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Someone is interested in whether democratic countries are less like to engage in conflict _ and conducted the following regression analysis_Conflict = 4 _ 0.1 Trade...

Question

Someone is interested in whether democratic countries are less like to engage in conflict _ and conducted the following regression analysis_Conflict = 4 _ 0.1 Trade 0.8 - Democracy 0.2 Democracy TradeIn the above regression, the dependent variable Conflict measures the amount of conflict country initiates in sear: The Trade variable is the total amount of trade (in millions of US dollars) for country: The variable Democracy is duimy variable. indicating whether country is a democratic country (i

Someone is interested in whether democratic countries are less like to engage in conflict _ and conducted the following regression analysis_ Conflict = 4 _ 0.1 Trade 0.8 - Democracy 0.2 Democracy Trade In the above regression, the dependent variable Conflict measures the amount of conflict country initiates in sear: The Trade variable is the total amount of trade (in millions of US dollars) for country: The variable Democracy is duimy variable. indicating whether country is a democratic country (i.e . country democratic country and 0 otherwise) . Finally, Democracy Trade is an interaction term between Democracy and Trade (5 points. What would be the predicted conflict for a country that has 10 million US dollars of trade and is a democratic coun- try? (10 points_ What is the estimated intercept for & democratic country? What is the estimated intercept for non-democratic country? (10 points. What is the estimated Islope of Trade for a democratic country? What about for non-democratic country?



Answers

Consider the version of Fair's model in Example $10.6 .$ Now, rather than predicting the proportion of
the two-party vote received by the Democrat, estimate a linear probability model for whether or not the
Democrat wins.
$\begin{array}{l}{\text { (i) Use the binary variable demwins in place of demvote in }(10.23) \text { and report the results in }} \\ {\text { standard form. Which factors affect the probability of winning? Use the data only through } 1992 \text { 2 }}\end{array}$
$\begin{array}{l}{\text { (ii) How many fitted values are less than zero? How many are greater than one? }} \\ {\text { (iii) Use the following prediction rule: if demwins }>.5, \text { you predict the Democrat wins; otherwise }} \\ {\text { the Republican wins. Using this rule, determine how many of the } 20 \text { elections are correctly }} \\ {\text { predicted by the model. }}\end{array}$
$\begin{array}{l}{\text { (iv) Plug in the values of the explanatory variables for } 1996 . \text { What is the predicted probability that }} \\ {\text { Clinton would win the election? Clinton did win; did you get the correct prediction? }} \\ {\text { Clse a heteroskedasticity-robust } t \text { test for } A R(1) \text { serial correlation in the errors. What do you }} \\ {\text { find? }}\end{array}$
$\begin{array}{l}{\text { (v) Use a heteroskedasticity-robust test for AR (1) serial correlation in the errors. What do you }} \\ {\text { find? }} \\ {\text { (vi) Obtain the heteroskedasticity-robust standard errors for the estimates in part (i). Are there }} \\ {\text { notable changes in any } t \text { statistics? }}\end{array}$

So far, this question variable smokes is a binary favorite cause toe one if the one person smokes on zero. Otherwise so what's used data in the smoker giving with the estimates A linear probably see model for smoke on the first question wants us to find out either any important differences between the 62 states. Su sets off standard Eros. So we started with the first question. So from the, um, such we're giving from data about giving. No, there's no difference. There is no much difference in the usual. And editors could dust ity. We bust standard errors. Okay, Okay. Not the second question. Oh, the other factors fixed education increases by four years. What happens? The estimated probability of smoking. So after eight after. So why education increases by four years, then probably see which off the smoking we're full bye. Four multiplied by 0.29 and then publish will fall by zero points. 116 So the next question At what point does another year off age reduced the variability of smoking? So is to be after age. That's the AIDS. Because this is when another year of, um this way another year of off age reduce the probability of smoking softer. Yet that's a It's a tight that see it under that yelled age reduces the probability of smoking and calculated by differentiating the question on, he said, and says, It's equal to me. So the next question is interpret the coefficient on the binary dribble. Rich tone. Yeah. So when the restaurant is, he calls toe one. That means if a person reside in the state with the rest of us smoking restrictions, that means the probability off smoking for by probably see off. Smoking falls by 0.101 when the restaurant is across the one. So the next question yeah, So a person number two or six in the data? Sure set as the following characteristics. So we asked her 36 as the C I. G. We are. I see because the 67.44 the process income is he calls to 6500. The present education is a cost to 16. Mrs Ages equals to 77 Person is worse. Don't is across Zero on DWhite is equals. Zero smokes the cost zero now computer predictor probability off smoking for this personal comment on the results. So for this person, for the person about Su 06 have been all these characteristics. They predicted poverty of smoking would be would be 0.6 56 minus 3.6 There were six 91 log See I geep Price plus 0.0 wants to log off income my nose. 0.20 education plus 0.20 age minus 0.2 six age too minus zero points 101 restaurant minus 0.26 whites. So the probability that I smokes would be 0.656 plus rather minus zero points. 0691 Log 67.44 plus 0.121 Logs 6500 My No. 0.20 What's died by 16 plus 0.20 What supplied by +77 minus 0.0 0 to 6 months. Fly by 77 Squared minus zero points 101 must by by zero minus 0.26 months by by zero. So the parents guy smokes would be cost. 0.656 minus zero points. Wants to six LA zero points. 045 minus 0.32 Lost 1.54 minus 1.541 54 On When you solve this out, you get 0.253 46 So, therefore, for ability or smoking for this person's equals 0.25 346 and that's the answer to the last question.

Well, this is a very unique and interesting question. If we break a stick into three pieces, can we make a triangle from it? Well, let's think about there's a couple of different triangles, we can make just an equal lateral one, maybe an isosceles. And of course the right triangle. Now if we were to take a stick of some sort and then break it up into two different pieces um we would find that we usually are able to make a triangle, so what we notice is that any collateral one, all the side lines are the same and the isosceles we got to that are the same and one that's different And then for the other one we got all three sides that are difference. So what does this mean? Well, let's try to think about what doesn't make a triangle. For example, what if we tried to make a triangle that had just one really long length and then to really short legs actually, maybe we'll expand this to be a little bit more in line with this thing right here. All right, so if these things are the same, then we cut off these two sidelines right here. So in blue and blue we got this line segments and this line segment. So this is all going to be right here and then maybe we could keep extending it a little bit more so that we have Okay, well maybe we'll do it all the way out here. So we could do like this and like this and there is a limit to how far we can reach. And this limit occurs. And what happens is that as long as we are taking from half, if we are breaking from half of the stick, half the life. So right here, we will never reach a full triangle. So we could add another moral right here. And maybe we need to change the angle a little bit. But at the half length this isn't exactly to scale. But if we have, you know right here, our length for the triangle a little bit longer. These blue lengths right here, there, no matter how shall we make them, they're still going to end up just a little short. And of course if we tried rotating them, we would end up with like a sort of criss cross. And you have to imagine that they're over here rotating. Oh so I can rotate like this. So we would end up criss crossing want, we don't want any excess length like that. And this just happens when there's half the length and for our proportions. Well, if we have to send things that are half divided by multiplying the two lengths that we take. This turns out that one out of four breaks in this stick are going to lead to triangles that don't end up being triangles. So incomplete triangles like this one


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