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Run a regression analysis on the following bivariate set of data_with y as the response variable_111.6 91.4 83_ 76.4 85.4 69.6 72.8 48.7 93 . 124.4 89.8 113.11642 ....

Question

Run a regression analysis on the following bivariate set of data_with y as the response variable_111.6 91.4 83_ 76.4 85.4 69.6 72.8 48.7 93 . 124.4 89.8 113.11642 . 96 _ 46 . 89 . 52 119.4 36.4 53_ 50. 23_Find the correlation coefficient and report it accurate to three decimal places_What proportion of the variation in y can be explained by the variation in the values of x? Report answer as percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5% . you would e

Run a regression analysis on the following bivariate set of data_with y as the response variable_ 111.6 91.4 83_ 76.4 85.4 69.6 72.8 48.7 93 . 124.4 89.8 113.1 16 42 . 96 _ 46 . 89 . 52 119.4 36.4 53_ 50. 23_ Find the correlation coefficient and report it accurate to three decimal places_ What proportion of the variation in y can be explained by the variation in the values of x? Report answer as percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5% . you would enter 84.5 without the percent symbol ) Based on the data, calculate the regression line (each value to three decimal places) Predict what value (on average) for the response variable will be obtained from a value of 117.6 as the explanatory variable Use significance level of & 0.05 to assess the strength of the linear correlation: What is the predicted response value? (Report answer accurate to one decimal place.



Answers

The following data resulted from an experiment performed for the purpose of regression analysis. The input variable, $x,$ was set at five different levels, and observations were made at each level. a. Draw a scatter diagram. b. Draw the regression line by eye. c. Place a star, $\star,$ at each level approximately where the mean of the observed $y$ values is located. Does your regression line look like the line of best fit for these five mean values? d. Calculate the equation of the regression line. e. Find the standard deviation of $y$ about the regression line. f. Construct a $95 \%$ confidence interval for the true value of $\boldsymbol{\beta}_{1}$. g. Construct a $95 \%$ confidence interval for the mean value of $y$ at $x=3.0$ and at $x=3.5$. h. Construct a $95 \%$ prediction interval for an individual value of $y$ at $x=3.0$ and at $x=3.5$.

So this is our question number 237 here with their expertise. And why will use so in t 83 calculator for every one column you need to enter the X values. And for a two column you need to enter the old wiring loose. My resting enter we have is it will do minus. You're a point, man. 01 Next, then be easy. Goto 26 point Therefore now, as you know, the equation of lion is wise equal to express me. Okay, Now put the value and B here. East negative. 0.90 Onyx and hear the east 26 points. 04 So this is your questionable least red line. Okay, Now, in our computer, we got our square is equal to your 0.937 Okay, now taking square root word sites. So here we have our is equal to negative 0.968 It is Our correlation coefficient are okay. Thank you.

All right, so we want to create a scatter plot of this data. So I'm gonna go over here to the plus sign. I'm in Dez Mohs and add a table. My ex values are negative. 2.3, 1.8 negative. One point. Oh, 4.61 point for 3.7. And I'm just understanding this Table two does most once the exes. Aaron, I'm gonna go back up and add the Y values that go with those all right values. Now, if you're beta doesn't show up on your graph has change your window. You can do that from the little wrench key here in the top, right? Um, and so looking at your data set, you want to make sure you have a range that fits. Um, looks like our smallest number is negative. 2.3 on the X axis. So maybe we go from negative four. Um, highest value. Looks like it's around five. So maybe negative or just seven X or Y x is if we look at that. Looks like Oliver members air positive so we could start at zero. Um, it looks like the biggest number of see is like 89.5. So we want to go above that. Maybe just to make it nice and pretty will go to 100. Click out of that and you should see all of your points line up. Now, if I look at that noticed that that is coming down. Um, it's not going through 00 so I really think that this is probably an exponential, um, equation. And so I want to use this exponential regression. So again, we've got our Y one and x one. And so if we want to use our exponential regression, that's gonna be why one we're gonna use the tilde key, which usually is up in the top left corner, and then our exponential standard form, um, is gonna be a B minutes raised to the x of one. I noticed that when we do that, um, we're gonna get that nice, pretty curve going through our data. So here is our problem. Here's our day, Our aggression. It's been done for us. Um, R squared is close to one. If we were gonna plot are residuals, we could do that. And if you notice they're all very close to zero. So that's awesome. And now we can write our equation. Your regression equation would be y equals. You're a is eight point 784 times your B, which is 1.5 for six, and you're raising that to the X power on notice. What happens is that that shows up directly on that line, and you can see how they are the exact same. And so that would be the regression equation, right for this set of data.

All right. So they gave us a data set. The first thing they want us to do is create a scatter plot. I'm using Dez most. It's an online graphing tool. And so when you open up dez most dot com, you can go over here and click the plus sign, and we're gonna enter a table of values. So I'm gonna go through an inter mo table. You're my exes, and then I'm gonna enter my wives ground. When you look at your chart, you can move your graph around so that you can see it. This looks like it could be an exponential curve. It looks like it's starting up and coming down, but it's staying inside this positive. Why access thing? So we're gonna try Exponential, you're exponential general form. Okay, It's gonna be why one and then we want to use the tilde for their aggression. Let's try a B to the X of one. Oh, my goodness. I don't think we could get any prettier going through those notice. How close are squared is toe one. And if we plotted our residuals there almost sitting on ze road, which is amazing, it's a great, great regression there. So to write that equation, we would have y equals R A value 3.141 times are be value 0.8 of eight. And we're gonna raise that to the X. Make sure you put your be in parentheses or you won't get that same look. But there is our regression equation for this data set.

So decision or version number 3 27 We have the extra news and my real use. So in our ta ta trickle builder or ever got nominated 20 extra juice and pour a little contaminated booty. My release. My missing Enter. We have the video there. That is 1.82. And the body will be That is now Indu seven point or do you fight? And the correlation coefficient are that is here. Oh, my doubling for now. As you know, the equation off line that is X plus Be now here he's 1.82 weeks less. Be 90 77 point 35. Well, this is a regression of regulation line, and this is our or listen, coefficient are Thank you.


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