(2, 18), (4, 27), (8, 53), (16, 106), (32, 124) Which model (exponential, logart

Question

(2, 18), (4, 27), (8, 53), (16, 106), (32, 124)

Which model (exponential, logarthmic, logistic, or none of these) fits the given data the best?

For the correct model, choose the regression function of best fit.

Round calculations to two decimal places.

a) logistic, f(x) = 124.56/(1 + 9.95e-0.25x)

b) logarithmic, f(x) = -21.70 + 41.98ln(x)

c) exponential, f(x) = 23.97(1.06)x

d) none of these

a) logistic, f(x) = 124.56/(1 + 9.95e-0.25x)

b) logarithmic, f(x) = -21.70 + 41.98ln(x)

c) exponential, f(x) = 23.97(1.06)x

d) none of these

Explanation / Answer

Mean Square error is used to decide the best fit.

Step 1: Calculate y from each model

Step 2: calculate error of each observation from acutal y and square it

Step 3: take mean of this square error and compare

Logistic works best.

y-model Error^2 = (ymodel - y)^2 x y logistic log exp logistic log exp 2 18 17.7 7.4 26.9 0.1 112.4 79.8 4 27 26.7 36.5 30.3 0.1 90.2 10.6 8 53 53.1 65.6 38.2 0.0 158.6 218.9 16 106 105.4 94.7 60.9 0.4 127.8 2034.7 32 124 124.1 123.8 154.7 0.0 0.0 941.7 MSE = 0.1 97.8 657.2

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