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Warm-Up What is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108} will be divisible by both 2 and 3 ? F. 1/4 G. 3/8 H. 3/5 J. 5/8 K. 7/8

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**6.4 Fitting Linear Models to Data**

Learning Goal: To be able to find the least-squares line.

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Least-Squares Line The process of fitting a curve to a set of data is called regression. Although several linear regression models my be used, the least-squares line is most common. You can find the least-squares line by using your calculator and the equation could be used to predict unknown values.

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Over a number of years the weights of prize-winning pumpkins at the annual Topsfield Fair have tended to increase. Predict the winning pumpkin weight for the year 2005. Winning Pumpkin Weights- Topsfield Fair Year 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 Weight (lb) 433 515.5 530.5 604.5 490 614 470 617.5 718 698

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**Step 1- Make a scatter plot of the data**

Let x = the number of years since 1983 Let y = winning pumpkin weight that year Use your calculator to find the linear regression. It should be y = 23.99x

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**Step 2- Use the equation of the least-squares line to predict the unknown value.**

y = 23.99x 2005 is 22 years after 1983. = 23.99(22) = The winning pumpkin weight for the year 2005 will be about 965 lb.

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The Kumar family planted a tree when they moved into their new home in Predict the height of the tree in 2015. Year Height 1991 47 1992 56 1993 72 1994 85 1995 93 1996 110 1997 118 1998 136 1999 164 2000 185

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Homework Page 355 # 5 – 7

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