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	   "source": [
       "# Chapter 10: Curve Fitting Regression"
	   ]
	},
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		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.1: Fitting_a_Straight_line.sce"
		   ]
		  },
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"//Example No. 10_01\n",
"//Fitting a Straight Line\n",
"//Pg No. 326\n",
"clear ;close ;clc ;\n",
"\n",
"x = poly(0,'x')\n",
"X = 1:5\n",
"Y = [ 3 4 5 6 8 ];\n",
"n = length(X);\n",
"b = ( n*sum(X.*Y) - sum(X)*sum(Y) )/( n*sum(X.*X) - (sum(X))^2 )\n",
"a = sum(Y)/n - b*sum(X)/n\n",
"disp(b,'b = ')\n",
"disp(a,'a = ')\n",
"y = a + b*x"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.2: Fitting_a_Power_Function_Model_to_given_data.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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"source": [
"//Example No. 10_02\n",
"//Fitting a Power-Function model to given data\n",
"//Pg No. 331\n",
"clear ;close ;clc ;\n",
"\n",
"x = poly(0,'x');\n",
"X = 1:5\n",
"Y = [ 0.5 2 4.5 8 12.5 ]\n",
"Xnew = log(X)\n",
"Ynew = log(Y)\n",
"n = length(Xnew)\n",
"b = ( n*sum(Xnew.*Ynew) - sum(Xnew)*sum(Ynew) )/( n*sum(Xnew.*Xnew) - ( sum(Xnew) )^2 )\n",
"lna = sum(Ynew)/n - b*sum(Xnew)/n\n",
"a = exp(lna)\n",
"disp(b,'b = ')\n",
"disp(lna,'lna = ')\n",
"disp(a,'a = ')\n",
"printf('\n The power function equation obtained is \n y = %.4Gx^%.4G',a,b);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.3: Fitting_a_Straight_line_using_Regression.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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"source": [
"//Example No. 10_03\n",
"//Pg No. 332\n",
"clear ;close ;clc ;\n",
"\n",
"time = 1:4\n",
"T = [ 70 83 100 124 ]\n",
"t = 6\n",
"Fx = exp(time/4)\n",
"n = length(Fx)\n",
"Y = T ;\n",
"b = ( n*sum(Fx.*Y) - sum(Fx)*sum(Y) )/( n*sum(Fx.*Fx) - (sum(Fx))^2 )\n",
"a = sum(Y)/n - b*sum(Fx)/n\n",
"disp(b,'b = ')\n",
"disp(a,'a = ')\n",
"printf('The relationship between T and t is \n T = %.4G*e^(t/4) + %.4G \n',b,a)\n",
"deff('T = T(t)','T = b*exp(t/4) + a ')\n",
"T_6 = T(6)\n",
"\n",
"disp(T_6,'The temperature at t = 6 is')"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.4: Curve_Fitting.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example No. 10_04\n",
"//Curve Fitting\n",
"//Pg NO. 335\n",
"clear ; close ; clc ;\n",
"\n",
"x = 1:4 ;\n",
"y = [6 11 18 27 ];\n",
"n = length(x) //Number of data points\n",
"m = 2+1       //Number of unknowns\n",
"disp('Using CA = B form , we get')\n",
"for j = 1:m\n",
"    for k = 1:m\n",
"        C(j,k) = sum(x.^(j+k-2))\n",
"    end\n",
"    B(j) = sum( y.*( x.^( j-1 ) ) )\n",
"end\n",
"disp(B,'B = ',C,'C = ')\n",
"A = inv(C)*B\n",
"disp(A,'A = ')\n",
"printf('Therefore the least sqaures polynomial is\n   y = %i + %i*x + %i*x^2 \n',A(1),A(2),A(3))"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 10.5: Plane_Fitting.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Example No. 10_05\n",
"//Plane Fitting\n",
"//Pg No. 342\n",
"clear ; close ; clc ;\n",
"\n",
"x = 1:4\n",
"z = 0:3\n",
"y = 12:6:30\n",
"n = length(x) //Number of data points\n",
"m = 3         //Number of unknowns\n",
"G = [ ones(1,n) ; x ; z]\n",
"H = G'\n",
"C = G*H\n",
"B = y*H\n",
"D = C\B'\n",
"disp(C,B)\n",
"disp(D)\n",
"mprintf('\n The regression plane is \n y = %i + %f*x + %i*z ',D(1),D(2),D(3))"
   ]
   }
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