%% MATLAB Session 2 - OLS models and residual diagnostics % 2026 % Goal: Estimate OLS models, interpret regression output, % and perform residual diagnostics. clear; % Clears all variables from the workspace close all; % Closes all open figure windows clc; % Clears the Command Window %% 1. Load data scriptDir = fileparts(mfilename('fullpath')); % Finds the folder where the current script is saved if isempty(scriptDir) % Checks whether scriptDir is empty, for example if the script has no saved path scriptDir = pwd; % If scriptDir is empty, uses the current working directory instead end % Ends the if statement load(fullfile(scriptDir,'wage1-matlab.mat')) % Loads the file wage1-matlab.mat from the script folder load('wage1-matlab.mat') % Loads the file wage1-matlab.mat from the script folder %% 2. Scatterplot: education and wage figure % Opens a new figure window scatter(educ,wage) % Creates a scatterplot of wage against education title('Scatterplot: education and wage') % Adds a title to the plot xlabel('Years of education') % Adds a label to the horizontal axis ylabel('Hourly earnings') % Adds a label to the vertical axis grid on % Adds a grid to the plot lsline % Adds the least-squares regression line to the scatterplot %% 3. First regression: wage on educ % Model: wage = b0 + b1*educ + u % The first model regresses wage on education. my_model = fitlm(educ,wage) % Estimates a simple OLS regression with wage as the dependent variable and educ as the explanatory variable myres = my_model.Residuals.Raw; % Stores the raw residuals from the regression myfit = predict(my_model,educ); % Computes the fitted values of wage from the estimated model figure % Opens a new figure window subplot(2,2,1) % Divides the figure into a 2 x 2 grid and selects the 1st plot plot(myres) % Plots the residuals title('Residuals') % Adds a title to the residual plot grid on % Adds a grid to the plot subplot(2,2,2) % Selects the 2nd plot in the 2 x 2 grid ksdensity(myres) % Plots the kernel density estimate of the residuals title('Kernel density') % Adds a title to the density plot grid on % Adds a grid to the plot subplot(2,2,3) % Selects the 3rd plot in the 2 x 2 grid scatter(myfit,myres) % Creates a scatterplot of residuals against fitted values title('Residuals vs fitted') % Adds a title to the plot xlabel('Fitted values') % Adds a label to the horizontal axis ylabel('Residuals') % Adds a label to the vertical axis grid on % Adds a grid to the plot subplot(2,2,4) % Selects the 4th plot in the 2 x 2 grid autocorr(myres) % Plots the autocorrelation function of the residuals title('Autocorrelation') % Adds a title to the autocorrelation plot [h_ks1,p_value_ks1] = kstest((myres-mean(myres))/std(myres)); % Performs the Kolmogorov-Smirnov normality test on standardized residuals p_value_ks1 % Displays the p-value of the Kolmogorov-Smirnov test [h_JB1,p_value_JB1] = jbtest(myres); % Performs the Jarque-Bera normality test on the residuals p_value_JB1 % Displays the p-value of the Jarque-Bera test %% 4. Second regression: wage on educ and tenure % Model: wage = b0 + b1*educ + b2*tenure + u % The second model regresses wage on education and tenure. close all; % Closes all open figure windows my_model2 = fitlm([educ, tenure], wage) % Estimates a multiple OLS regression with wage as the dependent variable and educ and tenure as regressors myres = my_model2.Residuals.Raw; % Stores the raw residuals from the second regression myfit = predict(my_model2,[educ, tenure]); % Computes the fitted values of wage from the second model figure % Opens a new figure window subplot(2,2,1) % Divides the figure into a 2 x 2 grid and selects the 1st plot plot(myres) % Plots the residuals title('Residuals') % Adds a title to the residual plot grid on % Adds a grid to the plot subplot(2,2,2) % Selects the 2nd plot in the 2 x 2 grid ksdensity(myres) % Plots the kernel density estimate of the residuals title('Kernel density') % Adds a title to the density plot grid on % Adds a grid to the plot subplot(2,2,3) % Selects the 3rd plot in the 2 x 2 grid scatter(myfit,myres) % Creates a scatterplot of residuals against fitted values title('Residuals vs fitted') % Adds a title to the plot xlabel('Fitted values') % Adds a label to the horizontal axis ylabel('Residuals') % Adds a label to the vertical axis grid on % Adds a grid to the plot subplot(2,2,4) % Selects the 4th plot in the 2 x 2 grid autocorr(myres) % Plots the autocorrelation function of the residuals title('Autocorrelation') % Adds a title to the autocorrelation plot [h_ks2,p_value_ks2] = kstest((myres-mean(myres))/std(myres)); % Performs the Kolmogorov-Smirnov normality test on standardized residuals p_value_ks2 % Displays the p-value of the Kolmogorov-Smirnov test [h_JB2,p_value_JB2] = jbtest(myres); % Performs the Jarque-Bera normality test on the residuals p_value_JB2 % Displays the p-value of the Jarque-Bera test %% 5. Third regression: log(wage) on educ and tenure % Model: log(wage) = b0 + b1*educ + b2*tenure + u % The third model regresses the logarithm of wage on education and tenure. close all; % Closes all open figure windows my_model3 = fitlm([educ, tenure], log(wage)) % Estimates a multiple OLS regression with log(wage) as the dependent variable myres = my_model3.Residuals.Raw; % Stores the raw residuals from the third regression myfit = predict(my_model3,[educ, tenure]); % Computes the fitted values of log(wage) from the third model figure % Opens a new figure window subplot(2,2,1) % Divides the figure into a 2 x 2 grid and selects the 1st plot plot(myres) % Plots the residuals title('Residuals') % Adds a title to the residual plot grid on % Adds a grid to the plot subplot(2,2,2) % Selects the 2nd plot in the 2 x 2 grid ksdensity(myres) % Plots the kernel density estimate of the residuals title('Kernel density') % Adds a title to the density plot grid on % Adds a grid to the plot subplot(2,2,3) % Selects the 3rd plot in the 2 x 2 grid scatter(myfit,myres) % Creates a scatterplot of residuals against fitted values title('Residuals vs fitted') % Adds a title to the plot xlabel('Fitted values') % Adds a label to the horizontal axis ylabel('Residuals') % Adds a label to the vertical axis grid on % Adds a grid to the plot subplot(2,2,4) % Selects the 4th plot in the 2 x 2 grid autocorr(myres) % Plots the autocorrelation function of the residuals title('Autocorrelation') % Adds a title to the autocorrelation plot [h_ks3,p_value_ks3] = kstest((myres-mean(myres))/std(myres)); % Performs the Kolmogorov-Smirnov normality test on standardized residuals p_value_ks3 % Displays the p-value of the Kolmogorov-Smirnov test [h_JB3,p_value_JB3] = jbtest(myres); % Performs the Jarque-Bera normality test on the residuals p_value_JB3 % Displays the p-value of the Jarque-Bera test %% 6. Extract information from the final OLS model my_model3.Coefficients % Displays the table of estimated coefficients, standard errors, t-statistics, and p-values my_model3.Coefficients(1,1) % Displays the element in row 1 and column 1 of the coefficient table, corresponding to the estimated intercept my_model3.Coefficients.pValue % Displays the p-values of the estimated coefficients in the final model my_model3.Rsquared % Displays the R-squared measures of the final model my_model3.Rsquared.Ordinary % Displays the ordinary R-squared of the final model coefCI(my_model3) % Computes and displays confidence intervals for the estimated coefficients