imple Linear Regression

imple 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.
2. 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 G