Linear Regression Solution

In this exercise, you will implement linear regression and get to see it work on data.   Before starting  on this programming  exercise, we strongly  recom- mend watching  the  video lectures  and  completing  the  review questions  for the associated topics.

To get started with the  exercise, you will need to download the  starter code and unzip its contents  to the directory where you wish to complete the exercise.  If needed, use the cd command  in Octave/MATLAB to change to this directory  before starting  this exercise.

You can also find instructions  for installing Octave/MATLAB in the “En- vironment Setup Instructions” of the course website.

 

 

Files included in  this exercise

 

ex1.m - Octave/MATLAB script that  steps you through  the exercise

ex1 multi.m - Octave/MATLAB script for the later parts  of the exercise ex1data1.txt - Dataset  for linear regression with one variable ex1data2.txt - Dataset  for linear regression with multiple variables submit.m - Submission script that  sends your solutions to our servers [?] warmUpExercise.m - Simple example function in Octave/MATLAB [?] plotData.m - Function  to display the dataset

[?] computeCost.m - Function  to compute  the cost of linear regression

[?] gradientDescent.m - Function  to run gradient descent

[†] computeCostMulti.m - Cost function for multiple variables

[†] gradientDescentMulti.m - Gradient descent for multiple  variables

[†] featureNormalize.m - Function  to normalize features

[†] normalEqn.m - Function  to compute  the normal equations

 

? indicates  files you will need to complete

† indicates  optional exercises

 

 

 

 

 

Throughout the exercise, you will be using the scripts ex1.m and ex1 multi.m. These scripts set up the dataset for the problems and make calls to functions

that  you will write.  You do not need to modify either of them.  You are only required  to modify functions  in other  files, by following the  instructions  in this assignment.

For this programming exercise, you are only required to complete the first part  of the  exercise to implement linear regression with  one variable.   The second part  of the  exercise, which is optional,  covers linear regression with multiple variables.

 

 

Where to get help

 

The exercises in this course use Octave1   or MATLAB, a high-level program- ming language  well-suited for numerical  computations.  If you do not  have Octave or MATLAB installed,  please refer to the installation instructions  in the “Environment Setup Instructions” of the course website.

At the Octave/MATLAB command line, typing help followed by a func- tion name displays documentation for a built-in function.  For example, help plot will bring up help information  for plotting.  Further documentation for Octave  functions  can be found at  the  Octave  documentation pages.  MAT- LAB documentation can be found at the MATLAB documentation pages.We also strongly  encourage using the online Discussions to discuss ex- ercises with other students. However, do not look at any source code written by others or share your source code with others.

 

 

1    Simple Octave/MATLAB function

 

The first part of ex1.m gives you practice with Octave/MATLAB syntax and the  homework submission process.  In the  file warmUpExercise.m, you will find the outline of an Octave/MATLAB function.  Modify it to return  a 5 x

5 identity  matrix  by filling in the following code:

 

 

A  =  eye(5);

 

 

1 Octave  is a free alternative to MATLAB.  For the programming exercises, you are free to use either  Octave  or MATLAB.

 

 

 

 

 

When  you are finished, run  ex1.m (assuming  you are in the  correct  di- rectory,  type “ex1” at  the  Octave/MATLAB prompt)  and  you should  see output similar to the following:

 

 

ans  =

 

Diagonal Matrix

 

1              0              0              0              0

0              1              0              0              0

0              0              1              0              0

0              0              0              1              0

0              0              0              0              1

Now ex1.m will pause until you press any key, and then will run the code for the next part  of the assignment.  If you wish to quit,  typing ctrl-c will stop the program in the middle of its run.

 

 

1.1     Submitting Solutions

 

After  completing  a part  of the  exercise, you can submit  your solutions  for grading by typing submit at the Octave/MATLAB command line. The sub- mission script  will prompt  you for your login e-mail and  submission token and ask you which files you want  to submit.   You can obtain  a submission token from the web page for the assignment.