Bell Ringer

Find each slope:

1. (5, –1), (0, –3) 2. (8, 5), (–8, 7)

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

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.