MATLAB

X = [ones(size(conc)),conc]; % build the matrix X for linear model z = X'*conc; % right hand side of the Normal Equations S = X'*X; % Left hand side of the Normal Equations U = chol(S); % Cholesky decomposition w = U'\z; % solve the normal equations using the Cholesky decomposition c = U\w

c =

-0.0000 1.0000

plot(year,conc,'o') % plot the data points q = year; % define a vector for plotting the linear fit fit = c(1)+c(2)*q; % define the linear fit hold on plot(q,fit,'k'); % plot the linear fit together with the data points fit = c(1)+c(2)+c(3)*q {Attempted to access c(3); index out of bounds because numel(c)=2. }

3. Among the important inputs in weather-forecasting models are data sets consisting of temperature values at various parts of the atmosphere. These values are either measured directly with the use of weather balloons or inferred from remote soundings taken by weather satellites. A typical set of RAOB (weather balloon) data is given next. The temperature T in Kelins ay be considered as a function of p, the atmospheric pressure measured in decibars. Pressure in the range from 1 to 3 decibars correspond to the top of the atmosphere, and those in the range from 9 to 10 decibars correspond to the lower part of the atmosphere. 1245 678910 T 222 227 223 233 244 253 260 266 270 266 Enter the pressure values as a column vector p (use the colon: operator), and enter the temperature values as a column vector T. The goal of this problem is to find the cubic polynomial y = cit cpt+c3r2 +C4r3 that gives the best least square fit to the data