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Given are data for two variables, $x$ and $y$a. Develop an estimated regression equation for these data.b. Compute the residuals.c. Develop a plot of the residuals against the independent variable $x .$ Do the assumptionsabout the error term seem to be satisfied?

a. $\hat{y}=-7.022+1.587 x$b. $3.5,-2.435,-4.783,-1.544,5.282$c. $\mathrm{No}$

Intro Stats / AP Statistics

Chapter 12

Simple Linear Regression

Linear Regression and Correlation

Missouri State University

Piedmont College

Idaho State University

Lectures

0:00

06:43

The following data were us…

00:48

The r.m.s. error of the re…

04:33

Define the standard error …

12:47

Five observations taken fo…

03:18

(a) Compute the power regr…

07:01

04:24

In Exercises 43–46, tell w…

02:03

04:37

02:54

00:59

Using the regression outpu…

05:34

In $3-5 :$ a. Determine th…

01:47

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03:46

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02:19

problem number 45. We have a small little data set here. Just five data values for the X. And five for the Y. And we're supposed to develop an estimated regression equation for these. And I'm gonna go to the quick way since we know how to do it now. It's an excel. So you go to data analysis and it's regression and just to save some time. So my Y input is B two to B. Six and then the excess A two to a. six. I would go ahead and use get the residuals and go and get a residual plot to and you know, you can pick as many as you want there. But those are the really the two things that you need at least for this question and then click. Ok. And our regression equations to the first part of this or part A is to get The regression equation and it's right here. So the intercept is negative seven um 0 to 2 And then plus 1.5873. X. Okay. And I would not say that those are significant, possibly the slope there that the f statistic looks significant but that's not really important. That's not what I asked Part B asks us to compute the residuals. So here they are down here. So the way that you would do that is you just take the actual y value minus that predicted. So here they're predicted Y values and you would subtract and so you get about 3.5 negative 2.4, -4.8 -5 -1.5 and 53. So those are the residuals. So this is part B. Right here and then part C. Make a residual plots apart. See I went ahead and just made a residual plot here. And if you notice these residuals they they kind of look like they have a pattern here. So they go down and then they go back up. Now. In reality you're gonna want more than five data values to make this a good study. But um you know for practice you you don't want to see a pattern for these. This is not the scatter plot. So that's important. This is not the scatter plot. This is just the residual plot. And you do not want a pattern of residuals. You want kind of randomness to these residuals. So they're kind of bouncing around everywhere. Then we would say that let a linear model would be appropriate. But this does not appear that way. So it says do the assumption about the error term seem to be satisfied. No. And to make a better answer, linear model does not seem appropriate. Okay so it doesn't look Too Good. I mean your multiple are your are correlation coefficients .9 in your score 2.81. Which is pretty good. But I bet it can get better if I had to guess this is probably more of an exponential. In fact you can even look at it by making a scatter plot here. So if you go insert and then a scatter plot. Yeah. See this looks a little bit more exponential in nature, so in reality you probably want to use an exponential regression line here.

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