Question

problem on mathematical modelling in engineering (please answer from (a )to (d)))

thank you

7. a. In the following data, W represents the weight of a fish (bass) and / represents its length. Fit the model W kl3 to the data using the least-squares criterion. 12.625 14.125 12.625 17.75 17.25 14.5 14.5 12.5 Length, I (in.) 23 16 17 49 26 17 41 Weight, W (oz) 27 kig2 to the b. In the following data, g represents the girth of a fish. Fit the model W data using the least-squares criterion. 14.125 12.625 12.625 17.75 14.5 17.25 12.5 14.5 Length, I (in.) 8.5 12.5 9,0 8.5 9.75 11.0 9.75 8.375 Girth, g (in.) 23 16 17 49 26 17 41 27 Weight, W (oz) I c. Which of the two models fits the data better? Justify fully. Which model do you prefer? Why? d. Use the data presented in Problem 7b to fit the models W =cg' and W=kgl2. Interpret these models. Compute appropriate indicators and determine which model is best. Explain

Answer 1

Long th (1in) |14.5 Shi jzt 2 25 S 14.123 12:62d L 26 IW=216 ht Coz.) | 27 16 23 3 Wk mean sqpome W-K3 Ernon neco to memimize (Mse) urat w rdh Tejpeot -fo We &CE) 2 Cw-k3) = 0 w-K3 W co.OO8y 2.5618o W = o0084l Jutteng ation so ZMSE= 12.2982 Crth (b) [ 9.75 8 35 11 9FS 8.5 12.5 9.0 ay aboue fir best k in w we hane Pro e Now 2 16 W O.O188ls Oo188 MSE now t9tb tl- dada o model Q)fifs beter S o MSE HE ) so /2 0 o28 wO.02& fir HSE Now 1 281 betueen thcie to model So