Create a mathematical model based on raw empirical data obtained from a certain sensor equipment. The data given in the MATLAB data file is :

Values for W and V continue up to 100000 value , the values shown above are just a sample . The final value for V is 10 , and the final value for W is 8.0481. There are two variables in the data file, V and W. V is a certain independent variable in the sensor system and W is the observation variable that is affected by the variable V.

1. By using curve fitting method, find mathematical model using i) Power law model, ii) Exponential model and iii) Saturation growth rate model. For each of the mathematical model :

a. Linearized the data and calculate the coefficients(values of 1 and 0) that minimizes the error between the model and the data. Discuss all steps to obtain these variables for each model using MATLAB. Do not use polyfit function.

b. Write the final equation for each model.

c. Calculate the linear fit 2 value for each model.

d. Plot the graph using each model. Include the sample data plot in each of the plot (Use the dot plot for the sample data. Example: plot(x,y,.) ). Use appropriate scaling to observe the data.

E. Make sure the code has suitable variables naming and documentations.

2. Which one of these mathematical models is the most suitable to represent the data? Discuss reasoning in detail.

I 1x100000 double 1 8 9 12 16 18 2 1.0000 3 1.0000 4 1.0001 5 1.0001 6 1.0001 7 1.0001 10 1.0002 11 1.0002 13 1.0003 14 1.0003 15 1.0003 17 1.0004 19 1.0004 20 1.0004 1 1 1.0002 1.0002 1.0003 1.0003 1.0004 W 1x100000 double 1 2 3 4 6 7 8 9 11 12 15 16 19 20 5 0.0088 10 0.0123 13 0.0086 14 0.0104 17 0.0112 18 0.0087 1 0.0104 0.0113 0.0103 0.0138 0.0158 0.0144 0.0084 0.0126 0.0073 0.0077 0.0137 0.0090 0.0098 0.0106 I 1x100000 double 1 8 9 12 16 18 2 1.0000 3 1.0000 4 1.0001 5 1.0001 6 1.0001 7 1.0001 10 1.0002 11 1.0002 13 1.0003 14 1.0003 15 1.0003 17 1.0004 19 1.0004 20 1.0004 1 1 1.0002 1.0002 1.0003 1.0003 1.0004 W 1x100000 double 1 2 3 4 6 7 8 9 11 12 15 16 19 20 5 0.0088 10 0.0123 13 0.0086 14 0.0104 17 0.0112 18 0.0087 1 0.0104 0.0113 0.0103 0.0138 0.0158 0.0144 0.0084 0.0126 0.0073 0.0077 0.0137 0.0090 0.0098 0.0106