The calorie requirements for males is shown in the table below. Use your calculator to find the line of best fit for the data.
Calorie Requirements (Male), 159 years
Age Range,

13  46  710  1114  1518  1959 

Calorie Needs,

1230  1715  1970  2220  2755  2550 
The age is measured in years. Source: www.fatfreekitchen.com
Watch This
Watch the first part of this video, until about 3:30.
Keep in mind that a line of best fit can also be called a linear regression .
James Sousa: Linear Regression on the Graphing Calculator
Guidance
In the previous lesson, we learned how to find the linear equation of best fit by hand. This entire process can also be done by your graphing calculator. It is recommended that you use a graphing calculator for two main reasons: accuracy and consistency. The graphing calculator will be more accurate than a calculation by hand and it will also be more consistent between students, or a greater likelihood that everyone will get the same answer.
Example A
Below is a table for the total number of home runs hit from 19902000. Make a scatterplot using your graphing calculator.
1990  1991  1992  1993  1994  1995  1996  1997  1998  1999  2000 

3317  3383  3038  4030  3306  4081  4962  4640  5064  5528  5693 
Solution:
Recall pair is a point; (1990, 3317), for example. In the graphing calculator, we need to enter these as
To create a list:
1. Press STAT.
2. In EDIT, select 1:Edit…. Press ENTER.
3. The List table appears. If there are any current lists, you will need to clear them. To do this, arrow up to L1 so that it is highlighted (black). Press CLEAR, then press ENTER. Repeat with L2, if necessary.
4. Now, enter the data into the lists. Enter all the entries into L1 (years) first and press enter between each entry. Then, repeat with L2 and the total home run numbers. Your screen should look something like this when you are done.
5. Press
6. Press
7. Clear any equations that are in the
8. Press
9. Press GRAPH. Nothing may show up. If this is the case, press ZOOM and scroll down to 9:ZoomStat . Press ENTER. Your plot should look something like this.
Example B
Find the equation of best fit for the data from Example A. Use a graphing calculator.
Solution: Here are the directions for finding the equation of best fit. In the TI 83/84, it is also called Linear Regression, or LinReg.
1. After completing steps 15 above, press STAT and then arrow over to the CALC menu.
2. Select
4:LinReg
3. You will be taken back to the main screen. Type
(L1,L2)
and press ENTER.
L1 is
4. The following screen shows up. To the calculator,
5. If you would like to plot the line on the scatterplot from Example A above, (after Step 9 in Example A) press
Example C
Use the equation found in Example B to predict the number of home runs hit in 2015.
Solution:
Use
Because we cannot have a fraction of a home run, round up to 9625.
Intro Problem Revisit
Following the steps outlined in this lesson on your calculator, the line of best fit is
Guided Practice
Round all answers to the nearest hundredth.
1. Use the data set from Examples A and B from the previous concept and find the equation of best fit with the graphing calculator. Compare this to the answer we found in Example B. Use both equations to find the sales for 2010.
2. Use the data set from the Guided Practice in the previous concept and find the equation of best fit with the graphing calculator. Compare this to the answer we found.
Answers
1. From Examples A and B in the previous concept, we did not have a table. You need to estimate the values from the scatterplot. Here is a sample table for the scatterplot. Remember, this is years vs. money, in billions.
1999 (0)  2000 (1)  2001 (2)  2002 (3)  2003 (4)  2004 (5)  2005 (6)  2006 (7)  2007 (8)  2008 (9)  2009 (10) 

14.8  14.1  13.8  13  12  12.8  13  12.3  11  9  6.2 
Now, using Examples A (Steps 15) and B (Steps 14) from this concept, determine the equation of best fit. If you used the data set above, you should get
2. Using the calculator, we get
Explore More
Round all decimal answers to the nearest hundredth.

Using the Apple data from the previous concept (repeated below), find the equation of best fit with your calculator. Set Oct. 2009 as
x=0 .
The price of Apple stock from Oct 2009  Sept 2011 source: Yahoo! Finance
10/09  11/09  12/09  1/10  2/10  3/10  4/10  5/10  6/10  7/10  8/10  9/10 

$181  $189  $198  $214  $195  $208  $236  $249  $266  $248  $261  $258 
10/10  11/10  12/10  1/11  2/11  3/11  4/11  5/11  6/11  7/11  8/11  9/11 
$282  $309  $316  $331  $345  $352  $344  $349  $346  $349  $389  $379 
 Predict the sales for January 2012.

Using the Home Run data from the previous concept (repeated below), find the equation of best fit with your calculator. Set 2000 as
x=0 .
Total Number of Home Runs Hit in Major League Baseball, 20002010 . source: www.baseballalmanac.com
2000  2001  2002  2003  2004  2005  2006  2007  2008  2009  2010 

5693  5458  5059  5207  5451  5017  5386  4957  4878  4655  4613 
 Predict the total number of home runs hit in 2015. Compare this to the answer from Example B.
 The table below shows the temperature for various elevations, taken at the same time of day in roughly the same location. Using your calculator, find the equation of best fit.
Elevation, ft .  0  1000  5000  10,000  15,000  20,000  30,000 

Temperature
,

60  56  41  27  9  8  40 
 Using your answer from #5, what would be the estimated temperature at 50,000 feet?

The table below shows the average life expectancy (in years) of the average male in relation to the year they were born. Using your calculator, find the equation of best fit. Set 1930 as
x=30 .
Year of birth  1930  1940  1950  1960  1970  1980  1990  2000  2007 

Life expectancy, Males  58.1  60.8  65.6  66.6  67.1  70  71.8  74.3  75.4 
Source: National Center for Health Statistics
 Based on your equation from #7, what would you predict the life expectancy of a male born in 2012 to be?

The table below shows the average life expectancy (in years) of the average female in relation to the year they were born. Using your calculator, find the equation of best fit. Set 1930 as
x=30 .
Year of birth  1930  1940  1950  1960  1970  1980  1990  2000  2007 

Life expectancy, Males  61.6  65.2  71.1  73.1  74.7  77.4  78.8  79.7  80.4 
Source: National Center for Health Statistics
 Based on your equation from #9, what would you predict the life expectancy of a male born in 2012 to be?
 Science Connection Why do you think the life expectancy for both men and women has increased over the last 70 years?