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### Course: Algebra 1 (Eureka Math/EngageNY)>Unit 2

Lesson 12: Topic D: Lesson 14: Modeling relationships with a line

# Interpreting y-intercept in regression model

Interpreting y-intercept in regression model.

## Want to join the conversation?

• So the more you pay your coach, the better your winning percentage! Ha ha ha.
• it doesn't mean the more you pay your coach the better the winning percentage. it simply means expensive coaches have a reputation of winning thus explaining the reason of their high salary in the first place and vice versa.
• Does the model showing that a salary of \$0 gets you a 39% winning percentage imply that the relationship between salary and winning percentage isn't linear? Is a regression model even appropriate for this data?
• Not really. You can tell visually, that the two values seem to be correlated, although a bit loosely.

The way I look at it it is that you need to consider what domain of the function is appropriate (in this case, that's the salary). E.g. negative salaries don't make sense. Positive, but too low values probably won't make much sense either.
Similarly, the line can't go on infinitely, it's certainly unrealistic to have a winning percentage of over 100%.

So, even though this specific model can theoretically be applied for all real numbers, it makes sense to restrict its domain to (let's say) what's shown in the graph (starting at e.g. the minimum salary paid in this field).

How much it is then appropriate to use.. I don't have practical experience, but it certainly seems better than a blind guess.
• since the x axis is in millions, When it is 0 on the x axis, does it mean that they are making 0 million in the sense that they are making less than a million or are they making no money at all?
• I think you could interpret the model as saying that you can expect teams without any coaching to win 39% of the games. If you want to win more games, then you have to increase your budget for the coach position.
• It pays to be winning 80% of your games huh?
• what do you use the energy points that you get from doing mini tests on khan what do you use the energy points for?
(1 vote)
• You use them to commenting too.
Ex: if you don't have enough points then you can't ask a question.
• I think the more precise commentary would not be that a coach making 0 dollars would still win 39%, but rather that coaches who don't make quite 1 million dollars still win 39% (for instance, a salary of \$999,999 or lower). Yeah?
• Your interpretation is more precise and accurate. It's indeed more appropriate to say that coaches who earn less than one million dollars may still have a winning percentage close to 39%, rather than implying that coaches earning exactly zero million dollars will have that winning percentage. The model's prediction should be interpreted within a reasonable range, especially considering that salaries are typically not exactly zero or one million.
(1 vote)
(1 vote)
• Hi!

Is it safe to say that coaches who win less than 39% of their games earn less than one million? For example, a coach earning \$800,000 technically earns "zero million dollars", but he still gets paid.
(1 vote)
• Regarding your question, it's not necessarily safe to make that assumption. While the model predicts that teams with coaches who had a salary of zero million dollars will average a winning percentage of approximately 39%, it doesn't directly imply that coaches earning less than one million will necessarily have a winning percentage below 39%. There could be other factors at play, and individual cases may vary.
(1 vote)
• How do you know what data will go in the y and x axis?
(1 vote)
• uff that's like most basic math, but if you are talking about the variables, then the answer is simple, there are 2 types, independent and dependent variables, the salary in this case is the independent, and the winning percentage is the "dependent", in "" because it is an assumption.
An to make it clear, the independent goes always in the X axis, because it should define the Y axis values.

## 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.