# Add constants and time trends to multivariate regression Matlab

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Simon Christensen il 14 Mar 2024
Commentato: DGM il 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');
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### Risposta accettata

Dr.GADDALA JAYA RAJU il 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:
1. Constant Term: Add a column of ones to your independent variable matrix. This column represents the constant term in the regression equation.
2. Time Trend: Create a column representing the time trend for each independent variable. This could be a sequence of integers representing time points.
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.
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DGM il 26 Mar 2024
Why did you post a python example to a question about MATLAB mvregress()?
Why was it accepted?

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