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Math III Accelerated

Chapter 11Data Analysis and Statistics

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Warm Up 11.5 Find the value of y if x = 15.

xxy

y

xxy

x

9.163.57.3

878.03.68.2

2.107.005.0.1

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2

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11.5 Modeling Two-Variable Data

Objective: Create regression equations for data.

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Types of Functions We use different types of functions to model data.

Given a set of (x, y) points, we will use the graphing calculator to create a modeling equation.

Function General Form

Linear y = ax + b

Quadratic y = ax2 + bx + c

Cubic y = ax3 + bx2 + cx + d

Exponential y = abx

Power y = axb

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Example 1 The table shows the teacher’s

salary y (in dollars) for x years of teaching experience. Write a linear regression equation to model this data. Enter data into L1 and L2. Select “4:LinReg” from the

STAT CALC menu. Command:

LinReg (ax + b) L1, L2

x y

1 30,6242 32,4363 34,1674 35,9895 37,6846 39,3117 41,098

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Create a Scatter Plot from (x, y) Data

Enter data into L1 and L2. Select “4:LinReg” from the STAT CALC menu. Command: LinReg (ax + b) L1, L2, Y1 Use STAT PLOT to configure the graph.

Set WINDOW based on data values. GRAPH.

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Checkpoint 1 Write a linear regression equation to model

this data.

x 0 1 2 3 4 5 6 7

y 2 9 19 29 40 51 61 73

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Example 2 The table shows a deer

population y counted x years after a hunting ban began. Write an exponential regression equation for this data. Enter data into L1 and L2. Select “0:ExpReg” from the

STAT CALC menu. Command:

ExpReg L1, L2

x y

0 5005 729

10 127115 220620 3765

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Checkpoint 2 Write an exponential regression equation to

model this data.

x 1 2 3 4 5 6 7

y 462 318 181 107 75 62 55

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Example 3 The table shows the number of

people y who rode a roller coaster x hours after an amusement park opened. Write a quadratic regression equation to model this data. Enter data into L1 and L2. Select “5:QuadReg” from the STAT

CALC menu. Command:

QuadReg L1, L2

x y

0 852 1634 2826 3418 398

10 38112 304

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Checkpoint 3 Write an quadratic regression equation to

model this data.

x 0 2 4 6 8 10 12

y 100 178 273 314 349 324 289

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Homework 11.5

Practice 11.5