1. Cover 1.4 if time; non-Algebra 2 objective
Teaching note
Cover 1.4 if time; non-Algebra 2 objective
Gasaway going over briefly: get students to narrow down, positive verse negative correlation just by appearance and how to do on calculator

2. Bell Ringer
Find each slope:
1. (5, –1), (0, –3) 2. (8, 5), (–8, 7)

3. 1.4 Objectives
Fit scatter plot data using linear models with and without technology.
Use linear models to make predictions.
A line of best fit may also
be referred to as a trend line.

5. Four Kinds of Correlations (you will learn about in Transition)
Positive Correlation
Negative Correlation
No Correlation
Constant Correlation

6. Teaching note: **Practice how to use calculator with following slide
** make sure all steps are included for students
**Need uncooked spaghetti for this unit (optional).
Be patient, allow students time to copy question and data.
Offer students graph paper

7. Scatter Plots + Calculator
1) STAT 
#1 
L1 (x) , L2 (y) (enter data; use arrow keys to select column) 
STAT 
CALC 
4enter LinReg(ax+b) 
2nd 
8) y= 
plot1 
on 
TYPE
X list L1 & Y list L2 
mark (select on) 
GRAPH

8. Example 1 How to: Calculator data entry
That’s to much work with paper & pencil
Albany and Sydney are about the same distance from the equator. (a)Make a scatter plot with Albany’s temperature as the independent variable. (b)Name the type of correlation. (c)Then sketch a line of best fit and (d)find its equation.
Tables:
ACT
How to:
Calculator data entry
Enter ______ in list L1 by pressing STAT and then 1.
Enter _______ in list L2 by pressing 
Make scatter plot in the following way:
Press 2nd Y=
PLOT 1
set up desired type
when done, press GRAPH
cont
inued

9. Does yours look like this ? example 1 continued
Albany and Sydney are about the
same distance from the equator.
(a)Make a scatter plot with Albany’s
temperature as the independent variable.
(b)Name the type of correlation.
(c)Then sketch a line of best fit and
(d)find its equation. (hint: what is m? b?) o • • • • • • • • • • •

10. Example 2
(a)Make a scatter plot for this set of data. (b)Identify the correlation
(c)sketch a line of best fit
(d)find its equation.

11. Teaching note: following slide
Do not advance to next slide until students have had time to finish previous slide

12. • • • • • • • • • • example 2 continued Step 1 Plot the data points.
Step 2 Identify the correlation.
Notice that the data set is positively correlated–as time increases, more points are scored • • • • • • • • • •

13. • • • • • • • • • • example 2 continued
Step 3 Sketch a line of best fit.
Draw a line that splits the data evenly above and below. • • • •
Step 4 Identify the equation
for the data. • • • • • •
end

14. Example 3: Anthropology Application
Anthropologists can use the femur, or thighbone, to estimate the height of a human being. The table shows the results of a randomly selected sample.
(a)Make a scatter plot for this set of data. (b)Identify the correlation
(c)sketch a line of best fit
(d)find its equation.

15. • • • • • • • • example 3 continued
a. Make a scatter plot of the data with femur length as the independent variable. • • • • • • • •

16. Example 3 Continued
b. Find the correlation coefficient r and the line of best fit. Interpret the slope of the line of best fit in the context of the problem.
Enter the data into lists L1 and L2 on a graphing calculator. Use the linear regression feature by pressing STAT, choosing CALC, and selecting 4:LinReg. The equation of the line of best fit is h ≈ 2.91l

17. What does the slope indicate about problem?
Example 3 Continued
What does the slope indicate about problem?

18. c. A man’s femur is 41 cm long. Predict the man’s height.
Example 3 Continued
c. A man’s femur is 41 cm long. Predict the man’s height.
The equation of the line of best fit is h ≈ 2.91l Use the equation to predict the man’s height. For a 41-cm-long femur,
h ≈ 2.91(41)
Substitute 41 for l.
h ≈
The height of a man with a 41-cm-long femur would be about 173 cm.
end

19. • • • • • • • • • • Example 4 The gas mileage for
randomly selected cars
based upon engine
horsepower is given
in the table. • • • • • • • • • •
a. Make a scatter plot of the data with horsepower as the independent variable.

20. Example 4 Continued
b. Find the correlation coefficient r and the line of best fit. Interpret the slope of the line of best fit in the context of the problem.
Enter the data into lists L1 and L2 on a graphing calculator. Use the linear regression feature by pressing STAT, choosing CALC, and selecting 4:LinReg. The equation of the line of best fit is y ≈ –0.15x

21. What does the slope indicate ?
Example 4 Continued
What does the slope indicate ?
The slope is about –0.15, so for each 1 unit increase in horsepower, gas mileage drops ≈ 0.15 mi/gal.
c. Predict the gas mileage for a 210-horsepower engine.
The equation of the line of best fit is y ≈ –0.15x Use the equation to predict the gas mileage. For a 210-horsepower engine,
y ≈ –0.15(210)
Substitute 210 for x.
y ≈ 16
The mileage for a 210-horsepower engine would be about 16.0 mi/gal.
end

22. Teaching note:
Exit Question long

23. Exit Question: complete on graph paper attached to Exit Question sheet
(a)Make a scatter plot for this set of data using your calculator
(b)find its equation.