LINEAR/QUADRATIC REGRESSIONObjective:To write linear and quadratic equations that model real-world data. To make predictions from those equations.

DO YOU REMEMBER THIS FROM ALG 1???

Yr 2000 2001 2002 2003

Sales 49 54 65 74

(000’s)

Find the line of best fit where x is number of years since 2000.

Sales in 2015?________________

Yr 1990 1995 2000 2005 2010

Earn 25 26.8 28 30 31.5

(000’s)

Find the line of best fit where x is the number of years since 1990

Earnings in 2014? _______________

6.476.8 xy

6.176

02.25324. xy

796.32

Define – scatter plot – graph of data. Define – correlation – relationship between data sets Define – line of best fit – the line that gives the most

accurate model of the related data Define – Correlation Coefficient – indicates the strength of

the correlation. (the closer r is to 1 or -1 the more accurate your line is)

Steps: (Stat, edit) Type data into L1 and L2

(Stat, Calc) find linear or quadratic regression

(y=, Vars, Stats, EQ, REGEQ) Type regression line into y =

Year # cell phone subscribers in U.S.

2000 109,478,031

2002 140,766,842

2004 182,140,362

2006 233,000,000

2008 262,700,000

2010 300,520,098

1) Find a linear regression. Let x be the numbers of years since 2000.

2)Graph points and linear regression (on calc) Predict the # of subscribers in the year 2015.

3) Find a quadratic regression. Graph and predict the # of subscribers in the year 2015.

7.880,776,10696.134,598,19 xy

071.905,748,400linear

6.10594130654.815,224,20058.668,62 2 xxy

612.226,213,395quadratic

Data from www.infoplease.comDo you think this is an accurate prediction? WHY?

PRACTICE

Linear / quadratic modeling practice Pg 96 # 12Pg 212 #16, 17

Review for unit 1B test:

Pg. 187 #1-13 (solve the systems by graphing or matrices)

LINEAR MODELING

The chart below gives the year and population in thousands for a city

Yr 1960 1970 1980 1990 2000

Pop (000’s) 18 24 27 30 37

Find the line of best fit where x is the number of years since 1960

What will the population be in the year 2012?

What Year will the pop be 42.6?

NUMBER OF PEOPLE TRAVELING 100 MILES OR MORE ON THANKSGIVING (SOURCE: USA TODAY)

YearNumber of People

(in millions)1990 25.01992 28.41994 30.31996 32.01998 33.21999 33.8

Find a Quadratic Regression (line of best fit) for the data. Let x be the number of years since 1990.

Use this line of best fit to predict the average age in 2010.

LINEAR MODEL

Weight(tons) 1.3 1.4 1.5 1.8 2 2.1 2.4

Miles per Gallon

29 24 23 21 ? 17 15

The Table give the approximate weights in tons and estimates for overall fuel economy in miles per gallon for several cars.

Find a Linear Regression (line of best fit) for the data.

Use this line of best fit to predict the value of the missing value.

NUMBER OF ATMS (SOURCE: USA TODAY)

Year

Number of ATMs

(thousands)1991 901993 981995 1191997 1591999 227

Find a Quadratic Regression (line of best fit) for the data.

Use this line of best fit to predict the average age in 2010.

LINEAR MODEL

year 1998 2000 2002 2004 2006 2008 2020

Average cost per Gallon

2.65 2.89 3.00 3.01 3.20 3.77 ?

The table below gives the average cost of whole milk for several recent years.

What is the equation for the line of best fit?

What would you expect to pay for a gallon of whole milk in 2020?

EXTRA PRACTICE(LINEAR)Year (x) Postage (y)

1995 .32

1999 .33

2001 .34

2002 .37

2006 .39

2007 .41

2008 .42

The table above shows the various postage rates for the years 1995- 2008.

a. what is line of best fit?

b. based on the line of best fit, approximately what would the postage have been in 2010?

Hours Studied xGrade y (%)

6 82

2 63

3 75

1 57

2 68

a. Predict the score for a person who studied 4 hours

b. predict the number of hours you would have to study to score above 93%

a.write the line of best fit

b. What is the average yrly change in the hourly wage?

c. Predict wage in year 10