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Problem 28 Hard Difficulty

The table shows average US retail residential prices of electricity from 2000 to 2012, measured in cents per kilowatt hour.

(a) Make a scatter plot. Is a linear model appropriate?
(b) Find and graph the regression line.
(c) Use your linear model from part (b) to estimate the average retail price of electricity in 2005 and 2013.

Answer

a. A linear model would not be the best way to model the data
b. [Please see graph and explanation]
c. $2005 : y=9.7277$ $2013 : y=12.3749$

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Video Transcript

Okay, here's another problem. That would be a great one to do on a graphing calculator. We have a table of data, which shows the prices of electricity over time, and we want to start by making a scatter plot. So we go into the stat menu and then into the edit menu, and we type our numbers into list one endless, too. From here. We want to turn on the scatter plot so we go into the staff plot menu, which would be second. Why equals go into the menu for plot number one, Turn it on and make sure that it's a scatter plot using list one and list, too. Once we have those settings done, we can go into the zoo menu and choose Zoom Stat number nine, and it will set a good window based on our numbers. So here's the scatter plot. So the question is, does it seem like a linear model is appropriate? Well, it's actually looking kind of curvy, and it's looking like maybe it's tapering off. Maybe it grew faster, and then now it's growing slower. So perhaps a linear model is not the most appropriate, however, even if that's the case, we're finishing the rest of the problem using a linear model. So maybe the results of the rest of the problem aren't going to be as accurate as if we used a different model. So we'll move on to part B, finding graph the regression line. So what we want to do is go back into stat and then over to calculate and go down to choice Number four, Linear regression and press Enter. We're using List one and list, too. We don't need to worry about frequency list. And because we do want to graph the line, we're going to store the regression equation in our Y equals menu. So from here we go to the variables button over to why variables choose function and choose why one. And now let's calculate the linear regression line. So we get approximately. Why equals 0.33 x plus 8.1. And when we press y equals, we see that that was pasted in to the Weichel Zeman units ready to graph. So now we press graph and there's a line and there's our scatter plot. Finally, let's use the linear model to estimate the average retail price of the electricity in the year 2005. So the year number in our X column was a year since the year 2000. So we're going to use X equals five to represent the year 2005 and I'm going to use a table to do this. So I'm going to go into my table set menu, which is second window. Make sure that I have independent ask, which allows me to type in my own X values. And then I go into the table menu, which is second graf, and I type in my five for the year 2005. Don't worry. If there are other numbers there left over from other problems, they don't matter. So for your five the year 2005 we have 9.73 approximately since per kilowatt hour, and then we can repeat that for the year 2013 which would be X equals 13 and we get 12.38 since per kilowatt hour.

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