L INEAR /Q UADRATIC REGRESSION Objective: To write linear and quadratic equations that model real-world data. To make predictions from those equations.

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Presentation transcript:

L INEAR /Q UADRATIC REGRESSION Objective: To write linear and quadratic equations that model real-world data. To make predictions from those equations.

D O YOU REMEMBER THIS FROM ALG 1??? Yr Sales (000’s) Find the line of best fit where x is number of years since Sales in 2015?________________ Yr Earn (000’s) Find the line of best fit where x is the number of years since 1990 Earnings in 2014? _______________

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 ,478, ,766, ,140, ,000, ,700, ,520,098 1) Find a linear regression. Let x be the numbers of years since )Graph points and linear regression (on calc) Predict the # of subscribers in the year ) Find a quadratic regression. Graph and predict the # of subscribers in the year Data from Do you think this is an accurate prediction? WHY?

P RACTICE Linear / quadratic modeling practice Pg 96 # 12 Pg 212 #16, 17 Review for unit 1B test: Pg. 187 #1-13 (solve the systems by graphing or matrices)

L INEAR M ODELING The chart below gives the year and population in thousands for a city Yr Pop (000’s) 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 ) Year Number of People (in millions) Find a Quadratic Regression (line of best fit) for the data. Let x be the number of years since Use this line of best fit to predict the average age in 2010.

L INEAR MODEL Weight(tons) Miles per Gallon ?1715 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) Find a Quadratic Regression (line of best fit) for the data. Use this line of best fit to predict the average age in 2010.

L INEAR MODEL year Average cost per Gallon ? 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?

E XTRA P RACTICE (L INEAR ) Year (x) Postage (y) The table above shows the various postage rates for the years 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 (%) 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