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the percent of adults who smoke recorded every year every few years since 1967 suggests a negative linear association with no outliers on average the percent drops by 0.5 points each year which of the following plots suits the above description so let's see this looks like a negative linear correlation or Lin as the years go by you know a smaller percent of smokers this one does too as years go by you have the number of smokers go down and down this one down here also looks like that although it's not as smooth if you were to fit a line here it looks like you have a few outliers well this is a positive correlation so we can definitely rule out graph for now the other thing that they told out they told us is that there are no outliers suggest a negative linear association with no outliers if you were to try to fit a line to graph three you could fit a line pretty reasonably that would go someplace like that but it would have this outlier it would have this outlier right over here it looks like it's 12 or 13 years I look about 13 years after 1967 so that would be 1980 looks like an outlier there but they said it doesn't have any outliers so we would rule out graph number three and so we have to pick between graph one and graph two and so the other the other hint they gave us or a piece of data they give us is that the percent drops by 0.5 each year 0.5 percent each year so here what's happening as 10 years go by let's see as we go from let's start with let's see in 1967 where it looks like what about 55% and then 10 years go by we are roughly at around 45 a little under 45% so we dropped 10% in 10 years that seems to be how much this is dropping about roughly 10% in 10 years another 10 years go by we'll go from 45 or a little more than 10% in 10 years and so that would mean that we're dropping on average more than one percentage point per year that seems more than what's going on here now let's look over here over here we're starting it looks like it around 40 2% and then after 10 years it looks like we're at like 37% so it looked like we it looks like we've dropped about 5% in 10 years which is consistent with this if you drop 5% in 10 years that means you drop half a percent per year so we'll go with graph 2