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This table lists the cost (in dollars) of a hotdog in Philadelphia and the bus fare in the same year. Following scatter plot of the data. Do not use excel Year 1960...

Question

This table lists the cost (in dollars) of a hotdog in Philadelphia and the bus fare in the same year. Following scatter plot of the data. Do not use excel Year 1960 1973 1986 1995 2002 2003 2009 2013 2015Hotdog Cost0.15 0.35 1.00 1251.75 2.00 225 2.30 2.75Bus fare (S)0.15 0.351.00 135150 2.00 225250 275Hotdog Cost vs_ Bus fare over timeHotdog Cost (S)Which the estimated value of the correlation coefficient? -0.9912 05124 0.5124 0.9912 2) Can we conclude that the cost of hotdog has direct causal

This table lists the cost (in dollars) of a hotdog in Philadelphia and the bus fare in the same year. Following scatter plot of the data. Do not use excel Year 1960 1973 1986 1995 2002 2003 2009 2013 2015 Hotdog Cost 0.15 0.35 1.00 125 1.75 2.00 225 2.30 2.75 Bus fare (S) 0.15 0.35 1.00 135 150 2.00 225 250 275 Hotdog Cost vs_ Bus fare over time Hotdog Cost (S) Which the estimated value of the correlation coefficient? -0.9912 05124 0.5124 0.9912 2) Can we conclude that the cost of hotdog has direct causal effect on the bus fare and wby? 3) Find or estimate r2, What docs this value tell us? 4) Does appear tbat the best-fit line above can be used make reasonably Bood prediction of bus fare given the cost of & hotdog? 5) Using the cquation fcr the best-fit [ line , We find that whcn & botdog costs 51OOQ ta Eedicled bus fe [s SLOIL . Is that predicled bus fare likcly to be accurale prediction? FuLy orgy pot



Answers

Construct a scatterplot, and find the value of the linear correlation coefficient $r$ Also find the $P$ -value or the critical values of $r$ from Table $A$ - $6 .$ Use a significance level of $\alpha=0.05 .$ Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section $10-2$ exercises.)The "pizza connection" is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the data listed below to determine whether there is a significant linear correlation between the cost of a slice of pizza and the subway fare.$$\begin{array}{l|l|l|l|l|l|l|l|l|l}\hline \text { Year } & 1960 & 1973 & 1986 & 1995 & 2002 & 2003 & 2009 & 2013 & 2015 \\\hline \text { Pizza cost } & 0.15 & 0.35 & 1.00 & 1.25 & 1.75 & 2.00 & 2.25 & 2.30 & 2.75 \\\hline \text { Subway Fare } & 0.15 & 0.35 & 1.00 & 1.35 & 1.50 & 2.00 & 2.25 & 2.50 & 2.75 \\\hline \text { CP1 } & 30.2 & 48.3 & 112.3 & 162.2 & 191.9 & 197.8 & 214.5 & 233.0 & 237.2 \\\hline\end{array}$$

Here we're taking a look at a data set, which contains information on the amount of bills for dinner at a particular restaurant and the tips that were left on that particular bill. We'd like to determine whether or not there is any linear correlation that exists here. So let's start by inputting the status set into our graphing calculator stat list, then producing a scatter plot. Here you can see the window I've used. You can replicate that if you'd like, and it looks as though we may have a little bit of a linear correlation going on. We could maybe draw a line somewhere through here. Let's go ahead now and run a linear regression T test on our calculator. Doing that, we find that we have a correlation coefficient R, which is equal to 0.8 to 8. That's suggesting a fairly strong, positive linear correlation. Let's determine its significance by taking a look at our T values and R P values. We've got a T value equal to 2.95 and a P value, which is equal to 0.4 so it looks as though this is in fact, significant at the 5% level. Therefore, we can conclude that there is a positive linear correlation of 0.8 to within this data set. Now let's consider if everyone were to tip the same percentage. So say everyone tipped 20% on each of their bills. What exactly should we expect that our value to be on that case? We should expect it to be equal to one because in that case, our slope would remain the same throughout all of it. And our line would fit each point perfectly because each one is having that same slope. That same change, which would be that 20% tip or 10% or whatever constant we're using there.

Here were given a set of data. Uh, what we would like to do is determine the linear regression equation for pizza cost and subway fare. To do that, let's input both of these variables into our stat list option on our graphing calculator and run a linear regression T test. By doing that, What our calculators should give us is a predicted Y, which is equal to negative 0.11 plus 1.11 x. We find that we have a correlation coefficient, which is equal to 0.992 So it's very close to one suggesting a very, very strong, positive linear correlation. And we get a P value, which is equal to 1.669 times 10 to the negative. Seven threaten scientific notation. If we were to write that normal forms, we would find that it is practically zero. So working with a null hypothesis that R is equal to zero and an alternative hypothesis that are is not equal to zero. We could certainly reject the null hypothesis in favor of the alternative, suggesting that it is a significant correlation coefficient and that we could in fact, use this refreshing equation. So suppose that we wanted to find what the subway fare might be if the slice of the cost of pizza is $3. So to do this, let's go ahead to find a predicted y value. Let's just plug three in for X By doing that, we should get Let's see, negative 0.11 plus one point. It gives us a predicted Y hat is equal to 3.0 to 2 right there. And so what do you think? I mean, what is this likely something that might be implemented to use an equation like this for determining subway fare based upon the cost of pizza? Well, there's, you know, this longtime theory that they are almost always going to that they're almost always equal to each other just by chance. So do you think anyone's actually following something like this? Well, maybe, maybe not. But if we look at this when we had a cost of pizza equal to $3 we got a very, very similar subway fare cost, suggesting that they really maybe are very similarly priced, almost always

So this question is quite a long question. Looking at income and housing, which is originally from chapter six, Extras 32 I've written on the left all the important days that we're gonna need as one of the rough sketch. So let's start with pot. A part A is asking us is restrict those of regression analysis appropriate. Now, for this is just a simple as looking our plot and what we're looking for is some kind of linear trend. Now, if I was drove around something like that or even a little bit learn something like that, you can see that that is a positive relationship on something that you can see could show linear trend. So I would definitely say, based on that graph, you need to say yes. So, Pop be is asking us what the equation is that predicts the housing cost index from the medium family income. This is where we're gonna need this data on the corrosion above it as well. So the main equations you're gonna need to marry for this is that be, is all correlation times a stunt deviation of why over Austin, a deviation off x a is I mean why? Which is often written as why about hair used mu A minus bi axle not be is to be from the first Parisian. So we need to look out. Be first and these were work. Now, if we have ah, regression equation that looks like something like this. This is what the a and the B what we're trying to work out now. As we are predicting housing cost index housing cost index is all why? Which leaves meeting from the income as our X. So now I just need to subtitle the right values. And do you have a baby? Is that all of the correlation, which is no 0.6 life? Well, times are by standard deviation of why which is our hatred, Alex 116.55 And that is over the standing ovation of X, which is seven. A 72.4 to. That's in your answer. No point. Not 17 now a. We need to take a mean of why which is 338.2. Only kneed Teoh minus be times all mean of X. I mean, if x is 4 6200 32 that you fool, sir. And that gives us an answer to a of minor since point from the sign minus under gruesome 0.6 full. So we put all that together to give Haixia. But little, however, um is 557.6 full class No find not well, 17 And then our X is, um I the is a Christian we're gonna be using in the rest of this question Looking put C Part C is asking us with a state with an M if I of 44,193 what would our predicted Hate CRB And this is just a simple substitution case. So we're gonna do well. Haiti. I is Mona's 157.6 full Plus no point no. +17 And then I am If I we are told it's 44. None. No, sorry. And that's what we need to do. We just need to something it gives us now. NSA 323 point 79 rounded to two. There's more places. That's the answer part. C d is gonna use our answer from parts. See, because it's asking us if Washington D. C has an Emam 5 44,993 Onda Hate See, I have 548.0 to how far off is our prediction in parts See on this is effectively asking us for the residual. So for this one, we need to dio 148. What 02 is is what we are told is the actual value I mean to take away from the all prediction No, which gives us an answer 224.2 three. So what was that saying is our prediction was 224.23 lower than the actual value on the last two passes Question But looking at standardizing variable So party asked if we standardize both are variables What would be the regression equation that predicts the standard Haiti I from the standard MF I on when you standardize variable It's been represented by Zet. So for this one, we would be are standardized. Hey, see Copy Onda. We want to know how we gonna predict that. It's quite simple, really. We just need to use on a correlation. We just times standardized I'm a fly by that correlation, that's for you need to do similarly part effort else's to do it the other way around. So now we're predicting em. If I from Haiti on with coronation, it works both by around, so we need to do exactly the same thing age. So it's just the opposite of party.


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