Regressions analysis

Regressions analysis is the statistical method you use when both the response variable and the explanatory variables are continuous variables.it is a very important statical tools which has a wide use in statistical analysis business decisions making and eco nomic research.

We will discuss some important kinds of regression analysis.

Linear regressions

Polynomial regressions

Piecewise regression

Robust regression

Multiple regression

Non linear regression

Non parametric regulations

Linear regression is the simplest and much the most frequently used in statistics and econometrics.the regression analysis is using simple Tata to estimate parameters value and their standard errors.we need to select the model which describe the relationship between the response variable and the explanatory variables. The simplest of all is the linear model

y=a+bx

There are two variables and two parameters. The response variable is y and x is is a single continuous explanatory variables. The parameters are a and b the intercept is a the value of Y when x is equal to zero and the slope is be the change in Y divided by the change in X which brought it about.

Analysis of variance in regression

SSY=SSR+SSE

We take the total variance in y ,SSY and partitions it into components that tell us about the explanatory powers of our model. The variations that is explained by the model is called the regression sum of squares (SSR), and the unexplained variations is called the error sum of squares (SSE).

Multiple regression

Multiple regression is a statistical model with two and more continuous explanatory variables. Multiple regression model provides some of the most profound challenges faced by the analyst because of some crucial issues.

Over sitting; we often have more explanatory variables than data points.

Parameters Proliferation; we might want to fit parameters for curvature and interactions.

Correlation between explanatory variables is called collinearity.

choice between contrasting models of roughly equal explanatory power.

we achieve this by fitting a maximum model and then simplify it by following one or more of these steps

Remove non significant interaction terms

Remove non significant quality or other nonlinear terms

Remove non significant explanatory variables

Gamut explanatory variables that have similar parameter value.

There are several important issue involved in carrying out from multiple regression.

Which explanatory variables to include

Curvature in the response to the explanatory variables.

Interaction between explanetary variables

Correlation between explanatory variables

The rest of over parameterization.

Y(1)=B0+B1x(1i)+B2x(2i)+e(i).