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Question 5Run a regression analysis on the following bivariate set of data with y as the response variable.20.8 58.9 34.4 -13.3 44.7 9.6 15.5 71.1 20.0.2 131.6 128....

Question

Question 5Run a regression analysis on the following bivariate set of data with y as the response variable.20.8 58.9 34.4 -13.3 44.7 9.6 15.5 71.1 20.0.2 131.6 128.2 4.3 152.2 41.9 42.2 235.4 104.9 37.1 47.6 62.3 58 125.6 86.4 41.8 122.913.2 19.2 17.9 47.7 6.9 23.9 25.2 Verify that the correlation is significant at an & 0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 30.4 on the response variable_What is th

Question 5 Run a regression analysis on the following bivariate set of data with y as the response variable. 20.8 58.9 34.4 -13.3 44.7 9.6 15.5 71.1 20. 0.2 131.6 128.2 4.3 152.2 41.9 42.2 235.4 104.9 37.1 47.6 62.3 58 125.6 86.4 41.8 122.9 13.2 19.2 17.9 47.7 6.9 23.9 25.2 Verify that the correlation is significant at an & 0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 30.4 on the response variable_ What is the predicted explanatory value? (Report answer accurate to one decimal place: ) Question Help: Message instructor



Answers

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy.
$$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline x & {3} & {4} & {5} & {6} & {7} & {8} & {9} & {10} \\ \hline y & {21.9} & {22.22} & {22.74} & {22.26} & {20.78} & {17.6} & {16.52} & {18.54} \\ \hline x & {11} & {12} & {13} & {14} & {15} & {16} & {17} & {18} \\ \hline y & {15.76} & {13.68} & {14.1} & {14.02} & {11.94} & {11.94} & {11.28} & {9.1} \\ \hline\end{array}$$

The following is a solution to number six and were given a pretty small data set here. The X. Values 13558 And then the Y. Values five negative 22 negative one negative three. And the first part of this is to uh create a scatter plot. And you can do that normally manually just make a Cartesian plane and then plot these points like you wouldn't house over one here, these are all ordered pairs. So 153 negative 2525 negative one and eight negative three. But I'm going to use technology and you can use technology to because it makes it a lot neater and a lot nicer. So I'm using a. T. I. T. For but you can use any sort of technology want now if you're using the T. I. T. For then you're just gonna go to stat and then edit. And then in L. One you're gonna put those X. Values and then L. Two you'll put the Y. Values. Then if you go to second Y equals where's the stat plot. I like to have all these off and then this first one should be on so just make sure this is highlighted. And then this first graph here we don't want these grass over here, we're gonna do this. First type L. One is X. List, L. Two is the wine list and then the mark, you choose whichever one you want. I like this first one because it pops up pretty nicely. Then if you press graph you should see all those points. So those are the five data values. Now if you don't see all the points it just means your windows a little bit off. So if you just go to zoom and then this ninth option here zoom stat, click nine then you should be able to see all five points pretty nicely. Now if you were going, so there's a scatter plot, you can print that out or just copy it now. If you were to draw an imaginary line that kind of goes in the middle of all these points, the slope of that line would be negative. So that kind of answers this next part. It says predict the sign of our I'm thinking it's going to be negative, Okay, negative. And the big reason is the slope of that imaginary line is negative. Okay. But more importantly, if you look back at these data values, as the X increases 13558 it seems like the Y. Is kind of decreasing five negative 22 negative one and negative three. So it's getting smaller and smaller. So because of that, as X increases, y decreases, that means it's probably negative. Okay, the last part says actually compute r. And you can use the formula that can be kind of cumbersome. If you go to back to on the IT4, if you go back to stat talc I think this looks about linear so it's going to be a linear regression. So you can either choose the fourth option or the eighth option. It doesn't matter which one yet. So if you just go to four and excellent should be a one while it should be able to. And then we calculate then I see the are down here as negative 0.715 So R equals negative 0.715 Now if you don't see that that's fine. It just means you're diagnostics aren't on. So if you go to second zero and then scroll all the way down to the D's where it's as diagnostic on and click enter and then enter again. It'll say done. Then if you go back to stat calc four and then calculate, then you should see that R and R squared so R is negative 40.715 which verifies our previous answer. We thought that the R might be negative or the sign of our would be negative and it is verified there.

The following is a solution number four. And were given a data set here. The X values 1347 and nine. And the Y values are 556 negative three and zero. And the first part of this is to create a scatter plot. And you can do that manually just by making a Cartesian plane and just plotting these points like you normally would in algebra class or you can use technology and that's what I'm gonna do because it's a lot neither. And I'm really bad at making graphs to, so I'm using a. T. I. T. Four, but you can use any sort of technology want. But if you're using A T. I A T for if you go to stat and then edit in L. One, you should put the X values 1347 and nine. And then in L two put your Y values 556 negative three and zero. Then if you go to second y equals and just make sure this first step plot is on and I'm going to turn the other ones off. So if it's if it's off then you can just turn it on quite easily just make sure this is highlighted. So arrow over and click enter the first graph needs to be highlighted. So it's a scatter plot. X. List is a one, Y. List is L two. Unless you put it in different columns and then as for Mark, you kind of do whatever one you want. I like this first one because it shows up the nicest. So if you press graph, you should see the data values and if you don't that's fine, your windows just a little bit off. If you go to zoom and then this ninth option here zoom stat, then you should see everything. So those are the five data values. And it appears, so you would just copy that to print that out. But it appears that as X is increasing, so from left to right, it looks like why is decreasing. So it's kind of going downhill. Or if you were to draw like an imaginary line that kind of goes in the middle of all those points, the line, the slope of that line would be negative. So that kind of answers the next question, predict the sign of our, I think it's going to be negative. Okay, And the reason why I think it's gonna be negative for one, the slope appears to be negative, slope is negative. Okay. But more importantly, if you look at these data values as you're increasing, the X, the Y appears to be decreasing, so as X increases the wide decreases and anytime that happens, that means they are is probably negative. So the last part is actually to compute are, and we're going to verify that it is actually negative. You can use the formula if you want, but that can be a little cumbersome. I'm going to go back to the calculator. So if you go to stat cowpoke and then you can, this is linear regression because it kind of looks linear, but you either choose 48 where it says lin Wregget doesn't matter which one you choose. I'm gonna choose four X. List is all one wireless is all too, unless you chose different columns and then you calculate, and I'm seeing the R is negative 10.788 So I'm gonna write that down and if you don't see that that's fine. I'll show you how to make it pop up. So negative point 788 So that's my are, which is negative. So that's kind of verified. It is actually the same as our prediction. But if you don't see the R. And the R. Squared, it's okay. Just means we need to turn on your diagnostic. So if you go to second zero, where's this catalog? And then just scroll all the way down until you get to the DS. Where it says diagnostic on. So diagnostic off diagnostic on press enter and then enter again. And it will say done. Then if you go back to stat couch and then either 48 of them matter which one and You see the R. is negative .788.

Trouble. First, you have to enter all of the data into the tables. So list the ex values into L one and the Y values tell, too. And you access those tables by hitting stat and then hitting one. So after this go to stat moved to the Cal, commend you and hit the number eight. Make sure you have l wanna next list and l two and why list and then calculate the linear regression line. When you do that, you find that the equation is why equals 232 point 24 plus forms minus 18.6 expects. And you find the correlation coefficient to be negative. 0.44 nine and we're done.

This is our question number 238. We have the value of X and y so for at one column India 80 taken girder in or at one column. You need to enter the eggs, Williams. And for a two column you need to enter d y values. So as we know the equation of blindness X plus be okay now, in our regulator, he got the value of a That is negative. 2.20 and two and the radio B. That is 53 point the seven. Okay, now put W R and B in dis aggressions for here. Why is it good with negative two point 201 x plus Your bees do three point the selling. So is the ignition off this world line? No, we have Our square is equal to 0.9718 by taking square root board said we have plus or minus. You know 0.9. It vibrate as we can see. Your slope is negative. So you need to take the negative where you are. That is 0.985 So this is the correlation coefficient are okay. Thank you.


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