The following data represent the growth of a population of fruit flies over a 6-week period. Test the following models by plotting an appropriate set of data. Estimate the parameters of the following models. a. P = C1t b. P = ae^bt t (days) 7 14 21 28 35 42 P (number of observed flies) 8 41 133 250 280 297 a) Obtain the coefficients for the two models. b) Use the residual frame norm to verify which model best approximates the data.
1) The following data represent the growth of a population of fruit flies over a 6-week
period. Test the following models by plotting an appropriate set of data. Estimate the
parameters of the following models.
a. P = C1t
b. P = ae^bt
t (days) 7 14 21 28 35 42
P (number of observed flies) 8 41 133 250 280 297
a) Obtain the coefficients for the two models.
b) Use the residual frame norm to verify which model best approximates the data.
2) In the following data, x is the diameter of a ponderosa pine in inches measured at
breast height and y is a measure of volume—number of board feet divided by 10. Test
the model y D axb by plotting the transformed data. If the model seems reasonable,
estimate the parameters a and b of the model graphically.
x 17 19 20 22 23 25 28 31 32 33 36 37 38 39 41
y 19 25 32 51 57 71 113 141 123 187 192 205 252 259 294
a) use the transformation of variables to linearize the problem.
b) Use the linear fit to obtain the coefficients for the linear problem and for the original problem.
c) Calculate the residuals of the linear problem and the original problem.
. The following data represent (hypothetical) energy consumption normalized to the year
1900. Plot the data. Test the model QDaebx by plotting the transformed data. Estimate
the parameters of the model graphically.
x Year Consumption Q
0 1900 1.00
10 1910 2.01
20 1920 4.06
30 1930 8.17
40 1940 16.44
50 1950 33.12
60 1960 66.69
70 1970 134.29
80 1980 270.43
90 1990 544.57
100 2000 1096.63
a) obtain the coefficient of the model.
b) Calculate consumption for 1995.
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