winchester_royal Admittedly there may be other relevant variables that positively skew the relationship, but surely you must agree that there is some causality between possession? Even if it's as simplistic as more possession => more time with the ball => more opportunities to shoot.
Premier League this season:
Possession % per game:1	Swansea	59.5
2	Southampton 57.8
3	Manchester City	56.6
4	Arsenal	56.6
5	Everton	55.8
6	Tottenham 55.8
7	Liverpool	55.1
8	Manchester United 54.7
9	Chelsea	54.4
10	Newcastle United 48.6
11	Stoke	47.1
12	West Bromwich Albion 46.5
13	Fulham	46.4
14	Norwich	46
15	Sunderland 45.7
16	Cardiff	44.8
17	West Ham	43.8
18	Hull	43.3
19	Aston Villa 42.2
20	Crystal Palace 39.3	
Shots per game1	Manchester City	17.7	
2	Liverpool	16.7	
3	Tottenham	16.4
4	Chelsea	16.1
5	Everton	15.7
6	Newcastle United 15.1
7	Arsenal 14.8
8	Southampton 13.4
9	Manchester United 13.2
10	Swansea	13.2
11	Norwich	12.9
12	West Bromwich Albion 12.3
13	Sunderland 12.3
14	Aston Villa	12.2
15	West Ham	12
16	Hull	11.5
17	Fulham	11.2
18	Crystal Palace	11.2
19	Stoke	11
20	Cardiff	10.7	
If you separate teams into brackets of quality. i.e. accounting for the variable of quality then it becomes clearer imo.
If we say possession is the independent variable and shots per game is the dependent variable then for the bottom ten teams (in terms of possession) you get:
Stoke 11th  

 19th
West Bromwich Albion 12th  

 12th
Fulham 13th  

 17th
Norwich 14th  

 11th
Sunderland 15th  

 13th
Cardiff 16th  

 20th
West Ham 17th  

 15th 
Hull 18th  

 16th
Aston Villa 19th  

 14th
Crystal Palace 20th  

 18th
tbh ^ that is a pretty weak correlation by the looks of it.
The two teams with the greatest amount of possession are Swansea and Southampton. But they're a fair way off the top 7 when it comes to shots per goals.
In fact, despite having so much more possession than all of the teams in the bottom half of the league they've not had many more shots.
Swansea vs Crystal Palace. An extreme possession discrepancy of 20.2%. That 20.2% has "caused" an extra 2 shots per game.
Like others have said, your graph's correlation is skewed massively by top teams behaving like top teams. That's not a model that Reading have much chance in following. We can't pay players £100K per week, and we can't spend £20 million on individual transfers.
We can try to follow the model of Southampton but let's not forget that their model is not easily replicable or cheap either. They've spent a shitload on transfer fees and they've got one of the best youth academies in the country. Can we compete on either counts.
Plus the Southampton model involves sacking Adkins, so all in all I'm not sure why all the Adkinistas are so cheery.