1. 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

2. 6.4 Fitting Linear Models to Data
Learning Goal: To be able to find the least-squares line.

3. 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.

4. 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

5. 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

6. 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.

7. 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

8. Homework
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