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The committee dlecicled to focus on the number of police officers in the city, the percentage of arrested men who tested positive for drugs; the number of families ...

Question

The committee dlecicled to focus on the number of police officers in the city, the percentage of arrested men who tested positive for drugs; the number of families in the city below the poverty level, the number of people between 16 and 19 who were not enrolled in school and were not high school graduates and the number of single-female-parent households They were focusing on 23 large cities but not all of the data were available for all of the cities in the study; (a) The committee want to find

The committee dlecicled to focus on the number of police officers in the city, the percentage of arrested men who tested positive for drugs; the number of families in the city below the poverty level, the number of people between 16 and 19 who were not enrolled in school and were not high school graduates and the number of single-female-parent households They were focusing on 23 large cities but not all of the data were available for all of the cities in the study; (a) The committee want to find a model that will predict the number of serious crimes from one of the other chosen variables They initially choose "number of male arrests for drugs Use Data Analysis in Excel to investigate this linear regression model and use it to write one sentence to summarise how good predictor "male arrests for drugs" is. You do not need to include the full regression output but you do need to state clearly the value of any coefficients you have used to make your decision:



Answers

Please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$ (c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$ (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained? Answers may vary slightly due to rounding. Does prison really deter violent crime? Let $x$ represent percent change in the rate of violent crime and $y$ represent percent change in the rate of imprisonment in the general U.S. population. For 7 recent years, the following data have been obtained (Source: The Crime Drop in America, edited by Blumstein and Wallman, Cambridge University Press). Complete parts (a) through (e), given $\Sigma x=44.7, \Sigma y=-17.4$ $\Sigma x^{2}=315.85, \Sigma y^{2}=116.1, \Sigma x y=-107.18,$ and $r \approx 0.084$ (f) Critical Thinking Considering the values of $r$ and $r^{2},$ does it make sense to use the least-squares line for prediction? Explain.

In problem 17. We have a beard that relates the show print and the height over mill. In this list we have here the show print in centimeters 29.7, 99.7 31 buying food, 31 point it 2027.6 and the corresponding hide off the mill in centimeters. Also 175.3, then 77.8. Then we have 185 0.4 centimeters on seven 5.3 and finally 172.7 centimeters. We want to calculate the linear correlation coefficient, or then calculate the critical values, or from Table E six, with a significant level off 4.45 which means all four equals 4.45 Then we want to see if we can support a claim for a linear correlation between the two variables here or not. First, to calculate, or we need to calculate three other lists. We have X squared, which is the square value for all off the show print. For example, the first value will be 29.7 squared, which gives 882.9 and so on for the other five values. Then we have 10,000 and the second list will be for y. Squared will be the square value for the height. Then the first number will be 17 5.3 squared. Then we have 30 31612.84 34373.16 10 37 30.9 And finally we have 15727 one by in five, the finalist will be the variable X multiplied by the variable. Why, she means we will multiply 29.7 by 175.3 she gives. And for the second number with the second beer the third bear, the fourth bear. And finally we have year 4766.52 And to calculate, or we will need to calculate the sum for each off the 55. This the submission. We will add all the values together in this list, which she gives 150.2 on some mission of why is 886.5 Submission of Exist squared the summation of voice squared 15727 1.5 I'm finding that summation of ex boy 26649.69 Now we are. We can calculate the value off where R equals and multiplied by the submission of X y, which is given here minus You can substitute directly and multiplied by the submission and is the number off beers We have five years multiplied by summation of X Y given here 26649.69 Minus summation of X Multiply by summation Boy Commission of why given here minus submission Multiplied story Tabligh The submission of boy Divided Boy square root off in multiply by submission off X squared Submission of X squared given here 45 to 3.14 minus submission of access All the square submission of X is given here Squid multiplied boy square root 55 cheese n multiplied by some mission of why square some measure of voice squared is given here 157 271.5 minus submission. Avoid all square submission. Avoid Here it 86 0.5 square Then the value off equals 4.5 91 for three. The small places. We can get the critical values from table 86 at in equals five and significance equals four point or five. We can get the critical values of R equals post of or minus 4.878 as long as our is smaller and is between the critical values off. Our we have here are equals open 591 it's a smaller than 2.878 and this greater than minus a 0.878 As long as our between the critical values, we don't have evidence to support the claim, then no such evidence to support the claim off the linear relationship between the two variables. Which means policeman can't depend on show, print, toe, get the height off meals or to estimate it. Then we can really show print to the height over me, and this is the final answer off our problem.

A graphic you in here And it is a supplier that this the their bar. So's the drug offenses, drug offenses, all our criminal offenses. So these are the drug offenses and this or anyone. So it's all the other. All the other offenses offensive? No. In $1998. 1998. There were 60,000 inmates in federal prison for drug offenses, 60,000 for drug. And for the period, the graphics Soon this number increased by approximately 2.8000 year. Rate is increasing. That is to point it 1000. This is 60,000 and this is the 100,000. But again, But you know, it is asked to write a question. Let why, with the total number off prisoners or prisons. And so it will be 60 plus 2.8 x where all data isn't 1000 older ties in 1000 and excellent present here after 1990 years? No. For the second part, in 1990 years, there were 44,000 in mix for all other crimes for all other crimes. No, the increasing rate is 3.8000 per year to be blank it closer, but we have to write another question. So this is way and this way be white to is called toe 44. Or maybe why we can simply say why or white toe any of these notations. So this is 44 less to the 0.8 x No X is in here after 1 1998 And why is total number of prisons toe number? Oh, reasons? No for the third, But it didn't asked in which here, both the reasons have equal number. So for this, a great board de question. This is a question number one. And this is a question number toe equipped. Both of them. It quit both of them. So simply, this will be minus minus minus. So this is zero and this will with 16. And this is really with minus 1.0 X. So excess quarto 16 years means after 16 years, Decker is in 2000 for pain. There may be called number off border regions equal

We are given a sample of data points listed at the top of this document and using that data, we want to answer the following six questions they threw. Steph, we'll proceed together one by one as follows. First, in part A We want to produce a scatter plot of our data points. I've already included the scatter plot right below part AM left with the points X Y are marked with black Xs or crosses next directly to the right. We want to compute for part B. The sum is relevant to this data as well as the Pearson correlation coefficient. R I've already included the values of the sums since they are found simply by taking the exact formulas for those sums of some X is some of the X values and so on, correlation coefficient. R is given by the following formula which takes as input our sample size and and the someone who just calculated Putting those in, we get our equals .084 next in parts. Do you want to find the line of best fit for this? Do that To do so? We have to identify the following parameters. 1st. First are excelling and winning X bar and wine bar which are simply with some of our X and Y values about it. I am. We can use these now to find the slope, be an intercept A. Of the line of best fit first and left. The slope B is given by the formula here, which takes us input and and the sums again. This is very similar to the correlation coefficient. R formula From this. We get b equals .1-9. Next for a wee plug in ry bar expire and be to get intercept equals negative 1.66 or equation for line of best fit, Y equals negative. 1.66 plus 1.29 x. Next report. Do you want to return to the scatter plot and plot? Ry by that we just produced or rather our white hat doing so. And making sure we include our X. M and Y me produces the following plot. Finally, party we want to calculate a correlation or rather a coefficient of determination R squared and interpret the coefficient of determination. R squared is simply the square of our correlation coefficient. So .007. We take this to mean that .7 of our data or rather our variation in our data can be explained by the corresponding variation and x and the least squares line. However, that means that 99.3 of our variation cannot be explained by this. Finally important if we want to answer considering our value for R and R squared, should we trust why hot making predictions for why? Based on X? No, we should not, because R and R squared are so small that we aren't really seeing a very strong relationship between these variables.

That's problem. We're talking about the uh effect of budget cuts would have on crime in the city. So the number and one gives the project a number of drug-related crimes in the next 12 months. Um, the number and to give subject number of crimes in the same terror if the budget is cut. So we can see here that the budget cuts, we're gonna say crime is going to go up budget not cut, it's still going to go up. So what does it say here explain why? And again, I explain why it's kind of a weird way of putting this. I don't know why why crime is going up, but this graph tells us that it is um, the reason for this is probably very complex, but um, both and try and one and then two prime are both positive, which means that no matter what we do, budget cut or not, we expect crime to go up to increase. So, um, and one double prime is negative, but and two double crime is positive. And so what does that mean? Well, that means that without budget cuts we would expect the rate of crime, that rate of increase of crime to slow down. So hopefully, you know, we're not, you know, it looks like 12, maybe it's flat and maybe we hope that it goes down so that, you know, the number of crimes, um, it goes down, let's see here, um, start, you know, starts going down and or the number of new crimes anyway. And then, um, yeah, here, you know, we're basically saying that the rate of crime is going to, the rate of increase in crime is going to increase. So it's going to accelerate, its gonna kind of decelerated. So, again, it's basically saying the budget cuts are gonna hurt, predict, and in, uh, basically everybody says budget cuts are gonna hurt. But somewhere you have to make tradeoffs and whether those projections, and that's the problem with projections is that you can make them look like every however you want. Um, So here's their obviously making it look like if we cut the budget crime is going to go away up.


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