Using Matlab Code: Growth data of a sunflower plant is given in the following ta

Question

Using Matlab Code:

Growth data of a sunflower plant is given in the following table: Make a plot for each curve fit (a)-(d) (as lines) with the given data as symbols (use subplot to have all plots in one figure). (a) Curve fit the data with a linear regression line. (b) Curve fit the data with a 2^nd-order polynomial. (c) Curve fit the data with a 4^th-order polynomial. (d) Plant growth can be modeled as an exponential function called the "logistic equation" H(t) = C/(1 + A middot e^-B middot t), where H is the height. C is a maximum value for H, A and B are constants, and t is the number of weeks. The equation can be rewritten in the form (C/H) - 1 = A middot e^-B middot t, and linearized to ln ((C/H) - 1) = ln A - B middot t. Assuming C = 254cm. determine the constants A and B with least squares fitting. (e) Measure the quality of the least-squares fit for EACH model (a)-(d) by computing the "Coefficient of Determination'. Print the results in a FORMATTED TABLE. (f) Discuss the differences in visual fit between the graphs from (a)-(c) AND the results for the "Coefficient of Determination". Which fit is the best? Why?

Explanation / Answer

surfl(z) colormap(pink) % change color map shading interp % interpolate colors across lines and faces x = -2:.2:2; y = -1:.2:1; [xx,yy] = meshgrid(x,y); zz = xx.*exp(-xx.^2-yy.^2); [px,py] = gradient(zz,.2,.2); quiver(x,y,px,py) xlim([-2.5 2.5]) % set limits of x axis

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