Author Topic: Question about homework Q1e  (Read 926 times)

Shenxiong

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Question about homework Q1e
« on: February 15, 2017, 11:22:16 PM »
I have a question about homework Q1e, the second question(why or why not)


I have a loosely speaking idea: I find that when the control increases, although the coefficient of nox is negative, the absolute value of it decreases. This is because when you add more control (even if you fix the control variable), nox's individual effect to the price is weaken by other control variables. Or say, compared to the case that you add in control variables, nox's effect to the price is weaker when nox is the only treatment variables. Other control variables also have "some effects" to the housing price, if you don't add them, those effects will be secretly added to the nox's effect to price......


I don't know whether it is correct. Even if it is correct, I don't know how to express it formally.

Thomas VanDer Straaten

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Re: Question about homework Q1e
« Reply #1 on: February 16, 2017, 01:30:53 PM »

Hi Shenxiong, I believe you are thinking along the right track. One thing you might want to consider when expressing your answer formally is what happens to the unique effect of nox on median housing prices, when we add more controls. Do all of the new variables we added help us better predict all the other factors for which we are not controlling? If the coefficient on nox changed, we might have some reason to believe so. If not, then why not?


 If you are stuck, Notes 6 offers a really good discussion on this.

Shenxiong

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Re: Question about homework Q1e
« Reply #2 on: February 16, 2017, 10:33:28 PM »
Really make sense!
Thank you very much


Just on little question, when we look at the coefficient, the absolute value will give us only the magnitude of effect from treatment variable (or/ and control) to the outcome, and the true value(with negative or positive sign) will also give us the direction of the effect (for example, when y=a0-10a1, when a1 increases one unit, y will decrease a0-10 units).
Is my thought right?


Thank you so much!
« Last Edit: February 16, 2017, 10:40:45 PM by Shenxiong »

Thomas VanDer Straaten

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Re: Question about homework Q1e
« Reply #3 on: February 17, 2017, 12:42:33 PM »

Just to be clear, in general, just because coefficients change in response to adding more variables, does not mean we are doing a better job of constructing our model - as we see later in the course,for example, our estimators might become imprecise in certain situations. In this question however, I wouldn't worry too much about that. If you find that the coefficient changes, could it be that the new variables help us distill the unique effect of nox on median housing prices? Why might that be the case? What about those variables help us achieve that goal? That is one thing I would think about and consider, when answering the question.


To answer your question, I believe you are thinking about it in the right way, though you need to be careful of using words like "true effect" and "when x1 increases by 1 unit, y will change by XX units". The coefficient's meaning is tied to its size and direction (as well as significance, which is discussed later in the course). Imagine a very simple question; we are estimating the impact of class size (CS) on average test scores (Test Score). We are using data from 100 third-grade classes. Suppose we estimate that:


Test Score (hat) = 520.4 - 5.82*CS


Suppose we increase the size of a classroom from 19 to 20. What does our regression predict? Well, you can do this step by step:


Test Score (hat) = 520.4 - 5.82(19) = 409.82
Test Score (hat) = 520.4 - 5.82(20) = 404


What is the difference? -5.82. But that is just equivalent to the slope coefficient. We can say: the expected impact on the average test scores of a class, when we increase the class size by one student, is that it will decrease by 5.82 points. If we add more controls, we will need to clarify that our coefficient is the predicted effect of our variable of interest when we increase it by one unit, holding everything else constant. Remember, our model is built on a series of assumptions - and if those assumptions hold, this is what we would predict might happen.


Please let me know if that makes sense!

Shenxiong

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Re: Question about homework Q1e
« Reply #4 on: February 17, 2017, 10:19:09 PM »
Hi! Thank you very much!
This really makes sense.


So, after we added in control variables, the coefficient of nox is still negative, but the absolute value of it decreases. That means, when nox increases, the median housing price still decreases, but the unique effect of nox on median housing price is weaken or distilled by the control variables, because the variable we added as controls have their own effect on median housing price. For example, the house near a place with high crime rate is cheaper, and when the number of room increases, housing price increases. If we don't  add those variables as controls, their effects will be secretly counted on the unique effect of nox on median housing price, which will make us overestimate it. As a result, adding those variables as control is a good choice.


Is this a right thought?

Thomas VanDer Straaten

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Re: Question about homework Q1e
« Reply #5 on: February 18, 2017, 11:17:03 AM »
Though I believe you are on the right track, I would be careful of wording. After we include these new controls, are we closer to the unique effect of nox, or further away? I would refer to our discussion on confounders (notes #3) to understand what the role of the new controls might be.

Shenxiong

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Re: Question about homework Q1e
« Reply #6 on: February 19, 2017, 04:44:38 PM »
We are actually closer to it.


Thank you very much!!