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DAT‑1 (EU)

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Andriana gathered data on different schools winning percentages and the average yearly salary of their head coaches and millions of dollars in the years 2000 to 2011 she then created the following scatter plot and trend line so this is salary and millions of dollars in the winning percentage and so here we have a coach who made over four million dollars and it looks like they won over eighty percent of their games then you have this coach over here who has a salary of a little over a million and a half dollars and they are winning over 85 percent and so each of one of these data points is a coach and it's plotting their salary or their winning percentage against their salary assuming the line correctly shows the trend in the data and it's a bit of an assumption there are some outliers here that are well away from the model and this isn't it it looks like there's a linear a positive linear correlation here but it's not super tight and there's a bunch of coaches right over here in the lower salary area going all the way from 20-something percent to over 60 percent assuming the line correctly shows the trend in the data what does it mean that the lies y-intercept is 39 well if you believe the model and the flu then a y-intercept of being 39 would be the model is saying that if someone makes no money that they could with zero dollars that they could win that the model would expect them to win 39 percent of their games which seems a little unrealistic because you would expect most coaches to get paid something but anyway let's see which of these choices actually describe that so that me look at the choices the average salary was 39 million dollars no no one on our chart made 39 million on average each million dollar increase in salary was associated with a 39 percent increase in winning percentage of that that would be something related to the slope and the slope was definitely not 39 the average winning percentage was 39% no that wasn't the case either the model indicates that teams with coaches who had a salary of 0 million dollars will average a winning percentage of approximately 39 percent yeah this is the closest statement to what we just said if you believe that model and that's a big if if you believe this model then this model says someone making zero dollars will get 39% and this is frankly why you have to be skeptical of models they're not going to be perfect especially at extreme cases oftentimes but who knows anyway hopefully you found that useful