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Redo Example 4.10 by dropping schools where teacher benefits are less than 1$\%$ of salary.(i) How many observations are lost?(ii) Does dropping these observations have any important effects on the estimated trade off?

(i) there are 4 observations that are lost.(ii) among the various tradeoffs, the coefficient of $(b / s)$ changed majorly after excluding the observations where the teacher benefits are less than 1$\%$ of the salary.

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Chapter 9

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all right. Hello, everybody. Today we're gonna be looking back at some modeling exercises. You're gonna be comparing. Obviously. Um, now some different data sets with the same model, so let's get right into it. First thing. Of course. You want to install packages, Wooldridge and use Wilders is the library. If you haven't already, that just means that, you know, you're gonna be pulling your data from the right place. And I've also listed here the formula we're going to use that there's a pretty simple one. Log salary is equal to the ratio of benefits to salary. The reason I've written this out is because this isn't a variable given to us. It's something that we will have to calculate. So let's get into it. First experience. We need to open up our data set. That is the week 93 Data Center. If we view this really quickly, we will see. And I apologize if this clutching after you will see you know, all of these different things note up here salary and over here benefits, right. I also know that this ends that l salary. Um so sorry. I forgot. I've already worked with this data side a little bit, which is why it's a bit edited. But you should have, um but that shouldn't matter, Will go through anything anyways. So first thing we need to do is calculate our ratio of benefits. The salary way we're gonna do this is pretty simple. We're gonna do meet 93 and then we're gonna select the Ben Sal call, right? Just for the Rachel benefits to salary. Now, you won't have this column. So what are is gonna do is or whatever program we're gonna do is it's actually going to go in and create a new column for you to use. So now we have to specify the parameters. It is pretty simple again. We're gonna just say this is equal to our benefits. Divided by our X salary and then times 100 to give it a percent. It just makes our lives a little bit for the latest. So now we can write in our model. Where were saying his model one, By the way, where we're gonna say law salary is equal to Ben Cell using our data set of meat 93. When we do this, you will get this summary Okay, Um, pretty stand. Now, what we're being asked to do is we're gonna drop off all the schools where the benefits are less than 1% of the salary. So this is one multiplying by 100 earlier. Kind of comes in handy. Now we're gonna say, um, we're gonna say meek sub. That's what we're going to call our new data set. This is gonna be a subset of the meat 93 and our criteria is going to be rents out is greater than one. So wherever the benefit to salary ratio is greater than one i e. The benefits are more than 1% of the salary that's going to be in this new. So how many observations to re loose from this? All right, well, let's check. Meet 93. Originally had 400 ft are meek. Sub now has 404. So we've lost four observations by taking out those schools where the benefits are less than 1% of this out. If we start to model, if we model this one, we're gonna do the same process model to now on our data instead of Meat 93 is gonna be army except. And when we summarize this, I'm actually gonna summarize both of them. So they're close together. Rest ruling involved. We'll see that this would have some slightly different numbers. The coefficient of the ratio of benefits. The salary has changed fairly significantly. There's a pretty important change, because it went from 0.832 point 0077 which is significant when you consider how small these numbers are. And you know that that's a significant change, because up here, this is significant at the 0.1 significance level over here. This is only significant at the 0.1 significant right, So this is 0.1% up here. This is 1% over here. That's a pretty drastic change. And it's important to note that when you're creating econometric models because you know you'll see the effects of outliers like this one. All right, that's it for today. Thank you very much. Have a good one.

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