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Chapter 1: Q33E (page 7)

(T) The table shows the world average daily oil consumption from 1985 to 2015, 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 your linear model to estimate the oil consumption in 2002 and 2017.

Short Answer

Expert verified

a. The scatter plot of the data is obtained and a linear model is appropriate.

b. The regression equation for \(y\) is \(y = 1124.86x + 60,119.86\).

c. The oil consumption in the year 2002 is \(y \approx 79,242\) thousands of barrels per day and in the year 2017 is \(y \approx 96,115\) thousands of barrels per day.

Step by step solution

01

Make a scatter plot of the data

a)

Consider the year since 1985 as the\(x - \)coordinates and thousands of barrels of oil per day as the\(y - \)coordinates.

The procedure to sketch the scatter plot of the given table of data by using the graphing calculator is as follows:

To make the scatter plot of the given data visuallyby using the graphing calculator as shown below:

  1. Open the graphing calculator. Select the “STAT PLOT” and enter the\(\left( {x,y} \right)\)point from the given data in the tab.
  2. Select the “GRAPH” button in the graphing calculator.

Visualization of scatter plot of the given data is shown below:

It is observed from the scatter plot in part (b) that a linear model is appropriate.

02

Determine and graph the regression line that models the data

b)

The procedure to use the computing device to obtain the regression line for \(y\) and graph of the regression line is as shown below:

  1. Open the computing calculator. Enter all the values of \(x\) in the \(x\) values tab and \(y\) values in the \(y\) values tab.
  2. Select the “Calculate the regression equation” button in the computing calculator

Obtain the regression equation is shown below:

The regression equation for\(y\)is\(y = 1124.86x + 60,119.86\).

Visualization of the graph of the regression line is shown below

03

Estimate the oil consumption in 2002 and 2017

c)

Use the linear model from part (b) to find the oil consumption in 2002 and 2017.

Substitute\(x = 17\)in the regression equation to obtain the oil consumption in 2002 as shown below:

\(\begin{aligned}y &= 1124.86\left( {17} \right) + 60,119.86\\ &= 19122.62 + 60,119.86\\ &= 79,242\end{aligned}\)

Substitute\(x = 32\)in the regression equation to obtain the oil consumption in 2017 as shown below:

\(\begin{aligned}y &= 1124.86\left( {32} \right) + 60,119.86\\ &= 35995.52 + 60,119.86\\ &= 96115.38\end{aligned}\)

Thus, the oil consumption in the year 2002 is \(y \approx 79,242\) thousands of barrels per day and in the year 2017 is \(y \approx 96,115\) thousands of barrels per day.

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