This data is taken from 'The Long and the Short of It' by Les Binet and Peter Field, based on award-winning ads. Similar results have been published by Kantar based on a broader cross-section of advertisers (i.e. Kantar clients) - see pages 113-117 from 'Marketing Knowledge' by Dominic Twose.
The Binet & Field analysis confirms that there is a relationship between 'Excess Share of Voice' and share growth. In other words, brands that spend more on advertising vs competitors than you'd expect based on their market share, are more likely to experience growth in market share.
The relationship is fairly weak. Other factors such as distribution, user satisfaction and price tend to have stronger relationships. The fact that there is a significant relationship (albeit a weak one) between excess share of voice and annual share growth suggests that advertising investment contributes to brand success. The relationship could be even stronger if the creative quality of the advertising was factored in or if new brands were split out from established brands. However, the relationship does not prove causality. It could simply be that brand owners spend more when they have something new they think consumers will love (i.e. market share would have gone up even without the boost in spend).
Check out this LinkedIn thread to hear a debate about how this graph should be interpreted.