Nonlinear Regression Worksheet Answers

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