Linear Regression

It is a statistical method which tries to find relation between the one dependent variable and a series of other changing variables known as independent variables. Linear regression is statistical method where in a relation between the scalar variable “Y” and one or more variables denoted in “X” of a graph. In this method the models of unknown parameter in “X” are determined using the linear function. Linear regression focuses on conditional probability distribution of Y given X. The linear regression primarily focuses on only one independent variable.

Linear regression is given by the formula

X=a + bY + u

Where,

X=Variable which we are trying to predict.

Y=Variable which we are using to predict Y

a= the intercept

b= the slope of the curve.

U=the regression residual.

The relation in regression will be usually in the form of straight lines that best approximate all the individual data points. Regression is often used to determine how many specific factors such as the price of a commodity, interest rates, particular industries or sectors influence the price movement of an asset.

Some of the practical uses of linear regression are,

• It is widely used to predict the stock and other security price based on the linear relation of the stock with the market.

• It is widely used in determining the performance of a script based on the performance of the market.

• It is used as a tool in some of the investment decisions.

Two basic assumptions are made in linear regressions they are,

• The design matrix has full column rank. P .For this property to hold n > P where n is the sample size.

• The regressor b is assumed to be error free.

Questions:

• Define linear regression
• List some basic assumptions in estimating linear regression.