Download 2.5 Notes

Name: ________________________ Date: ________________ Period: ____________
Algebra 2: Section 2.5 Linear Regression Notes
Calculator Reference: Linear Regression
If you have a data table, the calculator can help you find an equation or rule for the function.
X
Example: Given the following data set, find an equation for Y.
-4
-2
0
2
4
6
STEPS
TYPE IN…
Input data table
1.
2.
3.
4.
Y
-16.5
-10.5
-4.5
1.5
7.5
13.5
Press [STAT]
Choose “EDIT”
Enter X values on “L1”
Enter Y values on “L2”
Note: if there are already values in L1, you should move the cursor to L1 and
press [CLEAR].
Find the Regression
Equation
5. Press [STAT] again
6. Choose “CALC”
7. Choose option 4 “LinReg (ax + b)”
8. Next in order input which lists to use for the regression, press [2nd], then
[1] for L1, next press [,] to separate your two lists and last press [2nd] and
[2] to bring up your L2 list. Press [,] [VARS] and scroll to the right, now
press [1] [1].
9. Hit [ENTER]
Interpret the results
10. For a final answer, rewrite the y= ax + b equation by substituting the
specific values for “a” and “b.”
11. This equation will be y = 3x + -4.5 or y = 3x – 4.5. This equation is now
saved as Y1.
If your calculator doesn’t
show an r or r2 value
12. Go to the “CATALOG” by pressing [2nd] then the [0] key.
13. Press the [x-1] key. This allows you to skip ahead to the D’s.
14. Arrow down until you select “DiagnosticOn”
15. Hit [ENTER] two times.
16. Repeat steps 5-8 above to see your r and r2 values.
(More on this to come)
Plotting the Scatter Plot
17. Press [2nd] and then press [STAT PLOT] to enter the stat plot menu,
next press [1] to enter plot 1
18. In the next menu highlight ON and then press [ENTER] to turn on the stat
plot, and be sure that Xlist is L1 and Ylist is L2
19. Next press [ZOOM] and then press [9] for ZoomStat
20. You should see the scatterplot and the linear regression line!
21. To find a specific value press [TRACE] and type in any x value.
Name: ________________________ Date: ___________________ Period: ____________
Algebra 2: Section 2.5 Linear Regression
Make a scatter plot on your calculator and Write the equation of a line of best fit.
1. {(1, 2.1), (3, 3.1), (5, 4.0), (7, 5.2), (9, 5.9)}
2. {(2, 3.9), (1, 1.8), (0, 0.1), (1, 1.9), (2, 3.8)}
3. The table shows the number of misdirected bags and the number of late flight
arrivals by week, for one airline.
Incidents per Week for January
Number of Misdirected Bags
37
42
25
9
Number of Late Arrivals
14
20
12
6
SOURCE: http://www.nass.usda.gov/Statistics_by_State/Texas/index.asp#.html
4. The table shows the value of rice produced in Texas from 2001 to 2007.
Value of Rice Produced in Taxes
Year
Price per lb
2001
$.461
2002
$.416
2003
2004
$.735
$.735
2005
2006
$.777
2007
$1.00
$1.13
SOURCE: http://www.nass.usda.gov/Statistics_by_State/Texas/index.asp#.html
a. Use a calculator to find the line of best fit. Let x = the number of years since 2000.
b. Using your linear model, predict the value of rice in Texas in 2015.
c. Using your linear model, predict when the price is likely to reach $2.60 per pound.
5. The table shows the numbers of countries that participated in the Winter Olympics from 1984 to
2006.
Winter Olympic Partipation
Year
Number of Countries
1984
1988
1992
1994
1998
2002
2006
49
57
64
67
72
77
80
SOURCE: www.infoplease.com
a. Make a scatter plot. Let x = the number of years since 1980.
b. Use a calculator to find the line of best fit and write the equation for the line.
c. Predict the number of participating countries in 2022.