http://www.ck12.org Chapter 15. Concepts of Statistics
TABLE15.17:
Age(Years) Height (ft)
0 2
2 2.8
4 4
8 7.5
12 10
16 10.4
20 10.45- The following data represents the speed that Ben can kick a soccer ball at different ages. Determine the best
regression function to use and determine its equation.
TABLE15.18:
Age(Years) Speed (mph)
4 15
10 32
20 65
30 70
50 45
60 35- What are two weaknesses and two strengths of the model used to predict Ben’s kicking speed from Guided
Practice 2?
Answers: - Logistic is the best function family because it levels off over time indicating that the elephant ceases to grow once
it matures.
yˆ= 1 + 5. 452610.^7601 ·e− 0. 3199 x
- The best regression to use is a quadratic relationship because when Ben is little he cannot kick the ball very fast
and when he is old he also cannot kick the ball very fast. Ben can kick the ball the fastest when he is an adult
between the ages of 20 and 40.
yˆ=− 0. 05981 x^2 + 4. 0679 x+ 0. 6191 - One strength is that a quadratic model correctly describes the peak of kicking speed occurring in the middle of
Ben’s life. A linear regression might forecast Ben’s kicking speed increasing forever and a logistic regression might
forecast Ben’s kicking speed always staying fast despite his old age. A second strength of the model could be the