1. 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

2. Scatter Plots A graph of a set of data pairs (x, y)

4. Using TI-36x 1)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 [2 nd ], then [Data] 6)Select 2-Var Stats 7)Xdata = L1 and Ydata = L2, FRQ = One, then CALC 8)a = slope, b = y-intercept

5. Example 1: Consumer Debt The 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. Year19851990199520002003 Consumer Debt585789109616931987

6. 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

7. 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

8. Dog/Cat Years to Human Years

9. Homework Linear Regression Worksheet