acc. alg./geom. a unit question: can real world data be modeled by algebraic functions? standard:...

Acc. Alg./Geom. A

UNIT QUESTION: Can real world data be modeled by algebraic functions?Standard: MM2D1, D2

Today’s Question:Why is linear regression useful?Standard: MM2D2a, b

Scatter Scatter PlotsPlots

A graph of a set of data pairs (x, y)

Using TI-36x1) Press [Data], then [Data], then 4

2) Press [Data]

3) All x values go in L1

4) All y-values go in list 2

5) Press [2nd], then [Data]

6) Select 2-Var Stats

7) Xdata = L1 and Ydata = L2, FRQ = One, then CALC

8) a = slope, b = y-intercept

Example 1: Consumer DebtThe table shows the total outstanding consumer debt (excluding home mortgages)

in billions of dollars in selected years. (Data is from the Federal Reserve Bulletin.)

Let x = 0 correspond to 1985.

a) Find the regression equation appropriate for this data set. Round values to two decimal places.

Year 1985 1990 1995 2000 2003

Consumer Debt 585 789 1096 1693 1987

79.86 463.35y x

Example 1: Consumer Debt (cont)b) Find the approximate consumer debt in 1998.

c) Find the approximate consumer debt in 2008.

1501.53 billion

2300.13 billion

Example 1: Consumer Debt (cont)d) Using the regression equation, predict the year when consumer debt will reach

2,500 billion dollars.

25.5 years or

2010 and a 1/2 year

Dog/Cat Years to Human Years

Homework

Linear Regression Worksheet