Interpreting y-intercept in regression model | AP Statistics | Khan Academy

Adriana 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 in the winning percentage. Here we have a coach who made over $4 million, and it looks like they won over 80% of their games. But then you have this coach over here who has a salary of a little over $1.5 million, and they are winning over 85%.

Each 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.

It looks like there's a positive linear correlation here, but it's not super tight. There are a bunch of coaches right over here in the lower salary area, going all the way from 20-something percent to over 60%.

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 a Y-intercept of being 39 would suggest that if someone makes no money, 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 these choices actually describe that. So let me look at the choices:

1. The average salary was $39 million. No, no one on our chart made 39 million on average.
2. Each million dollar increase in salary was associated with a 39% increase in winning percentage. Now that would be something related to the slope, and the slope was definitely not 39.
3. The average winning percentage was 39%. No, that wasn't the case either.
4. The model indicates that teams with coaches who had a salary of $0 million will average a winning percentage of approximately 39%.

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 $0 will get 39%.

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.