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Warm-Up Making Predictions

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WK2

Lesson Question

Words to Know

Write the letter of the definition next to the matching word as you work through the lesson. You may use the glossary to help you.

linear regression equation

extrapolation

predict

interpolation

A. a prediction made within the range of the values in the data set

B. the equation of the most accurate straight line model for a set of data points

C. a prediction made outside the range of the values in the data set

D. to tell or state in advance

Lesson Goals

based on given data.Predict

Use existing relationships to make

.

Use trend lines and regressionequations to make predictions.

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Warm-Up Making Predictions

Trend Lines as Estimates

• The scatterplot shows the weight of pumpkins based on circumference.

x

yW

eigh

t (ki

logr

ams)

1

5

10 (100, 10)

(20, 2)

10 50 100Circumference (cm)

Choose two points on the trend line:(x1, y1) = (20, 2)

(x2, y2) = (100, 10)

Use the slope formula:

=−−

2 1

2 1

my y

x x

−

−=

10

100

=

= 1

8

80

Find the y-intercept :

y = mx + b

+= • b1

1010

10 = + b−10 −10

= b

Write the equation of the trend line in slope-intercept form:

=y

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Instruction Making Predictions

2Slide

Interpolating Data Graphically

Interpolation is a prediction made within the range of values in a data set.

Data is given between 0 and years.

Use the graph to predict the income of a teacher with 3 years of experience.

Prediction: $

Inco

me

in T

hous

ands

($)

Years of Experience

x

y

20

What Do Teachers Make?

30

40

50

60

2 4 6 8

(3, 37,000)

10

© Edgenuity, Inc. 4

Instruction Making Predictions

4Slide

United States Life Expectancy

Consider the following life expectancies in the United States from 1980 to 2010:

(1980, 73.7), (1985, 74.7), (1990, 75.4), (1995, 75.8), (2000, 76.8), (2005, 77.4), (2010, 78.7)

78

76

74

72

1980 1990 2000

y = 0.156x − 235

2010

x

y

Predict US life expectancy for 1997.

On the trend line when x = 1997, y is approximately going to be years.

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Instruction Making Predictions

Finding the Regression Equation

A linear regression equation is the equation of the most accurate straight line model for a set of data points.

Use the data to find the regression equation for life expectancies in the United States from 1980 to 2010.

78

76

74

72

1980 1990 2000

y = 0.156x − 235

2010

x

y The equation of the trend line:

y = 0.156x −

7Slide

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Instruction Making Predictions

Using the Regression Equation to Make Interpolations

EXAMPLE

Use the regression equation to predict life expectancy for 1981.

y = 0.156x − 235

y = 0.156(   ) − 235y = 309.036 − 235

y =

y ≈ years

78

76

74

72

1980 1990 2000Time (years)

US Life Expectancy

Age

(yea

rs)

y = 0.156x − 235

2010

x

y

8Slide

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Instruction Making Predictions

Using the Regression Equation to Predict Independent Values

Use the regression equation to predict the year when US life expectancy was 76.5.

y = 0.156x − 235

= 0.156x − 235

+ 235 + 235

= 0.156x

=311.5

0.156

0.156

0.156

x

= x

x ≈

78

76

74

72

1980 1990 2000Time (years)

US Life Expectancy

Age

(yea

rs)

y = 0.156x − 235

2010

x

y

10Slide

© Edgenuity, Inc. 8

Instruction Making Predictions

Extrapolating Data

Extrapolation is a prediction made

the range of values in

the data set.

Predict the year when US life expectancy will be 90 years.

y =

78

76

74

72

1980 1990 2000Time (years)

US Life Expectancy

Age

(yea

rs)

y = 0.156x − 235

2010

x

y

y = 0.156x – 235

= 0.156x – 235

+235 +235

325 = 0.156x

=0.156

0.156x

= x

x ≈

12Slide

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Summary

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Making Predictions

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Answer

Use this space to write any questions or thoughts about this lesson.

Lesson Question How do you use a trend line to make a prediction?