strong Correlation: Tune pages for links in web page with a value of at least 373
Strong Correlation: Tune pages for matches in web page H1-H6 tags with a value of at least 25
Strong Correlation: Tune pages for matches in web page LI tags with a value of at least 95
Strong Correlation: Tune pages for exact matches in web page span tags with a value of at least 1
Strong Correlation: Tune pages for do follow links in web page HTML source with a value of at least 364
Strong Correlation: Tune pages for matches in web page H1-H2 tags with a value of at least 12
Strong Correlation: Tune pages for kilobytes in web page html source with a value of at least 155
Strong Correlation: Tune pages for matches in web page alt attributes with a value of at least 3
Strong Correlation: Tune pages for matches in web page sentences with a value of at least 177
Strong Correlation: Tune pages for exact matches in web page strong tags with a value greater than 0
Strong Correlation: Tune pages for matches in web page H1-H3 tags with a value of at least 22
Strong Correlation: Tune pages for image tags in web page with a value of at least 57
Strong Correlation: Tune pages for matches in web page H2 tags with a value of at least 7
Strong Correlation: Tune pages for linkedin page in web page links with a value greater than 0
Strong Correlation: Tune pages for exact matches in web page option tags with a value greater than 0
Strong Correlation: Tune pages for image tags with alt text in web page with a value of at least 29
Strong Correlation: Tune pages for matches in web page class attributes with a value of at least 9
Strong Correlation: Tune pages for milliseconds in web page with a value of at least 2252
Strong Correlation: Tune pages for kilobytes in web page body tag with a value of at least 126
Strong Correlation: Tune pages for site links in Google result with a value greater than 0
Strong Correlation: Tune pages for https links in web page with a value of at least 136
Strong Correlation: Tune pages for kilobytes in web page script tags with a value of at least 29
Strong Correlation: Tune pages for matches in web page H4-H6 tags with a value of at least 3
Strong Correlation: Tune pages for matches in canonical URL with a value of at least 3
Strong Correlation: Tune pages for leading matches in web page H1 to H3 tags with a value of at least 1
Strong Correlation: Tune pages for subdomains in Google result URL with a value of at least 1
Strong Correlation: Tune pages for image tags without alt text in web page with a value of at least 29
Strong Correlation: Tune pages for kilobytes in web page stripped html text with a value of at least 10
Strong Correlation: Tune pages for leading matches in web page H4 to H6 tags with a value greater than 0
You can get there but you have a lot of time and effort to get through first. For example the average page 1 results has almost 900 match words in the HTML source. You have about 100... you need to research how your competitors get away with such high match counts without being penalized for keyword stuffing. Then you need to incorporate many of those tactics. So basically you need to put about ten times as much effort into your content and on page tuning... without getting penalized... AND once that is done you will need backlinks using those target search terms... also without getting penalized... And you need to survive a year to see the effects of that effort. It is doable but it is going to be quite hard. You might find faster/easier success with a lower competition keyword, but that really depends on what your goals are.
The factor correlations:
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