Artificial Intelligence Assignment

W5: Simple Linear Regression

Context/overview:  

One of the most important and broadly used machine learning and statistics tools that nowadays are used is a regression. Regression will allow you to make predictions from data by learning a relationship between data and response.  We can see a use of regression in many applications, such as predicting stock prices, real estate- house pricing, etc.

For this project, we will analyze the most basic regression model, that is very frequently studied-Simple Linear Regression.

Resources to consult:  

Artificial Intelligence- http://artint.info/html/ArtInt_179.html

Specific questions or items to address:  

1. In your own words, describe the simple linear regression. Explain why it is called a simple linear regression, and how do we use a model to make predictions on new data.  

1. Let  x1, x2, …xN be a set of input features.  A linear function that represent those features, will have a following form:

Fw(x1, x2, .. xn)= w0 + w1 * x1 + w2 * x2 +… + wn*xn

Also,  in order to implement simple linear regression, it requires that we calculate statistical properties from the data such as mean, variance and covariance.

Please implement a simple linear regression model by providing a following:

1. Implement the functions  Mean and Variance  that calculate mean and variance

2. Use the data that is returned by the Mean and Variance function and implement a function Covariance,  that will calculate  covariance

3. Use the all previous implemented functions, and develop a function called CalculateCoefficients.  Function  CalculateCoefficients  will take the dataset as an argument and returns the coefficients.

4. Implement a function SimpleLinearRegression that implements the prediction equation to make predictions on a test dataset.  To make predictions, use The coefficients prepared from the training data.

Criteria:  (# pages, APA format, etc.)  

Take screenshots of functions running in cLISP, and paste them in a Word or Google doc.  Provide a description for each screenshot.