Q. 1. The data set below represents an exponential function.: (a) Compute the va

Question

Q. 1. The data set below represents an exponential function.:  

                                          

(a) Compute the values of m and b hence the exponential relationship y=bem x.

(b) Compute the coefficient of correlation r2 for this exponential fit.

Hint: Compute the individual terms according the exponential fit relationships given below. Add columns to the table above to help with the house keeping of terms.  

m= [ n(?xi In(yi))-(?xi)(? In(yi)) ] / [n(?xi2 )-(?xi)2 ]

In(b)= [? In(yi)-m( ?xi)] / n

b= eIn(b)

r2 = [ [n(?xi In(yi))-(?xi)(?In(yi))] / [(n(?xi2)-(?xi)2)1/2] [(n(?In(yi)2)-(?In(yi))2)1/2]]2

                                                                         

  

Explanation / Answer

clc clear x = [0,1,2,3,4,5,6,7]; y = [2.3,1.1,0.55,0.27,0.13,0.06,0.03,0.01]; n = length(x);
m = (n*sum(x.*log(y))-sum(x)*sum(log(y)))/(n*sum(x.*x)-sum(x)^2); ln_b = (sum(log(y))-m*sum(x))/n; b = exp(ln_b); r2=((n*sum(x.*log(y))-sum(x)*sum(log(y)))/(sqrt(n*sum(x.*x)-sum(x)^2)... *sqrt(n*sum(log(y).*log(y))-sum(log(y))^2)))^2;
a = sprintf('m = %1.4f b = %1.4f r2 = %1.4f',m,b,r2); disp(a)

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