diff --git a/boussinesq_lookup.m b/boussinesq_lookup.m
new file mode 100644
index 0000000..5fe7f64
--- /dev/null
+++ b/boussinesq_lookup.m
@@ -0,0 +1,50 @@
+function [sigma_z]=boussinesq_lookup(q,a,b,z)
+fmn= [0.1,0.02926,0.03007,0.03058
+        0.2,0.05733,0.05894,0.05994
+        0.3,0.08323,0.08561,0.08709
+        0.4,0.10631,0.10941,0.11135
+        0.5,0.12626,0.13003,0.13241
+        0.6,0.14309,0.14749,0.15027
+        0.7,0.15703,0.16199,0.16515
+        0.8,0.16843,0.17389,0.17739];
+
+m = a/z;
+n = b/z;
+
+if (n>1.5)
+    n=1.6;
+elseif (1.3<=n)
+    if (n<=1.5)
+    n=1.4;
+    end
+elseif 1.3<=n
+    n=1.2;
+end
+
+c = ones(1,4);
+d = ones(1,4);
+
+for i=1:4
+[~,p]=min(abs(m-fmn(:,1)));
+M =fmn(p,1);
+fmn(p,1)=0;
+if n==1.2
+   t=fmn(p,2);
+elseif n==1.4
+    t=fmn(p,3);
+elseif n==1.6
+   t=fmn(p,4);
+end
+
+d(i) = M;
+c(i) = t;
+end
+
+b1=c(1);
+b2=(c(2)-c(1))/(d(2)-d(1));
+b3=(((c(3)-c(2))/(d(3)-d(2)))-((c(2)-c(1))/(d(2)-d(1)))/(d(3)-d(1)));
+b4=(((c(4)-c(3))/(d(4)-d(3)))-((c(3)-c(2))/(d(3)-d(2)))-((c(2)-c(1))/(d(2)-d(1))))/(d(4)-d(1));
+f3=b1+(b2*(m-d(1)))+(b3*(m-d(1))*(m-d(2)))+(b4*(m-d(1))*(m-d(2))*(m-d(3)));
+sigma_z=q*f3;
+
+end
\ No newline at end of file
diff --git a/cost_logistic.m b/cost_logistic.m
new file mode 100644
index 0000000..0932489
--- /dev/null
+++ b/cost_logistic.m
@@ -0,0 +1,21 @@
+function [cost, gradient] = cost_logistic(a, x, y)
+cost = 0;
+gradient = 0;
+t = a(1)+a(2).*x;
+sigma = 1./(1+exp(-t));
+cost = sum(-y.*log(sigma)- (1-y).*log(1-sigma));
+costFun = @ (a) sum(-y.*log((1./(1+exp(-(a(1)+a(2).*x)))))-(1-y).*log(1-(1./(1+exp(-(a(1)+a(2).*x))))));
+gradient = (1/length(x))*sum((sigma-y).*t);
+ai = [0 0];
+% Set options for fminunc
+options = optimset('GradObj','on','MaxIter',400);
+% Run fminunc to obtain the optimal theta
+% This function will return theta and the cost
+[theta, cost] = fminunc(costFun, ai);
+t = theta(1)+theta(2).*x;
+sigma = 1./(1+exp(-t));
+plot(x,y,'xb', x, sigma);
+title('Regression')
+xlabel('Temp (Degrees F)')
+ylabel('Pass or Fail (1 or 0)')
+end
\ No newline at end of file
diff --git a/initializeData.m b/initializeData.m
new file mode 100644
index 0000000..01b2f4f
--- /dev/null
+++ b/initializeData.m
@@ -0,0 +1,26 @@
+c = [1.0000   53.0000    1.0000;
+    2.0000 57.0000    1.0000;
+    3.0000 58.0000    1.0000;
+    4.0000 63.0000    1.0000;
+    5.0000 66.0000         0;
+    6.0000 66.8000         0;
+    7.0000 67.0000         0;
+    8.0000 67.2000         0;
+    9.0000 68.0000         0;
+   10.0000 69.0000         0;
+   11.0000 69.8000    1.0000;
+   12.0000 69.8000         0;
+   13.0000 70.2000    1.0000;
+   14.0000 70.2000         0;
+   15.0000 72.0000         0;
+   16.0000 73.0000         0;
+   17.0000 75.0000         0;
+   18.0000 75.0000    1.0000;
+   19.0000 75.8000         0;
+   20.0000 76.2000         0;
+   21.0000 78.0000         0;
+   22.0000 79.0000         0;
+   23.0000 81.0000         0];
+a = c(:,1);
+x = c(:,2);
+y = c(:,3);
\ No newline at end of file
diff --git a/least_squares.m b/least_squares.m
new file mode 100644
index 0000000..57e99ab
--- /dev/null
+++ b/least_squares.m
@@ -0,0 +1,8 @@
+function [a,fx,r2] = least_squares(Z,y)
+a = Z\y;
+Sr = sum((y-Z*a).^2);
+r2 = 1-Sr/sum((y-mean(y)).^2);
+x = Z(:,2);
+fx = a(1)+(a(2)*x)+(a(3)*x.^2);
+end
+
diff --git a/plot1.png b/plot1.png
new file mode 100644
index 0000000..153bba4
Binary files /dev/null and b/plot1.png differ
diff --git a/problem_1_data.m b/problem_1_data.m
new file mode 100644
index 0000000..562afa4
--- /dev/null
+++ b/problem_1_data.m
@@ -0,0 +1,23 @@
+clear
+clc
+
+% part a
+xa=[1 2 3 4 5]';
+ya=[2.2 2.8 3.6 4.5 5.5]';
+
+Za = [ones(size(xa)), xa, xa.^-1];
+[a1,fx1,r2_1] = least_squares(Za,ya);
+
+% part b 
+xb=[3 4 5 7 8 9 11 12]';
+yb=[1.6 3.6 4.4 3.4 2.2 2.8 3.8 4.6]';
+
+Zb = [ones(size(xb)), xb, xb.^2, xb.^3];
+[a2,fx2,r2_2] = least_squares(Zb,yb);
+ 
+% part c
+xc=[0.5 1 2 3 4 5 6 7 9]';
+yc=[6 4.4 3.2 2.7 2.2 1.9 1.7 1.4 1.1]';
+
+Zc = [exp(-1.5*xc),exp(-0.3*xc), exp(-0.05*xc)];
+[a3,fx3,r2_3] = least_squares(Zc,yc);
\ No newline at end of file
diff --git a/setdefaults.m b/setdefaults.m
new file mode 100644
index 0000000..8c44cd6
--- /dev/null
+++ b/setdefaults.m
@@ -0,0 +1,3 @@
+set(0, 'defaultAxesFontSize', 16)
+set(0,'defaultTextFontSize',14)
+set(0,'defaultLineLineWidth',3)
\ No newline at end of file