**Table of Contents**show

**Regression**

- A regression model is a mathematical equation that describes the relationship between two or more variables
- A simple regression model includes only two variables: one independent and one dependent.
- The dependent variable is the one being explained and the independent variable is the one used to explain the variation in the dependent variable

**Remember this:**

A slope of 2 means that every 1-unit change in X yields a 2-unit change in Y.

**Linear Regression**

A (simple) regression mode that gives a straight-line relationship between two variables is called a linear regression model

**Simple Linear Regression Analysis**

- Scatter Diagram
- Least Square Line
- Interpretation of slope and intercept
- Assumptions of Regression Analysis

In the regression model, **y= A+Bx+C**

- A is called the y-intercept or constant term
- B is the slope
- C is the random error
- The dependent and independent variables are y and x respectively

**Sum of Squared Error (SSE)**

The sum of Squared error (SSE) is,

The values of a and b that gives the minimum SSE are called least square estimates and the regression line obtained with these estimates is called the least square line

**The Least Squares line**

For the least squares regression line,

**Interpretation of slope and intercept**

The value of intercept in the regression model gives the change in y due to change of one unit in x

**Assumptions of the Regression Model**

**Assumption 1:**The random error has a mean equal to zero for each x**Assumption 2:**The errors associated with different observations are independent**Assumption 3:**For any given x, the distribution of error is normal**Assumption 4:**The distribution of population errors for each x has the same (constant) standard deviation

**Degrees of FreedomÂ **

The degrees of freedom for a simple linear regression model are,

Standard deviation of errors is calculated as

Where,

**Total Sum of Squares (SST)**

The total sum of squares, denoted by SST, is calculated as,

**Regression Sum of Squares (SSR)**

The regression sum of squares denoted by SSR is,

**Coefficient of determination**

The Coefficient of determination denoted by**r ^{2}** , represents the proportion of SST that is explained by the use of the regression model. The computational formula for

**r**is,

^{2}and

**The higher the value of r ^{2}, the more successful is simple linear regression model in explaining y variation**

**Multiple Linear Regression**

**Multiple linear regression:** involves more than one predictor variable

- Training data is of the form (
**X**, y_{1}_{1}), (**X**, y_{2}_{2}),â€¦, (**X**, y_{|D|}_{|D|}) - Ex. For 2-D data, we may have: y = w
_{0}+ w_{1}x_{1}+ w_{2}x_{2}

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