# ML Regression in MATLAB®

How to make ML Regression plots in MATLAB® with Plotly.

## Simple Linear Regression

This example shows how to perform simple linear regression using the accidents dataset. The example also shows you how to calculate the coefficient of determination R2 to evaluate the regressions. The accidents dataset contains data for fatal traffic accidents in U.S. states.

Linear regression models the relation between a dependent, or response, variable y and one or more independent, or predictor, variables x1,...,xn. Simple linear regression considers only one independent variable using the relation

• y=β0+β1x+ϵ,

where β0 is the y-intercept, β1 is the slope (or regression coefficient), and ϵ is the error term. This can be simplified to Y=XB

From the dataset accidents, load accident data in y and state population data in x. Find the linear regression relation y=β1x between the accidents in a state and the population of a state using the \ operator. The \ operator performs a least-squares regression.

load accidents
x = hwydata(:,14); %Population of states
y = hwydata(:,4); %Accidents per state
format long
b1 = x\y

b1 =

1.372716735564871e-04


b1 is the slope or regression coefficient. The linear relation is y=β1x=0.0001372x.

Calculate the accidents per state yCalc from x using the relation. Visualize the regression by plotting the actual values y and the calculated values yCalc.

load accidents
x = hwydata(:,14); %Population of states
y = hwydata(:,4); %Accidents per state
format long
b1 = x\y;

yCalc1 = b1*x;
scatter(x,y)
hold on
plot(x,yCalc1)
xlabel('Population of state')
ylabel('Fatal traffic accidents per state')
title('Linear Regression Relation Between Accidents & Population')
grid on

fig2plotly(gcf);


Improve the fit by including a y-intercept β0 in your model as y=β01x. Calculate β0 by padding x with a column of ones and using the \ operator.

load accidents
x = hwydata(:,14); %Population of states
y = hwydata(:,4); %Accidents per state

X = [ones(length(x),1) x];
b = X\y

b =

1.0e+02 *

1.427120171726538
0.000001256394274


This result represents the relation y=β01x=142.7120+0.0001256x.

Visualize the relation by plotting it on the same figure.

load accidents;
x = hwydata(:,14); %Population of states
y = hwydata(:,4); %Accidents per state

X = [ones(length(x),1) x];
b = X\y;

yCalc2 = X*b;
plot(x,yCalc2,'--');
legend({'Data'},'Location','best');

fig2plotly(gcf);


If with to plot the data alongside the slope, you can do it in the following way.

load accidents
x = hwydata(:,14); %Population of states
y = hwydata(:,4); %Accidents per state

X = [ones(length(x),1) x];
b = X\y;

yCalc2 = X*b;
plot(x,yCalc2,'--');
legend({'Data'},'Location','best');

hold on
plot(x,y,'o');

fig2plotly(gcf);