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Use the data in COUNTYMURDERS to answer this question. Use only the year $1996 .$ The variable murders is the number of murders reported in the county. The variable execs is the number of executions that took place of people sentenced to death in the given county. Most states in the United States have the death penalty, but several do not.(i) How many counties are there in the data set? Of these, how many have zero murders? Whatpercentage of counties have zero executions? (Remember, use only the 1996 data.)(ii) What is the largest number of murders? What is the largest number of executions? Why is theaverage number of executions so small?(iii) Compute the correlation coefficient between murders and execs and describe what you find.(iv) You should have computed a positive correlation in part (ii). Do you think that more executionscause more murders to occur? What might explain the positive correlation?
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Chapter 1
The Nature of Econometrics and Economic Data
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Yannick W.
October 8, 2020
Use the data in COUNTYMURDERS to answer this question. Use only the year The variable murders is the number of murders reported in the county. The variable execs is the number of executions that took place of people sentenced to death in the given county
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Hey, we are in computer exercise six in Chapter one, and we need to use the data set called County Murders to enter this question. First of all, the questions says, wanting to use only the year 1996 and this is very important. We'll see. Let's just describe our data sets first to see what's going on here. We have 37 1003 149 observation, 20 variables, huge data set. And it would look what I got a date, a browser and we took at the Here's to see what what the question is asking us to do. We'll see that we have. Where is it? Here. Yes, we see that we have observation for many years. Indeed, as we can see here in the variable year, we have observation for six and years from 6 80 to 98 96. But what if he's only data for 99 6? So one thing we could do is do whatever command we write in Stada we have. We could use the condition if year equals 9 96 but because we want to make her life easier, not harder, but we can also do is drop all the data that are not in 19 96. The case awoken. Do you conceive? Drop if a year is not equal to 99 6 here, in state of the expression for not able to is this one he entered. Look how many observation have been deleted. So, goodbye, Data browser To make sure that we did the right thing. We can look at the variable here. And indeed, it's only data for 90 96. All right, quickly. Um, the variable murders is the number of murders reported in the county. The variable exact is a number of executions that took place of people sentenced to death in the given county. Most states in the U. S. Have the death penalty, but several do not, in part, a warming. As Thio find How many counties are there in the data set? Well, we don't need to do an account for this. We just need to look at the total number of observations that we did describe. The new one will be 2197 right? This is the number of counties because each observation corresponds to one county. Each set of observations of thes counties. How many have zero murders? Well, now we need to use accounted command count. If murders this was full able zero 1051 counties have zero murders. Right now we can do this count is, as we said here in the they just said we can see that for each county. Here's a county idea for exact Let's say, for the county that has the 81,011 is associated with certain number murders. Zero in this case. Okay, And we can do it. We can count for age county separately. Then we need to determine what percentage of counties have zero executions. Well, okay, let's count Personal. How many counties have your executions? 2166. And if we divide this number, where the total number of counties which is 2197 and it's like 100 we get 98.6% of counties have zero executions. Well, that's good news. This most of the countess has their executions, but still 1.4%. It's, um you know, in my opinion, a lot of counters with executions, but in a way, um, in part B uh, part B s. What is the largest number of murders? And what is the largest number of executions? Why's the average number of executions were small? Okay, but which isn't summarized some eyes of variables, that story with murders, we don't need to use detail, because the answer is just I hear this number, Max. So the the largest number of murders, just 1403 the minimum zero fortunately, and then we do the same summarize command for executions. And we see that the maximum number, the largest number fix, usually is three. The minimum is zero. Now, the question is, why is the average number of executions small indeed is it's nothing 0.1 way, way like almost zero practically zero executions. Well, because other we showed before, like almost old counties have their execution like 98.6% of counties have their execution. So one of you get the average we're gonna compute, uh, 2166 zeros. Plus, you know, the rest time, some small number of executions, we can see the maximum of three, and we divided by lunch number, which is 2197. Off course, the average will be a very small number. All right, part. See, compute the correlation coefficient between murders, an execution and describe what you find. Uh, the command command state A is for followed by the two variables of interest margins and executions is gonna give us a correlation table off course. We ignore the diagonal elements. This these are always one, because it's a correlation of each variable with itself. But we're gonna look at this number right here, which says that the, um, correlation coefficient the pier sense correlation coefficient is 0.21. What does this mean, A CZ? We remember this coefficient is a statistical measure of linear association, right? It ranges from minus 1 to 1. And your point? It was a mildly positive correlation. Not too crazy, you know. Doesn't mean that these two tables are highly correlated. But they are court late in some way. Anything. If we do this kind of plot of these two variables, we will see a mild, be positive association. Well, no, you don't see it here, but let's try the other way. Where's these? Are this creep? Variable doesn't work very Well, yeah, Well, you don't really see it, you know, forget about it. You didn't really see it, but we can. We can say that is ah, um and mildly positive association. And in part, a part four follows this one and that he should have computed a positive correlation Part three with it. Do you think that more executions caused more murders to occur? What might explain the positive correlation? Yeah, well, whenever we were being asked to if something causes something 95% of the time of the question, the answer will be no. Goes from such simple computations like the correlation coefficient, weaken. See nothing about causation. The only thing we can see is I remember the famous phrase Correlation does not imply causation accusation. But causation doesn't buy correlation. So correlation is just a necessary not sufficient condition for causation. So we know that maybe maybe there is. Maybe some chance there's some mild causation accusation, but there's just a chance. Doesn't mean that it exists. We can say anything about it now, On top of that, the question is, do you think that more executions caused more murders to occur? And, um, apart from the fact that we can't say anything about accusation. The correlation does not imply any direction in the causal relationship, right? Even if we assume that there does exist on causation in principle, we don't know if it comes from executions or for murders. Now. Ah, reasonable way to think about it Would be that maybe murders could cause more executions in principles. I would be very, very unlikely that executions cause more murders. If anything, this is the measure. Two incentivize people Thio commit less murders, right? So one possible explanation about this mildly positive correlation would be other. Is some sort, of course ality going from murders, two executions and, uh, the other way around. Um, another possible possible explanation would be that, um, the counties that have more strict laws, um, tend to have a higher number of murders. But in any case, in this question, we can't say anything apart from maybe making a conjecture about something. But again, what we have computed here does not allow us to make any predictions about those out
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