- Constant Term: Add a column of ones to your independent variable matrix. This column represents the constant term in the regression equation.
- Time Trend: Create a column representing the time trend for each independent variable. This could be a sequence of integers representing time points.

# Add constants and time trends to multivariate regression Matlab

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Simon Christensen
on 14 Mar 2024

Commented: DGM
on 26 Mar 2024

Hi Matlab,

I'm want to add a constant for each indepedent variable and a time trend for each independent variable in a multivariate regression.

Any suggestions how to do this?

Follwing this link https://se.mathworks.com/help/stats/mvregress.html it says 'to add a constant to a model, should use a col of ones.' Clearly,

we cannot add more than one col of ones.

Code follows below:

A = rand(200,1);

B = rand(200,1);

vX = [A B];

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%define independent and dependent variables

K1 = lagmatrix(diff(vX),1)

K3 = lagmatrix(vX,1)

K4 = diff(vX)

%make same size

K1(any(isnan(K1), 2), :) = [];

K3(any(isnan(K3), 2), :) = [];

K4(any(isnan(K4), 2), :) = [];

K3(1,:) = [];

K4(1,:) = [];

%one trend for each series

%one constant for each series

%constant

con = [ones(198,1) ]

%trend

trend = [(1:198)' ]

[beta,Sigma,E,CovB] = mvregress([con K3 K1 trend], K4, 'vartype', 'fisher');

##### 0 Comments

### Accepted Answer

Dr.GADDALA JAYA RAJU
on 15 Mar 2024

To add a constant term and a time trend for each independent variable in a multivariate regression, you can simply create additional independent variables that represent these terms. Here's how you can do it:

Let's say you have �n independent variables �1,�2,…,��X1,X2,…,Xn and �m observations. Your design matrix �X will then have �m rows and �+2n+2 columns: one column for the constant term, one column for the time trend for each independent variable, and �n columns for the original independent variables.

Here's a Python example using NumPy to illustrate how you can create such a design matrix:

import numpy as np

# Example independent variables

X1 = np.random.rand(100) # Independent variable 1

X2 = np.random.rand(100) # Independent variable 2

# Assume X1 and X2 are time series data

# Create constant term

constant_term = np.ones_like(X1)

# Create time trend for each independent variable

time_trend = np.arange(len(X1))

# Stack all independent variables together

X = np.column_stack((constant_term, time_trend, X1, X2))

# Print the shape of the design matrix

print("Shape of design matrix X:", X.shape)

In this example, X1 and X2 represent two independent variables (could be more in a real scenario). We create a constant term (constant_term) and a time trend (time_trend) for each independent variable. Then, we stack these together along with the original independent variables to form the design matrix X.

You can use this design matrix X along with your dependent variable y to perform multivariate regression using any regression method or library of your choice, such as statsmodels or scikit-learn in Python. These libraries typically provide functions or classes for fitting regression models with multiple independent variables.

##### 1 Comment

DGM
on 26 Mar 2024

Why did you post a python example to a question about MATLAB mvregress()?

Why was it accepted?

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