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Interpreting y-intercept in regression model

Interpreting y-intercept in regression model.

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Video transcript

- [Instructor] Adrianna gathered data on different schools' winning percentages and the average yearly salary of their head coaches in millions of dollars in the years 2000 to 2011. She then created the following scatter plot and trend line. So this is salary in millions of dollars and the winning percentage. And so here, we have a coach who made over $4 million, and looks like they won over 80% of their games. But 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%, and so each of one of these data points is a coach, and is 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 a, 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 line's y intercept is 39? Well if you believe the model, then the y intercept of being 39 would be the model is saying that if someone makes no money, that they could, zero dollars, that they could win, that the model would expect them to win 39% 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 this choices actually describe that. So let me look at the choices. The average salary was 39 million dollars, nope. No one on our chart made 39 million. On average, each million dollar increase in salary was associated with a 39% increase in winning percentage. That would be something related to the slope and the slope was definitely not 39. The average winning percentage was 39%, we know that wasn't the case either. The model indicates that teams with coaches who had a salary of zero millions dollars will average a winning percentage of approximately 39%. Yeah this is the closest statement to what we just said, that 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 in extreme cases oftentimes, but who knows. Anyway, hopefully you found that useful.