holt mcdougal algebra 2 1-4 curve fitting with linear models cover 1.4 if time; non-algebra 2...
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Fit scatter plot data using linear models with and without technology.
Use linear models to make predictions.
1.4 Objectives
A line of best fit may also
be referred to as a trend line.
Holt McDougal Algebra 2
1-4 Curve Fitting with Linear Models FOUR KINDS OF CORRELATIONS (YOU WILL LEARN ABOUT IN TRANSITION)
Positive Correlation Negative Correlation
Constant Correlation No Correlation
Holt McDougal Algebra 2
1-4 Curve Fitting with Linear Models 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
Example 1 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.
That’s to much work with paper &
pencil
How to:Calculator data entry
continued
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
Tables:ACT
o
o
••••••••••
•
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?)
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.
•
••••
•••••
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
example 2 continued
Step 3Step 3 Sketch a line of best fit. Sketch a line of best fit.
Draw a line that splits the Draw a line that splits the data evenly above and below.data evenly above and below.
example 2 continued
•
••••
•••••
Step 4 Step 4 Identify the equation Identify the equation for the data.for the data.
end
Example 3: Anthropology ApplicationAnthropologists 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.
••••
• • •
•a. Make a scatter
plot of the data with femur length as the independent variable.
example 3 continued
Holt McDougal Algebra 2
1-4 Curve Fitting with Linear Models
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 + 54.04.
Example 3 Continued
Holt McDougal Algebra 2
1-4 Curve Fitting with Linear Models Example 3 Continued
What does the slope indicate about problem?
c. A man’s femur is 41 cm long. Predict the man’s height.
Substitute 41 for l.
The height of a man with a 41-cm-long femur would be about 173 cm.
h ≈ 2.91(41) + 54.04
The equation of the line of best fit is h ≈ 2.91l + 54.04. Use the equation to predict the man’s height. For a 41-cm-long femur,
h ≈ 173.35
Example 3 Continued
end
•••••
•••••
Example 4
a. Make a scatter plot of the data with horsepower as the independent variable.
The gas mileage for
randomly selected cars
based upon engine
horsepower is given
in the table.
Holt McDougal Algebra 2
1-4 Curve Fitting with Linear Models
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 + 47.5.
Example 4 Continued
c. Predict the gas mileage for a 210-horsepowerengine.
Substitute 210 for x.
The mileage for a 210-horsepower engine would be about 16.0 mi/gal.
y ≈ –0.15(210) + 47.50.
The equation of the line of best fit is y ≈ –0.15x + 47.5. Use the equation to predict the gas mileage. For a 210-horsepower engine,
y ≈ 16
Example 4 Continued
The slope is about –0.15, so for each 1 unit increase in horsepower, gas mileage drops ≈ 0.15 mi/gal.
What does the slope indicate ?
end
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