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Listed below are the budgets (in millions of dollars) and the gross receipts millions dollars) for randomly selected movies_ Construct scatterplot find the value of...

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Listed below are the budgets (in millions of dollars) and the gross receipts millions dollars) for randomly selected movies_ Construct scatterplot find the value of the linear correlation coefficient and find the Pava Iue using 0 = 05. Is there sufficient evidence t0 conclude that there is linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed are 564,000,000,591,000,000, 549,000,000_ and So on? BBudget 192 104 roSsWhat are the null and alternat

Listed below are the budgets (in millions of dollars) and the gross receipts millions dollars) for randomly selected movies_ Construct scatterplot find the value of the linear correlation coefficient and find the Pava Iue using 0 = 05. Is there sufficient evidence t0 conclude that there is linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed are 564,000,000,591,000,000, 549,000,000_ and So on? BBudget 192 104 roSs What are the null and alternative hypotheses? 0A: Ho: p= H1: p < 0 Ho: 070 Hi: p=0 Ho: p= Ha: p#0 Ho: p= 0 Hi: p> Construct scatterplot Choose the correct graph below: 8004 8004 250 250 The linear correlation coefficient r is Round three decimal places as needed ) Enter your answer in the answer box and then click Check Answer parts remaining Clear AlI Check Answer



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Box Office Receipts U.S. movie box office receipts, in billions of dollars, are shown in 5-year increments from 1997 to 2017 . $$ \begin{array}{c|c} \text { Year } & \text { Receipts } \\ \hline 1997 & 6.366 \\ \hline 2002 & 9.155 \\ \hline 2007 & 9.664 \\ \hline 2012 & 10.838 \\ \hline 2017 & 11.072 \\ \hline \end{array} $$ These receipts $R$ are reasonably approximated by the linear model $$ R=0.2219 x+7.200 $$ where $x=0$ corresponds to $1997, x=5$ corresponds to $2002,$ and so on. Using the model, calculate the year in which the receipts first exceed each amount. (a) 8.1$ billion (b) 10.6$ billion

So for hurt. They were given this. We have some points. Um, and what these points we want to find, uh, slope. So what that's gonna look like is 57,000 1 84 Uh, we're all just for the sake of time, I'll just say it so way have 57,184 minus 53,504. And that's going to be divided by one. Because we would subtract the years 1995 and 1994. So with this, we would get a slope of 33,680 and then way can input this into an equation and choose the point we want. So we can choose, say, 53,504 equals 3680 times 1994 plus B. When we multiply these and subtracted way, get that B equals negative 7,284,416. And what that allows us to see now is that our equation will be Why equals our slope X minus R B value for plus are the values of 7 to +84416 So that is right there are equation. And then if we use a graphing tool and we're trying to predict the value in 1997 um, 1997 way will say looks about to be 64,500 um, 540 So be about are predicted value. It may be different for you, but just looking at the graph, that's what we can predict. And then the actual value were told is 63,010. So to find the percentage error, we're gonna take the actual value. So 63,010 minus are predicted value 64,005. 40. Take the absolute value of that and divide it by the actual value. So 64,000 5 40 way multiply this time 200 to get a percentage and we see that the percent error is going to equal about 2.4%

Mhm. So for problems 79, it's a multi step problem, we do have two different questions to answer. But What we're really looking at is a table from 1993 to 2013. So this is showing in billions of dollars. The box office receipts, movie box office receipts. So these receipts um are outlined to us in a linear model. Mhm. Which is our equals 0.2844. Mhm. X plus 5.535. Mhm. And then we're also told that the table shows us Years of five Year increments. So they also give it some Mhm. Clarification where X equals zero. That corresponds to 1993 X equals five, corresponds in 1998 and so on. So really, what X is the number of years after 1993 0 would be zero years? Because 1993 is where we started 1, 1994. And so on that way as well. So part a asked us uh to find where our uh what year where we first exceeded $7.6 billion. So I think that the text is very specific on how they word this because remember we are talking about inequalities, so they do want to know the year in which the receipts first exceeded each amount. Now, if we were to talk about the solid year in and of itself, of course we could round up to the nearest year and that's kind of what we're looking at in part A. And B. But since it did say the where it first exceeded, it's possible that we're going to be looking at a year of course where we've got more than one receipt because this has taken throughout the entire year. That's what we have to assume. So for part a we would set our problem up where it is greater than 7.6. Now all this is in billions. Of course. So we'd have 0.2844 X plus 5.535 Where this is greater than 7.6. Okay. To first exceed 7.6 billion. When we solve this, we would subtract and solve just like a normal uh inequality. Okay. Okay. And then that would leave us with two point to point to 844 X. greater than 2.065 and then divide both sides by .2844. Yeah, so X would be greater than About 7.3. No, I did around that to the nearest one decimal place. But remember we're talking about years. Okay, so 7.3 that's about .3 into the seventh year. So if we're going to look at that year in inside itself, then that's the seventh year After 1993. So we could say that that would be in the seventh year. Now, at that point we know inside the seventh year we are going to first exceeds $7.6 billion. You can look at that as an inequality here, but if we add that 7-1993 part a The answer will be year 2000. Okay. So but that's not saying that you're 2000 didn't have a different year, a different amount of US movie box office receipts. It just means that within that year that is where the amount first exceeded 7.6 billion. Okay. So that is a now when we look at be we're gonna be looking at the exact same type of setup. But this time we are wanting to first exceed 10 billion. So we've got 0.2844 x plus 5.53 five. And now we need to be greater than 10. I just solved exactly the same way. So we're going to subtract, yeah that leaves us with two point point 2844 X. greater than 4.465. And we're gonna divide Mhm. Mhm. Mhm. So X would be greater than 15.7. Again you have to remember I rounded this to the nearest decimal but we are talking about years from 1993. So within the 15th year because it did not exceed and go into 16 we could round up to 16. But because your text was very specific And wanted to know where it first exceeds that amount, we would still need to look at this year as the 15th year. Which is very interesting because your table will already show you the 15th year as a different amount. But that doesn't mean that it's the only amount that was recorded for that specific year. So that would be the interval notation. But for the year for part B, that would be year. Mhm. Oh, all right. Yeah. At the 19 anymore, Yeah, That would be year 2008. Alright, so part a year 2000, Part B, Year 2008. And we are finished.

Here we have a dataset giving us the ages of Oscar winners matched by the years in which there are one dividing them by the best actress and best actor. We want to determine whether or not there is a linear correlation that exists here. So we'll be using our graphing calculators to test for that correlation, running our linear regression T test and forming a scatter plot. So I started by forming the scatter plot, which I did after I entered the data into my stat list On my graphing calculator looks something like this. It doesn't really look like there's a whole lot of linear correlation going on here, so I'm going to assume that there's not. But let's run that linear regression t test to see what we actually find in doing this. We find that we have in our value, which is our correlation coefficient, which is equal to negative 0.287 So not very strong at all. We're pretty close to zero there. It looks like it's a negative association, but not by much. And looking at our T and P values, we can determine the significance or T value gives us a negative 0.949 Probably not significant, given that we have a P value, which is equal to 0.364 which suggests to us that it is actually insignificant. We cannot conclude that there is any linear correlation going on here. So scratch that, Um And now what would we have expected? That there would be correlation? Probably not. Um, it wouldn't really make sense intuitively to assume that each year the winners at the Oscars should be correlated at all by age is probably not much association there. It's probably fairly random, actually.

Today, we're going to be learning about how to draw a scatter plot, how to come up with the correlation coefficient, interpret the slope, find the domain and understand how this all works. And so today we're going to start off by understanding how to draw a scatter plot. And so we have our X and Y axis. You're going to make a scale of your X and Y axis in this question, our independent variable is our internet ads and our dependent variable is going to be based off of our magazines. So up here we will write magazines for our Y. Value and so our internet and our magazines, we use our table and we're going to create a scatter plot by plotting these points. So 8.2 and 14, bus 10.7 and 13.9, 14 and 12.5, 15.5 12 really 17.2 and 12 22 and 10.7. So you start to see a little bit of a pattern in this scatter plot. And finally, and so you start to see a pattern of the scatter plot based off of the independent verily internet and the dependent burial. The magazine. The magazine depends on what's going on with the internet in the context of this question. Understanding us advertising spending. And so the question is, does this appear to be linear? And so we look at the graph and it does appear to be linear with a negative slope. Right. And so we're now going to use a graphing utility to find the line of best fit. That would model the relationship between this. And so now that we've drawn it on paper, we're going to take our graphing calculator and we're going to use this data to fill in our information. And so we're going to go to stat. We're going to go to edit And we're going to put in our information of our percentages. And so we're going to put in 8.2, 10.7 14, 17.2 all the way down as our X. Values our independent variable. And then for L. two, we're gonna put our dependent variable, which is our magazine based off of these percentages. And we're going to keep everything as a whole number as a percentage. Understanding that they are percentages. We want to make sure all those accurate everything lines up nice and neatly and so we want to look and see now what is the line of best fit. And so you take your regression. And since it looks like a line, we're going to go to stat, we're going to go over to couch and we're going to go down to linear regression. Once you're in linear regression, you're going to put in your data lines, which is going to be L one comma L. Two. If you put it under L. Two and L. Three, that's what you would put uh in this little spot here. If you have an 84 plus, you can probably just go right to calculate. Just make sure your X. and Y is lined up and you're going to get a whole bunch of information in that information would be the line of best fit. And so your line of best fit based off of your graphing calculator is going to be why equals And your slope is going to be negative .24. And so we're gonna use negative .24. Which makes sense because the slope is looking downwards And then our y intercept going to be 16 two. And so this would be the line of best fit. That we would draw in our graphing calculator. And so if you take a look at your graphing calculator here, you would look at your stop plot and you would see you're a graph shown here below. And so when you see your graph, which in this case is going to be Y equals negative 0.24 X plus 16.2, you are then going to take go to stat. You're going to go over to help One of our stat again and you're going to take a look at your r value. And if you see your r value is negative .99, that is your correlation coefficient. That means we have a very very strong correlation coefficient because correlation coefficients the strongest one would be negative one or positive one, negative being that it's going in a downwards direction. And so we would label this as our correlation coefficient, which we now know is very strong, which means that it's going to be very close to a linear function. We use the right type of regression and so we have our line of best fit and we now have our correlation coefficient. And so that would answer questions be and questions see the only part about question be that we now have to add in is to write it as a function. And so instead of saying why equals, we're going to write it as F of X. F of X is in function notation. And so it's going to be F of X equals negative 0.24 X Plus 16.2, which is going to be our line of best fit. So this would be part B. And now this would be part six. And so the next part of this says, does the correlation coefficient support your conclusion from part A. And so. Exactly right. This will conclude it because we said that it looked linear and now this confirms that it is a linear graph because it has a really strong correlation coefficient. And so to interpret the slope and see how close we are from the slope, we can take two of these points and find the slope to interpret it. And so what we're gonna do is we're gonna pick out two points, I'll pick up one of these, you can pick any two points you want I'll pick out 17.2, common 12. And so we're going to do 17 points two comma 12. And then we're gonna pick out another point, such as let's pick 10.7 and 13.9. And so since it looks downward and our slope was negative .24, we see that it is going downwards. And so basically as your internet increases, as the price of internet increases, we know that magazines would decrease. Which makes sense right? The more you are using things on the internet, unless you're probably going to read a magazine. And so to prove that we would just do our slope formula, which is why to minus Y one Over X 2 -11, which in this case is 13 -12 Over 10.7 -17.2. And we're hoping to get a negative slope here to prove that we're doing this correctly. Well 13 -12 is one, 10.7 -17.2. And so you take your calculator, You would do 10.7 -17.2 And you get negative 6.5 and you would divide these values. And when you divide these values, you're going to get one Divided by negative 6.5 And you're gonna get negative .15, right? Which is very close to negative 2.4. Right? And so we're right in that ballpark of understanding our line of best fit the domain of this function. We know domain are going to be your X values. And so your domain of this function, you're going to use interval notation and we're going to talk about our X values. And so our X value, we look at our smallest X value here which is 8.2% And our largest x value is 35.1. So we say that all values From 8.2 to 35.1 is our domain. So this is what we call interval notation. You could also say 8.2 is less than or equal to X, which is less than or equal to 35.1. And then finally they want to know to predict the percentage of your spending on magazine ads when Internet ads are 26%. So we want to know what our why value is Given 26% as our x value of this function. And so the last part which is part F Is going to be to plug in f. 26. So when we plug in f of 26, We are going to set that equal to negative .24, which is our regression Times 26, which is our new percentage to figure out how much magazines would cost. Plus our 16.2. And so we say f of 26 or f of 26 would be what percentage from magazines. And so we take our calculator and we would do Negative .24 times 26 Plus 16.2 grounded. And you would get 9.96 person


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