multivariate-regression

Building the code

To build the code do as follows

git clone https://github.com/ConnorWhelan11/multivariate-regression.git
cd multivariate-regression
autoreconf -iv
./configure

Running the program

[cpf37@fishercat mpi]$ ./main
y = (0.080604)*x0 + (0.042525)*x1 + (0.018824)*x2 + error

The Data

The data used in this problem came from the UCI Machine Learning repository at https://archive.ics.uci.edu/ml/datasets/Auto+MPG. The following information has been copied from their website:

Source:

This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University. The dataset was used in the 1983 American Statistical Association Exposition.

Data Set Information:

This dataset is a slightly modified version of the dataset provided in the StatLib library. In line with the use by Ross Quinlan (1993) in predicting the attribute "mpg", 8 of the original instances were removed because they had unknown values for the "mpg" attribute. The original dataset is available in the file "auto-mpg.data-original".

"The data concerns city-cycle fuel consumption in miles per gallon, to be predicted in terms of 3 multivalued discrete and 5 continuous attributes." (Quinlan, 1993)

Attribute Information:

1. mpg: continuous
2. cylinders: multi-valued discrete
3. displacement: continuous
4. horsepower: continuous
5. weight: continuous
6. acceleration: continuous
7. model year: multi-valued discrete
8. origin: multi-valued discrete
9. car name: string (unique for each instance)

Multivariate Regressin to predict Auto MPG

The goal is to solve the Ax=b problem for the vector of coefficients x. My implentation does so through QR factorization of matrix A into the multiplication of an orthonormal matrix Q and upper triangular matrix R.