PreCalculus
Nonlinear Regression Worksheet
1) Suppose an object slides without friction down an inclined plane in a laboratory. Sparks are generated on paper tape every tenth of a second to mark the position of the object. The distance between parks on can be measured to generate a data set that relates position of the object with time since released.
Time
.1
2
3
4
.5
6
7
8
9
1.0
(sec)
Position (cm)
0.2
0.7
1.3
2.2
3.3
4.5
6.3
8.0
10.2
12.5
Time
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
(sec)
Position (cm)
15.0
17.7
20.6
23.8
27.2
30.8
34.8
38.9
43.1
Write the quadratic regression equation that models the data. y=11.43299x²+1.02173x-103725
What is the correlation coefficient? 99997
Is the model a good fit? Yes
Find the position when the time is 2 seconds?
x=2
47.73818
Is this interpolation or extrapolation? extrapolation
The diameter and volume of several trees are given in the table below.
2)
Diam. (inches)
17
19
20
23
25
28
38
39
41
Volume (100s of board ft)
19
25
32
57
71
113
252
259
294
Write the power regression equation that models the data. Y=.00254X
What is the correlation coefficient? 99619
Is the model a good fit? Yes
3.16219
Is this interpolation or extrapolation?. interpolation
Find the volume when the diameter is 26 inches? 7579.21684
75.792168
Find the diameter if the volume is 15,000 board feet. 12=150 32.26467
3)
The following data was gathered from a pendulum swinging.
Swing
Lgth.
14
28
42
56
70
84
98
112
126
140
154
1
168
(cm)
Time (sec)
8.34
11.32
13.25
15.54
16.78
18.49
19.81
21.07
22.62
23.78
24.66
26.24
Sketch the scatterplot.
Write the logarithmic regression equation that models the data. -12.78140 +7.265321nx What is the correlation coefficient? 97999
Is the model a good fit? Yes
Find the time in seconds when the swing length is 10 cm? 3.94762
Is this interpolation or extrapolation? extrapolation
Homework
1. Read page 258
2. Sketch the graph of the Gaussian Model.
3. Sketch the graph of the Logistic Growth Model.
4. Do #1-6 on page 266
5. Do #68 on page 271
6. Do # 70 on page 271
Nonlinear Regression Worksheet Answers
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