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Problem 27 Hard Difficulty

The table shows world average daily oil consumption from 1985 to 2010 measured in thousands of barrels per day.

(a) Make a scatter plot and decide whether a linear model is appropriate.
(b) Find and graph the regression line.
(c) Use the linear model to estimate the oil consumption in 2002 and 2012.

Answer

(a) See the scatter plot in part (b). A linear model seems appropriate.
(b) Using a computing device, we obtain the regression line
$y=1116.64 x+60,188.33$
(c) For $2002, x=17$ and $y \approx 79,171$ thousands of barrels per day.
For $2012, x=27$ and $y \approx 90,338$ thousands of barrels per day.

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Video Transcript

all right here we have another great problem for a graphing calculator. We have a table of data and we're going to start by making a scatter plot. So we go into the stat menu and then we go into edit and we type our data into list one and list, too. Once we have that done to turn on a scatter plot, we can go into the stat plot menu, which is second y equals. Go into the menu for plot number one and turn it on and make sure that it is a scatter plot using list one and list, too. Once we have those settings, we can go into the zoom menu and choose Zoom Stat, which is zoom number nine. And here's our scatter plot. It does look like those points are falling along the line, so I would say a linear model is appropriate for Part B. We want to find and graph the regression line, so we go back to the stat menu over to calculate down to linear regression. Number four Press enter. Yes, we went list one and list to. We don't need to worry about frequency list and because we want to draw the graph, we should store the regression equation in the y equals menu. So we go from here to vars over two y variables. Choose function and choose why one. And now we can calculate the regression model. So the equation of the line is approximately. Why equals 1116 x plus 60,000 won 88. And when we press, why equals we see that that was pasted into the y equals menu, and now it's ready to graph. So we compress graph, and we will see that line along with our scatter plot. Okay, Finally, we want to estimate the oil consumption in the year 2002 in the year 2012 based on this model. And so the year 2002 would be 17 years since 1995. So we're going to use 17 for X value and find its Y value. And I would like to use the table for this. So first I'm going to go into the table set when menu, which is Ah, second window and make sure that the independent variable is set to ask, which allows me to type in my own X values And then I'm going to go into the table menu, which is second graf, type in an X value of 17. That's for the year 2002 and we get 79,171 ah thousands of barrels of oil per day. And we can repeat that for the year 2012. 10 years later will use an X value of 27 and that would be 90,338 thousands of barrels of oil per day.

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